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Mathematica Classroom Gets Students Interested in Math
High school math will never be the same at Torrey Pines High
School in San Diego, California. Abby Brown and her students are pushing the
limits of traditional learning with Mathematica.
When
Brown first began teaching, she used a single Mathematica license
to quickly and accurately graph functions and typeset traditional math symbols
for tests, quizzes, and handouts. A few years later, her school in conjunction
with San Diego State University began a special program that gives advanced
math students a chance to earn college credit in Calculus II, Multivariable
Calculus, and Linear Algebra. To supplement these new courses, Brown used
Mathematica to create visual aids such as graphs of tangential planes
and matrix operation demos. She displayed the graphics during lectures with a
projector attached to her computer. "Visualization is so valuable, and
Mathematica is a tremendous tool for this," Brown explains.
Brown found even more ways to incorporate Mathematica into her
lessons when her school purchased enough licenses to allow students to use it
in math and science classes as well as in the central computer lab. "My
philosophy focuses heavily on teaching using multiple methods of
representation," says Brown. "My students' projects center on this, and
Mathematica works well for combining graphical, symbolic, numerical,
and verbal techniques."
Although Brown notes that she finds Mathematica most useful for
teaching advanced courses, even her Algebra I students are captivated by the
graphics and show improvement when she incorporates them into the course. One
year, several Algebra I students didn't believe that the curve 1/x would never
cross the x-axis. Using Mathematica, the students were able to
investigate their theory by zooming in on the plot repeatedly, searching for an
intersection. When they were satisfied that their teacher was correct, the
students presented their final graphs to the class.
Using Mathematica is sometimes a challenge for Brown's students, but
they are good at learning from their classmates' mistakes and helping each
other with nuances of the code. The most common problems involve forgotten
commas and capital letters. Brown has found that "with more practice, they
learn to spot these errors and make fewer of them." Giving students early
exposure to Mathematica will help them succeed in future math and
science courses and can help increase their interest in technology-related
fields.
Recently, Brown led several workshops to teach her colleagues how to take
advantage of Mathematica as a teaching tool. She also wrote a tutorial
titled "Exponentials vs. Factorials" to demonstrate how
Mathematica can aid teaching in ways that aren't possible with a textbook or
a graphing calculator.
Brown has also created a website that is a great resource for students and
teachers. There is an activity section with puzzles, problems, and codes for
students to solve. Ideas on how Mathematica can add a new dimension to
math courses are available, and sample teaching modules in Mathematica
notebook form can be downloaded. Brown has also included information on her
teaching philosophy, sample student presentations, and links to other
math-oriented web resources. View the site
for more details. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments* Assumes virtually no prior knowledge
* Numerous worked examples, exercises and challenge questions
Modular Mathematics is a new series of introductory texts for undergraduates. Builiding on both the skills and knowledge acquired at A level, each book provides a lively and accessible account of the subject. Examples and exercises are used as teaching aids throughout and ideas for investigative and project work help to place the subject in context.
Synopsis:
provides a lively and accessible account of the subject. Examples and exercises are used as teaching aids throughout and ideas for investigative and project work help to place the subject in context.
Synopsis"Synopsis"
by Elsevier,
provides a lively and accessible account of the subject. Examples and exercises are used as teaching aids throughout and ideas for investigative and project work help to place the subject in context.
"Synopsis"
by Elsevier, | 677.169 | 1 |
Specification
Aims
This course unit aims to introduce the basic ideas and techniques of linear algebra for use in many other lecture courses. The course will also introduce some basic ideas of abstract algebra and techniques of proof which will be useful for future courses in pure mathematics.
Brief Description of the unit
This core course aims at introducing students to the fundamental concepts of linear algebra culminating in abstract vector spaces and linear transformations. The first part covers systems of linear equations, matrices, and some basic concepts of the theory of vector spaces in the concrete setting of real linear n-space, Rn. The second part briefly explores orthogonality, and then goes on to introduce abstract vector spaces over arbitrary fields and linear transformations. The subject material is of vital importance in all fields of mathematics and in science in general.
Learning Outcomes
On successful completion of this course unit students will be able to
be able to solve systems of linear equations by using Gaussian elimination to reduce the augmented matrix to row echelon form or to reduced row echelon form;
understand the basic ideas of vector algebra: linear dependence and independence and spanning;
be able to apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix using Gauss-Jordan elimination;
know how to find the row space, column space and null space of a matrix, to find bases for these subspaces and be familiar with the concepts of dimension of a subspace and the rank and nullity of a matrix, and to understand the relationship of these concepts to associated systems of linear equations;
be able to find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial and will know how to diagonalize a matrix when this is possible;
be able to find the orthogonal complement of a subspace;
be able to recognize and invert orthogonal matrices;
be able to orthogonally diagonalize symmetric matrices;
be familiar with the general notions of a vector space over a field and of a subspace, linear independence, dependence, spanning sets, basis and dimension of a general subspace;
be able to find the change-of-basis matrix with respect to two bases of a vector space;
be familiar with the notion of a linear transformation, its matrix with respect to bases of the domain and the codomain, its range and kernel, and its rank and nullity and the relationship between them;
be familiar with the notion of a linear operator and be able to find the eigenvalues and eigenvectors of an operator.
Future topics requiring this course unit
Almost all Mathematics course units, particularly those in pure mathematics. | 677.169 | 1 |
Mathematics classes that will help with physics (list included)
Mathematics classes that will help with physics (list included)
I was wondering if anybody could give me some suggestions on which mathematics courses will be of the most use for theoretical physics. I am a sophomore at Wayne State university and am taking intro to quantum mechanics and a first course in optics this semester.
And I was just wondering if somebody could help me with finding out which classes would be most helpful to pursue studies in theoretical physics. I am dual majoring in mathematics, but I am mainly concerned not with getting a degree, as with getting knowledge
So I have to confine myself to an area and theorize there? The undergrad stuff at my school is this.. I have left (in semester order)
Thermodynamics/stat mechanics, mechanics 1
quantum physics 1, mechanics 2
Quantum physics 2, electromagnetism 1
Electromagnetism 2, modern physics lab
4 semesters. But over the summers they do not offer these classes, so I want to take a lot of math classes over the summers to be the best I can be, I really like quantum mechanics a lot, I want to take a lot of quantum mechanics classes as a grad student, if that helps isolate classes.
I was told elementary analysis (which is the class required to get into all those upper level classes on that list) is good, as well as partial differential equations and complex analysis, but then I heard algebra was good, probability theory, basically every teacher I ask tells me something different so I don't know what to do.
It is quite hard to say since little of math (at least at the level you are considering taking) is useless for physics... following your own interests towards math can help too!
But anyway definitely take an analysis class, and definitely an abstract algebra class (for QM). Taking classes like complex analysis, probability theory, more abstract algebra, more analysis etc can all definitely be useful, but understand that whenever math is necessary in a physics class, you usually learns that math within the physics class, just much more quick and dirty and bare-boned than in a full math class, but it's not like you'll ever get stuck if you don't take them. That being said two very important mathematics topics that usually get taught quite shabbily within a physics context (although it is definitely very useful to know them properly) are: representation theory (very important for QM) and differential geometry (very important for GR). (The problem is that they might be grad courses in your math department.)
If you are really planning on going to the mathematical physics sides of things, i.e. you know you will be studying a lot of math in the future, then take as much analysis, algebra and topology classes to ensure a firm foundation for self-study down the road! is a class called elementary analysis which is the prereq for all the higher math courses. I'm not great at math, I mean, I get A's, but I don't really feel like I understand it, so I want to focus on the things that I can apply towards physics. Unfortunately the elementary analysis is not offered this summer so I will have to take it next year so next summer I can take some algebra and perhaps something else. They do offer a lot of topology and things like that. I should just become a monk and go to school for the rest of my lifeNot at the undergrad level I think. I think for someone who sees himself as a future theorist, it makes sense to study (at least) linear algebra, real analysis, differential geometry, and maybe differential equations, representation theory, complex analysis, linear/harmonic analysis (i.e. Fourier series and stuff), and abstract algebra. Representation theory is super important, but some of it is taught in QM courses. So I can't say that it's essential to take a course on it, but I would definitely recommend it. A similar comment can be made about several of the other topics, in particular differential equations and stuff about Fourier series and integrals. You need some abstract algebra, but I'm not sure you need to take a course. It may be enough to read the early chapters in some book.
If you want to go into mathematical physics, you also need topology, measure and integration theory, and functional analysis.
Quote by Levi Tate was a course like that at my university. I thought it was pretty useless to be honest. In my humble opinion, it's better to take "real" math courses.
Quote by Levi Tate
There is a class called elementary analysis which is the prereq for all the higher math courses.
You will probably need this just to be able to read books on more advanced topics.
Thanks a lot. I suppose I will just reference this thread and reopen the conversation as I get a bit closer. There is so much, it is a bit boggling. I suppose for right now I will content myself to focusing on understanding my classes now.
And thank you everybody else as well. This gave me a lot to think about and I plan to revisit this question as I, and you, progressAs for linear algebra: I assumed one class treated both of those aspects, but if not yes I agree.
As for abstract algebra: actually I agree that the material itself in an abstract algebra is not that important for QM (as in, all the theorems) but what seems immensely valuable to me from such a class is the reasoning skills you obtain when thinking about algebra (and it is a kind of mathematical maturity that is the distinct from the maturity you get from an analysis class, at least in my own experience). My opinion is that once you get the basics down ice-cold, it is much more possible to add to that the specific relevant physics-related pieces that you can self-study (e.g. representation theory), whereas to get the basics down can easily take the length of a proper math course on analysis and abstract algebra respectively.
The weird thing about your classes is that the Advanced Linear Algebra class requires two previous Abstract Algebra Courses. I don't really understand that. I'm not saying that Abstract Algebra isn't useful to understand before Linear Algebra, but I wouldn't put it as prereq.
The weird thing about your classes is that the Advanced Linear Algebra class requires two previous Abstract Algebra Courses. I don't really understand that. I'm not saying that Abstract Algebra isn't useful to understand before Linear Algebra, but I wouldn't put it as prereqHis course doesn't cover modules. And you really don't need group theory to be able to understand quotient spaces and the isomorphism theorems. In fact, I might even say that it's better to first see quotient spaces in the setting of linear algebra than in group theory. | 677.169 | 1 |
Mathematics for Economists
Learning goals
In order to understand and apply modern economic theories and concepts as well as to meet the requirements for course study it is necessary for students to be able to use learn basic mathematical theories. This Course has the goal to provide students with these mathematical resources. | 677.169 | 1 |
Numbers in parentheses
indicate session (1-8) at which topic was covered.
Grade 8By the end
of grade eight,
students will understand various numerical representations, including
square roots, exponents and scientific notation; use and apply
geometric properties of plane figures, including congruence and the
Pythagorean theorem; use symbolic algebra to represent situations and
solve problems, especially those that involve linear relationships;
solve linear equations, systems of linear equations and inequalities;
use equations, tables and graphs to
analyze and interpret linear
functions; use and understand set theory and simple counting
techniques; determine the theoretical probability of simple events; and
make inferences from statistical data, particularly data that can be
modeled by linear functions. Instruction and
assessment should include the appropriate use of manipulatives
and technology use linear algebra to
represent, analyze and solve problems. They will use equations, tables,
and graphs to investigate linear relations and functions, paying
particular attention to slope as a rate of change.
M8A3. Students
will understand relations and linear functions. (1)
a. Recognize a relation as a correspondence between varying quantities.
(1) b. Recognize a function as a correspondence between
inputs and outputs where the output for each input must be unique.
(1) c. Distinguish between relations that are functions
and those that are not functions.
(1) d. Recognize functions in a variety of
representations and a variety of contexts.
(1) e. Use tables to describe sequences recursively and
with a formula in closed form.
(2) f. Understand and recognize arithmetic sequences as
linear functions with whole number input values.
(2) g. Interpret the constant difference in an
arithmetic sequence as the slope of the associated linear function.
(2) h. Identify relations and functions as linear or
nonlinear.
(1-2) i. Translate among
verbal, tabular, graphic, and algebraic representations
DATA ANALYSIS AND
PROBABILITY Students will use and understand set theory and simple
counting techniques; determine the theoretical probability of simple
events; and make inferences from data, particularly data that can be
modeled by linear functions.
M8D4. Students
will organize, interpret, and make inferences from statistical data
a. Gather data that can be modeled with a linear function.
b. Estimate and determine a line of best fit from a
scatter plot.
MATH
I
ALGEBRA
Students will explore functions and
solve simple equations. Students will simplify and operate with
radical, polynomial, and rational expressions.
(5) c.
Graph transformations of basic functions including vertical shifts,
stretches, and shrinks, as well as reflections across the
x- and y-axes.
(4) d. Investigate and explain the characteristics of a
function: domain, range, zeros, intercepts, intervals of increase and
decrease, maximum and minimum
values, and end behavior.
(4) e. Relate to a given context the characteristics of
a function, and use graphs and tables to investigate its behavior.
(4) f. Recognize sequences as functions with domains
that are whole numbers.
(4) g. Explore rates of change, comparing constant rates
of change (i.e., slope) versus variable rates of change. Compare rates
of change of linear, quadratic,
square root, and other function families.
(4) h. Determine graphically and algebraically whether a
function has symmetry and whether it is even, odd, or neither.
(2) i. Understand that any
equation in x can be interpreted as the equation f(x)
= g(x), and interpret the solutions of the
equation as the x-value(s)
of the intersection point(s) of the graphs of y = f(x)
and y = g(x).
Mathematics
2This is the second course in a
sequence of courses designed to provide students with arigorous program of study in mathematics. It
includes complex numbers; quadratic, piecewise, and exponential
functions; right triangles, and right triangular trigonometry;
properties of circles; and statistical inference. (Prerequisite: Successful
completion of Math 1). Instruction and assessment should include
the appropriate use of manipulatives and
technology investigate piecewise,
exponential, and quadratic functions, using numerical, analytical, and
graphical approaches, focusing on the use of these functions in
problem-solving situations. Students will solve equations and
inequalities and explore inverses of functions.
MM2A1. Students
will investigate step and piecewise functions, including greatest
integer and absolute value functions. (3)
a. Write absolute value functions as piecewise functions.
(3) b. Investigate and explain characteristics of a
variety of piecewise functions including domain, range, vertex, axis of
symmetry, zeros, intercepts, extrema, points of
discontinuity, intervals over which the function is constant, intervals
of increase and decrease, and rates of change.
(3) c. Solve absolute value equations and inequalities
analytically, graphically, and by using appropriate technology.
MM2A2. Students
will explore exponential functions. (6)
a. Extend properties of exponents to include all integer exponents.
(7) b. Investigate and explain characteristics of
exponential functions, including domain and range, asymptotes, zeros,
intercepts,
intervals of increase and decrease, rates of change, and end behavior.
(7) c. Graph functions as transformations of f(x)
= ax.
(8) d. Solve simple exponential equations and
inequalities analytically, graphically, and by using appropriate
technology.
(7) e. Understand and use basic exponential functions as
models of real phenomena.
(7)
f. Understand and recognize geometric sequences as exponential
functions with domains that are whole numbers.
(7) g.
Interpret the constant ratio in a geometric sequence as the base of the
associated exponential function.
MM2A4. Students
will solve quadratic equations and inequalities in one variable. (5)
a. Solve equations graphically using appropriate technology.
(5) b. Find real and complex solutions of equations by
factoring, taking square roots, and applying the quadratic formula.
(5) c. Analyze the nature of roots using technology and
using the discriminant.
d. Solve quadratic inequalities both
graphically and
algebraically, and describe the solutions using linear inequalities.
MM2A5. Students
will explore inverses of functions.
(8) a. Discuss the
characteristics of functions and their inverses, including
one-to-oneness, domain, and range.
(8) b. Determine inverses of linear, quadratic, and
power functions and functions of the form f(x) = a/x,
including the use of restricted
domains.
(8) c. Explore the graphs of functions and their
inverses.
(8) d. Use composition to verify that functions are
inverses of each other.
MM2D2. Students
will determine an algebraic model to quantify the association between
two quantitative variables. a. Gather and plot data that
can be modeled with linear and quadratic functions.
b. Examine the issues of curve fitting by finding
good linear fits to data using simple methods such as the median-median
line and "eyeballing".
c. Understand and apply the processes of linear and
quadratic regression for curve fitting using appropriate technology.
d. Investigate issues that arise when using data to
explore the relationship between two variables, including confusion
between correlation and causation.
MM3A1. Students
will analyze graphs of polynomial functions of higher degree.
a. Graph simple polynomial functions as translations of the function f(x)
= axn.
b. Understand the effects of the following on the
graph of a polynomial function: degree, lead coefficient, and
multiplicity of real zeros.
c. Determine whether a polynomial function has
symmetry and whether it is even, odd, or neither.
d. Investigate and explain characteristics of
polynomial functions, including domain and range, intercepts, zeros,
relative and absolute extrema, intervals
of increase and decrease, and end behavior. | 677.169 | 1 |
Math Center
The Math Center is a non-credit, Community Education class which provides assistance
in mathematics as a completely free service. Current Allan Hancock College students
as well as other individuals who are 18 years or older may fill out a simple registration
form and attend as frequently as they want. Registration forms may be found in the
Math Center or at Community Education in Building S.
The goal of the Math Center (sometimes called the Math Lab) is to assist students
in the successful completion of any Allan Hancock College mathematics class by providing
additional instructional resources. The Math Center offers many resources, including
one-on-one, drop-in tutoring by our staff of instructors and student tutors. Please
see the full list of resources below:
Free, drop-in tutoring
A place to study individually or in small groups
In-house loan of current textbooks and solutions manuals
A library of supplemental books, DVDs, and video tapes for check-out
Computers for mathematical purposes
Calculators
Handouts on math topics, including content from various math courses as well as information
on overcoming math anxiety and preparing for and taking math tests
Two private study rooms
Make-up testing
Workshops
Joining the math center group
Current students may access more detailed information by entering their myHancock
portal and joining the Math Center Group. Details may include information such as
the current schedule of instructors and student tutors who work in the Math Center,
a schedule of instructors and tutors who specialize in statistics, upcoming workshops
on selected topics, etc. To join the Math Center Group:
Enter myHancock
Look at the center of the Home page in the box titled "My Groups." Click on "View
All Groups" at the bottom of the box.
STAFF | 677.169 | 1 |
The total weight of two beluga whales and three orca whales is 36,000 pounds. As you'll see in this course, if given one additional fact, you can determine the weight of each whale. To answer this weighty question, we'll give you all the math tools you'll need. The setting for this course is an amusement park with animals, rides, and games. Your job will be to apply what you learn to dozens of real-world scenarios.
Equations, geometric relationships, and statistical probabilities can sometimes be dull, but not in this class! Your park guide (teacher) will take you on a grand tour of problems and puzzles that show how things work and how mathematics provides valuable tools for everyday living.
Come reinforce your existing algebra and geometry skills to learn solid skills with the algebraic and geometric concepts you'll need for further study of mathematics. We have an admission ticket with your name on it and we promise an exciting ride with no waiting!
Additional Materials Required
Graphmatica - graphing utility, free download from within course
United Streaming - student is automatically logged in from a link in the course
SAS Curriculum Pathways - access information provide by instructor
You will have access to MathType. Directions for downloading this product are located in the Course Information area of the course. | 677.169 | 1 |
By Carl Bialik
My print column this week explores a new search engine, Wolfram Alpha, that aims to make the world's information computable. It could also make the world's math problem sets and tests computable, by solving tough problems, including in calculus, and showing its work.
Some teachers see Wolfram Alpha as a tool liberating them and their students to focus on broader concepts, just as calculators obviated slide-rule instruction. It could also push math into a more visual realm and away from abstract notation, thanks to its plethora of graphs and charts. "Graphical aspect: I'm wondering how much mathematical notation will survive this big push of graphing and animation," said Rich Beveridge, a math instructor at Clatsop Community College who has blogged about the new site.
However, Roger Howe, a math professor at Yale university, worries that the basics will be forgotten. "Mathematics doesn't really become real unless students have a fairly direct contact with it," Howe says. "Doing a reasonable amount of computation seems to be important for mastering mathematics."
It's unclear how much will be lost, and how much that matters. "One worries we'll lose the underlying intuition," said Donald Berry, chairman of the department of biostatistics at the University of Texas M.D. Anderson Cancer Center. "I worry about that, but I'm not sure how important that is. We as a species have come to a point where we can do things because of what others have built for us."
Maria Andersen, a mathematics instructor at Muskegon Community College whose blog has hosted a lively discussion on Wolfram Alpha, is excited to use the new search engine in instruction. "I do see it as being a fantastic tool we can use to explore concepts," Andersen said. "I can't morally imagine walking into a classroom and having a student say, 'Why do I need to take a cube of a binomial when Wolfram Alpha can do it for me?' "
She added that teachers would have to change their homework. "I would say that at least 50% of the standard homework problems and assessment questions that would be assigned with traditional textbooks could be answered by Wolfram Alpha," Andersen said. "… find a math book, open it to a section of problems, and you'll quickly find lots of examples that Wolfram Alpha will do."
But Andersen worries about becoming reliant on a single online tool: "What if Wolfram Alpha disappears, after we all shifted to use it?"
"It's very flattering if people care enough about one's tools to be concerned about their longevity," says Stephen Wolfram, the founder and chief executive of Wolfram Research. "What can one guarantee in this world?"
He sees his new tool as a way to broaden access to math and science. "The more people have ready access to knowledge and the more they have the power to do things like the experts do, the more they can feel empowered and get motivated to understand what's going on," he said.
Some calculation systems can work too much like a black box, though, according to Colm Mulcahy, a mathematician at Spelman College. "If [students] can get an instant answer, does it add to their understanding or make it so they're just pushing buttons?" Mulcahy asks. "So many students are obsessed with calculators: 2+2 is 4 because that's what the calculator says, and if the calculator said otherwise, they'd go with that." He added, "Unless/until teachers — at all levels — teach and test more on the concepts (in addition to a certain level of computation), our students are doomed."
All these comments are based on an assumption that Wolfram Alpha will improve. It's already strong in math. The derivative of 5x is a fixed, universally agreed-upon quantity. And Wolfram Research has extensive experience doing such math with its Mathematica program, a fixture in many college courses.
The GDP of France, however, is continually updated and subject to revision. And the French government might decide tomorrow to add a column to the chart in its regular economic report, tripping up Wolfram Alpha's effort to peel the numbers out. "Wolfram Alpha seems to be quite poor at doing what it claims to do well — namely, adding value to something like a search engine by being able to carry out computations to generate data that's not already in place on someone's web page," said Jordan Ellenberg, a mathematician at the University of Wisconsin.
Jeff Witmer, who teaches statistics at Oberlin College, says he's already adjusted his curriculum to a more conceptual plane that wouldn't be majorly affected by this new tool. "I expect that Wolfram Alpha could be used to help answer questions that I asked on statistics exams 15 years ago, when I had my students do a lot of calculating," Witmer said. "These days I mostly ask students to interpret calculations that have already been made, which means that Wolfram Alpha would not be helpful."
Phil Hanser, a statistician with the Brattle Group, criticizes the search engine for not reporting its uncertainty about statistical calculations. "If Alpha is meant to be a pre-eminent mathematics search engine, it should also serve as a model of good mathematics practice, including statistics," Mr. Hanser says.
Other teachers noted that they'd already been using Mathematica in their teaching. "There's not a lot new there, besides that it's free as long as you have Internet access, which is not a small thing," said Dan Teague, who teaches math at the North Carolina School of Science and Mathematics. (Surprisingly, Wolfram said sales of Mathematica have increased since the launch of the new tool, thanks to increased exposure of his signature software package.)
What do you think? How will this new tool affect teaching? How will you use it, if at all? What searches make it stumble? Please let me know in the comments.
Comments (5 of 8)
I think that Wolfram is a very well put together engine. I don't think that it will slow down the growth of our students. The students are not like the teachers, they do not have the answers or the know how to solve certain questions as do the instructors. When the students are stumped, they can go onto wolfram and see the answer if it is not in the back of the book, and then continue from there and work it backwards. All mathematics problems can be worked both ways, this I think is an amazing oppertunity.
Thank you.
2:14 pm June 25, 2009
Lokki wrote :
I have a friend who is a chemical engineer. A few years ago, his company had a rather expensive piece of equipment ruined by a young engineer who missed the small fact that the amount of one chemical being put into a mixture was off by a factor of 10. My friend moaned that kids these days have no concept of what the numbers a calculator spews out mean… "If he'd ever used a slide rule, he might have been off, but he'd have notice a factor of 10."
thank you for your article on wolframalpha; wolframalpha opens a new trend on web search engines missed by google. it's a first step towards computing answers through search engines. And you touch on a delicate issue about how to teach maths when there are so many clever maths software around and now wolframalpha goes a step further into putting it a light version of their great 'mathematica' software online for free. But to make short my comment, I've myself taught maths to young economists, it is essential to first learn the 'basics' to get to understand and control the more complex issues. I believe that a maths teacher has to show to students the 'beauty' in maths by deconstructing theorems and maths algorithms so students see what's behind it and then they will able to make better use of formidable maths software in their research but not to take anything for granted and better control and judge whether their results are true, rational or not, as human mistakes can always creep in and could be devastating if one does not keep track of everything and does not omit to, somewhat, double check his/her results 'by hand'. Marwan Elkhoury, co-founder of 'Growth and Development Bridge' found at
About The Numbers Guy
The Numbers Guy examines numbers in the news, business and politics. Some numbers are flat-out wrong or biased | 677.169 | 1 |
This course is designed for students who have good basic math skills but with limited algebra background. This is the second level in the math progression leading to Beginning Algebra (Math 016). Repeatable.
This course is for students who needs intensive basic math review or has very limited math background. This is the first level in the math progression leading to beginning Algebra (Math 016). Repeatable. | 677.169 | 1 |
Gain knowledge on a variety of computational and mathematical problems
in discrete geometry and their applications.
Be able to utilize fundamental geometric data structures and algorithmic
design techniques for the solution of new computational problems in discrete
geometry.
Be able to implement basic geometric algorithms using standard programming
languages.
Be prepared for theoretical research in discrete and computational geometry.
Preparation:
This is an advanced graduate-level course on discrete and computational
geometry.
Solid mathematical, algorithmic, and programming skills are required.
The students are expected to explore the vast literatures of the field
and work on current research problems under the guidance of the instructor.
Prerequisite: CS5050.
Grading:
Homework (40%):
Homework 1 (due at the beginning of class on Mon Jan 14):
Read chapter 1. Browse through the whole book, pick your favorite chapter (the topic that you wish to be covered).
Homework 2 (due at the beginning of class on Fri Jan 18):
What is the probability that the convex hull of k random points on the boundary of a circle encloses the circle center?
Homework 3 (due at the beginning of class on Wed Jan 30):
Show that f(r,s)=(r+s-4 choose r-2)+1 is the solution to the recurrence
f(r,s)=f(r-1,s)+f(r,s-1)-1 (Hint: induction).
Homework 4 (due at the beginning of class on Mon Feb 4):
Prove: given a finite set of non-parallel lines on the plane not all through one point, there is a point intersected by exactly two lines.
Homework 5 (due at the beginning of class on Fri Feb 8):
Derive the parameterized equation for an ellipse with specified origin and axes.
Homework 6 (due at the beginning of class on Fri Feb 15):
Given a set of n points in the plane in general position,
design an O(n^2) time algorithm that computes for each point
the circular order of the other points.
Homework 7 (due at the beginning of class on Mon Mar 31):
Build a rhombic dodecahedron and check whether Euler's formula
works for this polyhedron.
The last day to drop this class without notation on your transcript is
January 28.
Attending this class beyond January 28 without being officially registered
will not be approved by the Dean's Office. Students must be officially
registered for this course. No assignments or tests of any kind will be
graded for students whose names do not appear on the class list.
Students are encouraged to discuss and exchange ideas on homework and projects,
but each student must write up the solutions independently.
Students who are caught cheating immediately receive "Fail" grades.
DRC statement:
Students with physical, sensory, emotional or medical impairments may be eligible for reasonable accommodations in accordance with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973. All accommodations are coordinated through the Disability Resource Center (DRC) in Room 101 of the University Inn, 797-2444 voice, 797-0740 TTY, or toll free at 1-800-259-2966. Please contact the DRC as early in the semester as possible. Alternate format materials (Braille, large print or digital) are available with advance notice. | 677.169 | 1 |
Description
The Calculus Workbook NCEA Level 3 offers students the tools they need for success in Calculus.
In the first part there are exercises at Achieved, Merit and Excellence levels. The author walks the student through each new concept, provides several worked examples, and then a set of problems for students to solve. The fully worked answers follow immediately, encouraging students to carefully compare their work with the worked examples and worked answers, and improve their results.
With a "practice makes perfect" attitude, the Calculus Workbook NCEA Level 3 also contains six full-length Practice Exams, written for the 2010 assessment specifications, with full answers, as well as Unit Standards Practice.
For those students who have mastered their Level 3 work, there follows a scholarship training programme. Students can work their own way through this material with minimum supervision from the teacher.
Author biography
Philip Lloyd is a Calculus teacher of many years standing, currently teaching at Epsom Girls Grammar School in Auckland. His students have consistently achieved very highly, with a good number achieving scholarship after using his material. | 677.169 | 1 |
Friday, August 3, 2012
Teaching Textbooks Review
I HATE Math.
There. I said it.
Math to me, is like a foreign language. One I don't understand. Sort of like Chinese.
In my day to day life, I don't ever use any of the advanced Math that I was tortured with in school. I only ever took up to Algebra 2, and I barely passed that. Ahhh.....good nightmares.....I mean.....memories.
So, for a Math hating homeschool Mom, how in the world are you supposed to teach advanced Math classes to your kids?
I did not learn of TT until my oldest daughter was in 8th grade, and we were about to do Pre-Algebra. We have always struggled with Math, and let me tell you, I was NOT looking forward to trying to teach her this.
We had started out with A Beka, which we struggled through from kindergarten until 3rd grade. For those of you who are not familiar with homeschooling curriculum, A Beka is one of the most commonly used curriculums out there.
However, it is advanced. Which is great, if you are working with an advanced student. My girls loved A Beka for Reading, Writing, Spelling, and Vocabulary. Things they were good at.
For Math however, it was just too much. So then, I tried Bob Jones (BJU). Yet another GREAT curriculum. I have often used this for Science and History, and have even used it for Spelling and Reading for my youngest.
While BJU was more tolerable than A Beka for Math, it was still not a good fit. There are many, many more Math curriculums out there, but those are the ones that I tried.
I can't remember exactly how I first heard of TT, but whoever told me about it, I now consider her an angel, sent straight from heaven, to help this poor Mama out!
I was reluctant to try it, because let's be honest, if you clicked on the link, you will notice that it IS pricey. It is much more expensive than most homeschoolers are willing to pay, or can even afford.
But, I figured, why not? We were at our wits' end as how to best teach this subject.
We purchased TT, and it was love at first sight. We have never used another Math curriculum since!
But, Amiee....what is SO special about TT, you may ask?
Well, for starters, it is all done on the computer. First, the child listens to a lecture from a teacher, and while the teacher is explaining that day's lesson, they are actually demonstrating how to do it. So, this works for auditory and visual learners alike.
You can listen to the lecture as many times as it takes for the child to grasp the information. While it is also possible for Mom to "replay" the info, her voice does tend to get raspy, and perhaps, there may even be a hint of irritation that tends to creep in, oh say around the third of fourth time she has to explain it. Not so with the computer teacher! He is extremely patient.
Then, the child is given some practice questions, to make sure they truly understand the lesson.
There is always the possibility of being "helped" and you can always view the answer once you get it wrong a set number of times (to be determined by the parent).
Once the child is ready, they can then begin to answer that day's questions about the lesson. There are usually around 20 questions, which seems to be an adequate amount. There is plenty of review from previous lessons included also.
My girls liked that, in the younger grades, they incorporate games for "bonus" rounds, and there are cute little creatures who will talk to you along the way.
There is also a parent side, where you can actually see the grade book, how many they got wrong, and be given the choice as to whether to make them do it over again or not.
What do I like best about it? That I don't have to do hardly anything! Unless one of my girls just isn't getting it, then, we go over the lesson together.
The lessons are self-grading, which is not only an awesome feature for Mom, but it also tells the child immediately if they got the answer right or wrong.
*Several of the advanced Math curriculums are still not self-grading, but they are working on changing that. They still come with an answer CD, and answer key. The lecture is listened to on the CD, but the child works out of a workbook. Hallelujah! Algebra 2 is now self-grading! Can you hear the excitement in my voice? Hmmm? Can you?!
TT is taught in a way that just makes it easier for a child to understand and be able to grasp information better. If you don't believe me, type the words, Teaching Textbooks review into your search engine, and read about other satisfied customers.
I must admit though, that the oldest is now at a point where I just cannot help her in Math anymore. That is now Hubs' job. We also did have a dear friend tutor her in Algebra for a little while, because she just wasn't getting it. So, there still could be some additional Math help needed, even though you are using excellent curriculum. That's just the way it is.
If your child is advanced in Math, this may not be the best curriculum for you, as it does tend to go at a slower pace, or, so I have read from people who have Math geniuses for children. For example, if your elementary school aged child is quoting algebraic equations in their sleep, it might be best to find a more challenging curriculum. Or, perhaps you should enroll them in college classes.
Yes, it is pricey. But, to me, it is worth every penny! Has it made my girls LOVE Math? Well....no. I don't think there is a curriculum in the world that could do that! Each child has their own set of strengths and weaknesses, and Math is one of our weaknesses. Although my youngest daughter tends to have a more "mathematical" mind than my older two, she still doesn't love Math.
Another nice thing about TT is that you are allowed to sell the curriculum to others once you are done using it. That is not the case with every curriculum. So, this year, I sold my used TT on eBay for the first time, and I was pleasantly surprised by how much money I was able to get back from my investment! If you do an advanced eBay search on TT, you will see that they have an excellent resale value.
Since I have been using TT for such a long time, I now have quite a collection of them, and I no longer have to buy three different Math curriculums for three different grade levels. This year, I only have to buy Algebra 2. My wallet just did a sigh of relief, as my oldest is about to take a few college classes for dual enrollment, and we are required to pay for it out of our own pocket. But, that's a tale for another time.
If you are a fellow homeschool family, and you are in the same boat as we used to be, struggling through Math, day in......and day out.....why not give Teaching Textbooks a try? You'll be glad you did!
* I did not receive any compensation or free products for this positive review.
2 comments:
I always like the idea of homeschool but what do you do when you are not good at something - so I see you have found the answer. Fortunately homeschool was not an option as we live in the City and by and large my kids walked to school. Not so the kids who live in the outback who are schooled over the radio. | 677.169 | 1 |
Chapter 1. Introduction - Pg. 1
1 Introduction 1.1 Why Numerical Methods? Engineers and scientists frequently encounter linear and nonlinear mathematical equa- tions, integrals, differential equations, and data to be manipulated. Sometimes the ma- nipulations to be performed are easy and straightforward; often they are not. This is particularly true of nonlinear problems, that is, problems in which variables occur as products, including products of themselves, or as functions of transcendental functions, like the trigonometric or logarithmic relations. If the mathematics to be performed can- not be done in closed form (i.e., an exact analytic symbolic solution is obtained), recourse must be made to numerical approximations. Fortunately, these methods, when properly understood and used, are powerful and accurate. It should be understood that recourse to a numerical solution is always a fall- | 677.169 | 1 |
Overview - PM PRACTICAL MATH ANSWER KEY
Presents practical life math applications.
This straightforward, easy-to-understand program provides students of mixed
abilities with key math concepts essential for successful adult living. From
buying groceries to budgeting for housing, education, and travel, the simply
stated subject matter delivered in a manageable format with a controlled reading
level makes content accessible to all students.
Student Edition - prepares students for understanding concepts in each
new chapter through strong vocabulary instruction and clear learning objectives
that preview and outline key concepts upfront. A manageable concept load introduces,
teaches, and practices one concept at a time and fosters student success. Frequent
opportunities for practice encourage computational proficiency.
Student Workbook - Reinforces new concepts through abundant practice
exercises and frequent review. Fosters content understanding and skill development
and retention through review, and applications, and with extensive practice
correlated to every lesson in the Student Edition. | 677.169 | 1 |
This software to download was designed by a teacher to help teachers teach algebra I, algebra II, trigonometry, probability and statistics, and 3D graphing. It approaches these topics from a uniquely teacher point of view. For example, it generates problems for students to solve such as systems of equations that are independent-consistent, dependent-consistent, and inconsistent.inconsistent. It generates graphs that students must identify in function notation and/or by exact formula.
3D graphing techniques are illustrated dynamically. Polar and parametric equations can be investigated with the help of a "lightning bug". Slider graphs of any functions can be created to help students visualize the effects of parameters. Piecewise-defined functions and equations that do not represent functions can be graphed. Implicitly defined equations can be graphed. Inequalities can be graphed in standared or "reversed" mode | 677.169 | 1 |
Search MSRI
Program
Organizers
David Austin, Bill Casselman and Jim Fix
Description
This workshop will introduce sophisticated techniques of computer graphics for use to explain mathematics in research articles, course notes, and presentations. It will begin with an introduction to graphics algorithms, and the languages PostScript and Java. Participants will spend afternoons and evenings during the first week in the computer labs on assigned exercises. The second week will be spent on assigned project themes, ending with student presentations. | 677.169 | 1 |
This webquest was designed for 8th grade math students who have had some exposure to solving equations. These students know and understand how to solve a one-step equation but struggle with anything more complicated. This webquest was designed to provide visual representations of the math concepts and tap into their prior knowledge in order to extend their understanding. | 677.169 | 1 |
The Algebra Challenge, CLMS/CLHS 7/27/09
For life in the 21st century, mathematics proficiency is as fundamental as literacy, and the keystone of mathematical proficiency is Algebra 1. Traditionally, algebra has distinguished the college-bound from other students. Today it denies many students a high school diploma and contributes to dropout rates. The challenge for K-12 schools is to prepare students for success in Algebra 1 and beyond by teaching algebraic thinking at all grade levels. This workshop focuses on ways to meet and beat the Algebra Challenge using strategies that engage students in a challenging, rigorous, thinking curriculum. | 677.169 | 1 |
Author's Description
Math Center Level 2 - Math software for students
Math software for students studying precalculus and calculus. Can be interesting for teachers teaching calculus. Math Center Level 2 consists of a Scientific Calculator, a Graphing Calculator 2D Numeric, a Graphing Calculator 2D Parametric, and a Graphing Calculator 2D Polar. The Scientific Calculator works in scientific mode. All numbers in internal calculations are treated in scientific format, like 1.23456789012345E+2 for 123.456789012345. You also can use scientific notation in formulas. If you get result NaN, like in ln(-1), that means that the function is not defined for given argument. Otherwise Scientific Calculator is similar to Simple Calculators. There are options to save and print calculation history, to change font, and standard editing options. Graphing Calculator 2D Numeric is a further development of Graphing Calculator2D from Math Center Level 1. It has extended functionality: hyperbolic functions are added. There are also added new capabilities which allow calculating series, product series, Permutations, Combinations, Newton Binomial Coefficients, and Gauss Binomial Coefficients . Graphing Calculator 2D Numeric has capability to build graphs for first and second derivatives, definite integral (area under curve) and length integral (length of curve). Since these calculations are done numerically, not symbolically, the calculator is called Numeric. Graphing Calculator 2D Parametric is a generalization of Graphing Calculator 2D Numeric. Now x and y are functions on parameter ?. If you are typing formula using keyboard, then you can use "tau" for ? . Since all calculations are done twice, for x and y, there was some sacrificing of precision in order to keep speed of calculations. So, although it is possible to build the same graph of y=f(x) in parametric calculator using x=?, y=f(?), the Graphing Calculator 2D Numeric will build it with greater precision. Graphing Calculator 2D Polar is a specialization of Graphing Calculator 2D Numeric.
Math Center Level 2 1.0.0.7 is licensed as Shareware for the Windows operating system / platform. Math Center LevelMath Center Level 2 Tvalx. Please be aware that we do NOT provide Math Center Level 2 cracks, serial numbers, registration codes or any forms of pirated software downloads. | 677.169 | 1 |
The ASC offers three math classes to help
prepare students for their college level math courses.
Placement in these courses is based on COMPASS, ACT and/or
SAT scores and advisor recommendations. Credits for these courses DO NOT apply toward
graduation requirements nor do they fulfill Academic
Foundations requirements. However, the credits do count
towards enrollment status for financial aid.
This course begins with a brief review of elementary
algebraic concepts and then covers more advanced factoring,
operations on rational expressions and radical expressions,
quadratic equations, the rectangular coordinate system, and
exponential and logarithmic functions.
Who should take this course?
Students with the following placement scores: COMPASS: 26-75 Pre-Algebra
and
0-15 Algebra
Students with the following placement
scores: COMPASS: 76-100 Pre-Algebra
16-26 Algebra SAT: up to 489 ACT: up to 14
Students with the following placement scores: COMPASS: 27-50 Algebra SAT: 490-530 ACT: 15-21
Course
Materials
There is no text required for this
course this semester. All materials will be provided to
students free of charge. | 677.169 | 1 |
Certificate in Senior Secondary Mathematics - Arithmetic and Algebra is a well organized, accessible and in-depth course book designed to teach the fundamental aspects of elementary mathematics that are indispensable in building interest, confidence and competence in mathematical reasoning and problem solving. This reader-friendly course book is presented in a format that encourages the average student and challenges the more able student, starting with the basic aspects and progressing to the more advanced aspects of secondary level mathematics.
With well over 1000 worked-through examples, more than 840 exercises (answers provided), 20 chapters and 4 appendices; numerous graphs, diagrams and tables, this comprehensive course book is a necessary text for students who desire to do well in secondary or high school mathematics.
Emphasis has been laid on detailed presentation and communication through out the course book with the intention of engaging to a greater extent, the attention of the reader. From fractions, logarithms, number system to graphs, equations (literal, simultaneous, quadratic), inequalities, sets and probability, this comprehensive course book furnishes detailed theories, practice and formulae that will ultimately benefit the reader.
Certificate in Senior Secondary Mathematics is a valuable course book created to tutor students studying privately to earn good grades in mathematics in certificate and matriculation examinations. Teachers and students in normal classroom studies will also find this book quite helpful.
Preview coming soon.
Dili Okay Nwabueze at various times taught mathematics at both Ordinary and Advanced (Pure and Applied) Levels. He was formally a Polytechnic/University lecturer in mechanical engineering.
He has written publishable books and papers in diverse areas including but not limited to Mathematics, Mechanical Engineering, Petroleum Engineering, Petroleum Refining, and Materials Management.
Dili Okay Nwabueze is a registered Engineer.
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She Does Math!
edited by Marla Parker
The range of applications is broad. The examples are easy to understand and are generally supported by interesting problems. The book is carefully edited and the graphic and text style are consistent from chapter to chapter—the hallmark of attention to detail in a book with numerous authors. — Mathematical Reviews
Finally—a practical, innovative, well-written book that will also inspire its readers. The wonder is...it is a mathematics text and a biography! The idea of women telling their own career stories, emphasizing the mathematics they use in their jobs is extremely creative. This book makes me wish that I could go through school all over again! — Anne Bryant, Executive Director, American Association of University Women
She Does Math! presents the career histories of 38 professional women and math problems written by them. Each history describes how much math the author took in high school and college; how she chose her field of study; and how she ended up in her current job. Each of the women present several problems typical of those she had to solve on the job using mathematics.
There are many good reasons to buy this book:
It contains real-life problems. Any student who asks the question, "Why do I have to learn algebra (or trigonometry or geometery)?" will find many answers in its pages. Students will welcome seeing solutions from real-world jobs where the math skills they are learning in class are actually used.
It provides strong female role models.
It supplies practical information about the job market. Students learn that they can only compete for these interesting, well-paying jobs by taking mathematics throughout theur high school and college years.
It demonstrates the surprising variety of fields in which mathematics is used.
Who should have this book? Your daughter or granddaughter, your sister, your former math teacher, your students — and young men, too. They want to know how the math they study is applied — and this book will show them. | 677.169 | 1 |
Links to the Web sites on the History of Mathematics This site, hosted by the British Society for the
Historyof Mathematics, offers a large collection of
links to sites related to the history of mathematics.
The list of contents includes General Sites, Web
Resources, Biographies, Regional Mathematics, Museums
with Mathematics Exhibits, Special Exhibits, Books
On-Line, Student Presentations, Miscellaneous,
Bibliography, Societies, Journals, Philosophy of
Mathematics, History of Computing, Scholarly Articles
and Education. The collection is very good, and from
there one can probably eventually connect to a site
where information one seeks can be found.
The Mathematical Atlas: a Gateway to Modern
Mathematics
This site is organized according to the Mathematics
Subject Classification devised by the American
Mathematical Society and its German counterpart. A guide
to mathematics that explains the various divisions of
math and provides links to appropriate pages on the Web
site, providing information generally easy to understand
and a unique look at the entire field of mathematics.
S.O.S.
MATHematics
Offers straightforward technical assistance primarily to
high school and college students, although some of its
sections will be useful to both adult learners and
professionals. A healthy variety of subjects already
appear-from simple fractions and algebra to calculus,
different equations, and matrix algebra-with the promise
of more to come. The organization is by topic, with
numerous cross-links so that navigation is
straightforward.
Professor
Freedman's Math Help
Freedman provides materials to accompany a basic algebra
course. The site not only provides algebra problems and
instruction, but also offers encouragement and specific
suggestions for success to its audience, including
strategies for note taking and test preparation.
Although a few of the instructions are a bit cryptic, a
good number provide thorough, step-by-step guides
through algebra problems, in the students' own words,
which makes it a clear and easy-to-follow site.
Mathematical Functions
This site includes elementary and special functions that
are significant not only in mathematics but also in the
natural sciences, engineering, and other fields. This is
the largest compilation of mathematical functions on the
Web, and they are committed to maintaining and expanding
it over time. The developers have created a citation
format that will allow validity of a citation over time.
BioMed
Central
BioMed Central represents a new model for access to
published results of research projects. Encompassing
many medical subjects in about 50 journal titles, the
site invites researchers to publish results online and
have their full-text information linked to PubMed, the
National Library of Medicine's premiere database of
mechanical research. Registration is not required but
takes only a few moments.
Cancer Mortality Maps & Graph Link The Cancer Mortality Maps & Graph Web Site provides
interactive maps, graphs (which are accessible to the
blind and visually-impaired), text, tables and figures
showing geographic patterns and time trends of cancer
death rates for the time period 1950-1994 for more than
40 cancers.
Harvard World Health News
World Health News is an online news digest produced by
the Center for Health Communication at the Harvard
School of Public Health. Covering critical public health
issues, it is an excellent resource for readers who are
interested in public health and related issues. The site
uses a newspaper format with three columns with an
excellent selection of information.
HighWire Press
HighWire Press is the largest archive of free full-text
science on Earth and is a division of the Stanford
University Libraries. It hosts the largest repository of
high impact, peer-reviewed content, with 1067 journals and 4,439,098 full text
articles from over 130 scholarly publishers. HighWire-hosted
publishers have collectively made 1,791,613 articles
free. These articles cover areas in biological, medical,
physical and social sciences and humanities.
HIV InSite
HIV insite is the only source of information on the
Internet about HIV disease written and edited by
researchers from a leading health science institution.
This resource is a leading Web site, not only because of
its user-friendly design and the depth, scope, and
quality of content, but also because it effectively
links together existing HIV resources on the Web.
Recommended for all levels of the academic community.
Intute: Health & Life Sciences
This a Web site of a consortium led and hosted by the
University of Nottingham and other UK partners. It
offers free access to an extensive array of high-quality
Internet resources in life and health sciences. Intute
provides access to the very best web resources for
education and research, evaluated and selected by a
network of subject specialists. There are over 31,000
resource descriptions listed here that are freely
accessible for keyword searching or browsing. This site
was previously called BIOME.
Lumen: Structure of the Human Body
This Web site provides significant resources for human
anatomy students to review structural nomenclature and
relationships using multimedia visual aids. Effective
use of multimedia, frames, and links to supplementary
study aids makes this site a superior learning tool.
Upper-division undergraduates; graduate students in
medical and nursing curricula.
National
Women's Health Information Center This site is an outstanding resource for anyone
interested in women's health issues. Sponsored by the US
government, it targets many of the most popular health
concerns and issues facing women today and offers
up-to-date information. the home page highlights current
educational campaigns, providing links to the primary
Web sites representative of each topic. A particularly
valuable resource is the Women's Health Indicators
database. Overall, this well-designed, easy-to-navigate
site provides a plethora of information.
NewScientist.com: Special Reports on Key
Topics in Science and Technology This resource is a commercial Web site tied closely
to the well-established New Scientist magazine in
Britain. It has a long list of free science and
technology hot topic news and short articles from which
to learn. Many general areas are updated weekly and some
really hot topics are updated almost daily. Some of the
hot topics covered recently are: Clone Zone, GM Food,
Quantum World, Mobile Phones, Emerging Technologies, and
Climate Change. Overall, this resource definitely keeps
one posted on the latest important science and
technology news with briefs and articles that are a joy
to read.
Nutrition Source Nutrition Source Web site is maintained by the
Department of Nutrition at the Harvard School of Public
Health. The aim of the site is to provide timely
information on diet and nutrition for clinicians, allied
health professionals, and the public. The content covers
nutrition news and healthy eating advice with access to
the following topics: interpreting news about diet; fats
and cholesterol; carbohydrates; protein; fiber; fruit
and vegetables; calcium and milk; vitamins; healthy
weight; food pyramids; and other general sources of
reliable nutrition information from books, linkages to a
few Web sites, and nutrition-related projects. Much of
the nutrition information is related to relationships
between diet and chronic diseases such as cancer and
heart disease.
BioNetbook
BNB consists of some 4,500 databases cross-listed into
searchable combinations of categories in three headings:
database types, organisms, and domain of science-or by
specific words or country of origin. This is strictly a
high-level index, not a "Web-crawler". It is more
broadly based than sites linked to it and gathers
together access to a heterogeneous collection that should
prove convenient for scientists, researchers, teachers,
and students in all kinds of higher education
institutions.
DOEgenomes.org
This site is sponsored by the National Institutes of
Health and the US Department of Energy and is a
fantastic compilation of detailed information. The
attractive main page contains abundant white space and
simple graphics that load quickly. Organized under six
major sections- About Education, Research, Medicine,
Ethical, Legal and Social Issues and Media - the site
allows users to focus quickly on the type of material
wanted. Much research is written for those in the field,
while the Education page has links for both teachers and
students, in appropriate format and vocabulary.
Genetics
Education Center
Everything anyone ever wanted to know about genetics and
the Human Genome Project is included in this site. This
is a rich source for educators, students from the
secondary level to graduate programs, and the public
interested in seeking information on genetic conditions,
progress on the human genome project, and related
topics.
Kimball's
Biology Pages
Biology Pages is an online reference manual designed for
introductory biology students but for higher levels too.
It includes an alphabetical list of terms with brief
definitions or, in some cases, a link to a brief essay
on the subject. Most of the terms used are in the areas
of cellular and molecular biology. The definitions are
clearly written, and many provide simple graphics and
links to related topics. The Web site is easy to
navigate by clicking on the first letter of the term of
interest, then scrolling through the terms to find the
desired word. An excellent resource for biology
instructors and students.
Linus Pauling and the Race for DNA This site features a first-person history about
the race to solve the structure of DNA, primarily from
Pauling's perspective. The site is divided into three
sections: the first is a narrative about the work that
led to solving the structure of DNA; a second section
consists of digitized documents, along with audio, and
video clips relating to the DNA structure. The final
section provides a day-by-day summary of Pauling's
activities from 1952-1953. The site is easy to navigate,
with many links between pages. The documents and images
reproduced in the site are of very high quality and have
the look of the original. This very focused site will be
particularly useful to those wishing to know more about
the history of molecular biology. The ability to view
original documents opens the study of the history of
science to a much broader group of researches and
students.
Nature Online The Natural History Museum in London has built a
large virtual museum modeled after and supporting the
physical entity. The educational, entertainment, and
commercial aspects of a museum are represented
throughout the site. Each area has a short topic page
with a drop-down menu leading to more short pages and
videos. The Life page offers the most information,
including many streaming videos, with sets of links
about birds, reptiles, insects, other invertebrates,
dinosaurs, plants and fungi and human origins. Evolution
features page's about the work and time lines of Darwin,
Wallace, Owens, Huxley and Willberforce. The other
topics offer similar introductions. This site is well
worth exploring and using in this way.
Neurosciences
on the Internet
This Web site is clear, organized, informative, more
accessible and intelligent than most. An important
quality is that it is visually simple. The subject
matter is divided into such topics as neuroanatomy,
biochemistry, medicine, and cognitive neurosciences. The
site has been recently updated. Related sites of
interest are
Elsevier Science.
Online Mendelian Inheritance in Man
This is the authoritative reference for information on
the inheritance of human characteristics. Recommended
for Genetics students, professionals, biology teachers
and physicians.
The Tree of Life
One of the early Web projects on biodiversity and
phylogeny, The Tree of Life, has continued to
grow and change. It now includes over 4,000 Web pages
and 526 scientist contributors worldwide. Each page
within the tree presents information written by experts
on a group of organisms. Most also provide images and
extensive bibliographies. These pages are "linked one to
another hierarchically, in the form of the evolutionary
tree of life". Visitors may thus focus on a specific
group, or travel up or down the tree to follow "the
genetic connections between all living things".
AMG
allmusic
Now in its 10th year, this site has a new interface and
added content and features. The designer's commitment to
accuracy, currency and comprehensiveness continues
compensating for the site's unrelenting advertisements.
Contributors provide biographies, review, and essays on
popular music and with the latest revision, classical
music. Those wishing to access all features (e.g.
advanced searching, music samples) must register. A
basic search by name, album, song or classical work
appears on all pages, a clunky advanced search allows
specialized searches, including full text. Coverage is
impressive: 786, 000 albums (263,000 reviews), 6 million
samples, 265,000 classical compositions and 76,000
biographies. The site's strengths continue to be the
biographies, recording credits, and internal links to
performers and reviews. Samples are often available for
all of a recording's songs at 30 second per song and for
specific recordings or performers with three 10-second
samples of limited usefulness. Discographies are updated
quickly, sometimes just days after release.
Music, Theatre & Dance
This remarkable Web site consists of several databases
that enable users not only to access different kinds of
music, photographs, manuscripts, letters and other
documents, but to come as close as possible to
experiencing materials of the Library of Congress's
collections by exploring various kinds of digital media.
Special Presentations exemplifies a fascinating
coordination of texts, sound recordings, pictures,
catalogs, supporting documentation, and searching and
zooming capabilities. The Library of Congress plans to
include new presentations and to add or incorporate more
materials to some of the presentations already
available.
Mutopia
Collection of several hundred classical music scores
available in various text formats, some with MIDI audio
files. Browse by composer, instrument, or musical style,
or search by keywords.
Performing Arts in America, 1875-1923 Created and maintained by The New York Public
Library for Performing Arts , this site makes available
a sample of the library's extensive holdings in the
history of performing arts. Wishing to "offer a glimpse
inside" a society in which "entertainment for the masses
became a thriving industry", the library selected for
viewing and listening 16,000 primary documents and
original resources - a unique and valuable collection of
newspaper clippings, promotional and production
photographs, sheet music, publicity posters and lobby
cards, moving images, programs, and recorded sound. From
the straightforward home page, one can go to About the
Collection for a brief general overview and links to
overviews of dance, music and theater. The database is
rich with images, many with zoom and enlargement
capabilities.
Passion for Jazz Music and all art is an essential part of the
"human experience." Today, Jazz music is played, studied
and taught at private and public institutions around the
globe. Whether you are a musician, or just someone who
happens to like Jazz you may visit this site to see the
wealth of material it contains. Read about the history
of Jazz, its philosophy, interact with the virtual piano
chords, learn about improvisation, or visit the photo
gallery to see portraits of many great Jazz musicians.
Classical Composer Database
Offers basic biographical information about composers,
both well known and obscure, and links to information
about them on the Web. Includes chronologies and a
composer's calendar.
Classical Music Navigator Provides information on over 400 composers, with
works listed by musical genre, a geographical roster, an
index of forms and styles, and a glossary of musical
terms. | 677.169 | 1 |
Mathematics
MATHEMATICS DEPARTMENT
Integrated Math II (418)
Integrated math provides students with a spiral curriculum that encompasses algebra, geometry, probability,statisticsand data analysis each and every year over the course of three years. The program is meeting our goal of getting everyone to algebra 2 before they graduate.
MAT418 1.0 credit Prerequisite: See chart on pages 42-44
Geometry 404
This course is designed to incorporate basic Algebra skills into a geometric setting. Students will be required to use problem solving skills, oral and written communications, projects and structured activities to develop their reasoning and logic skills. Emphasis in this course will focus on transitioning from abstract thinking to specific applications through inductive and deductive reasoning. Students will extend their knowledge through a fundamental geometric theory system. Topics include triangles, parallel lines, coordinate geometry, quadrilaterals, right triangles, similar figures, volume and area.
MAT404 1.0 credit Prerequisite:See chart on pages 42-44
Honors Algebra II 406
Algebra II 407
This course will extend and develop concepts learned in Algebra I and Geometry as well as prepare students for the fundamentals needed in Pre-Calculus and Calculus. Students will develop their problem-solving skills and drawing connections to real-life situations to give Algebra greater meaning. Graphing calculators will be used extensively to aid in data analysis and investigating mathematical concepts. Topics include systems of linear equations and inequalities, quadratic functions, matrices and determinants, functions and relations, radicals, complex numbers, exponentials, polynomial and rational functions, trigonometric ratios, sigma notation, logarithms, probability and statistics.Honors Algebra II 406will receive honors credit.
MAT406 1.0 credit Prerequisite:See chart on pages 42-44
MAT407 1.0 credit
Pre-Calculus/Trigonometry Functions 415
This course is designed for students planning to go to college. The course will cover the topics of trigonometry and elementary functions, circular trigonometric functions and their graphs, sum and difference formulas and related reduction identities, trigonometric equations, inverses of trigonometric functions, trigonometric solutions of triangles and the Law of Sines and Cosines. The course will also explore functions and their graphs, logarithmic and exponential functions and their graphs. This course is designed to give a solid foundation in topics mentioned and will prepare the student for entry into Freshman College Calculus.
MAT415 1.0 creditPrerequisite:See chart on pages 42-44
Honors Pre-Calculus/Trigonometry Functions 409
This course is designed for accelerated college preparatory students planning to takeAP Calculus. It is intended to give a foundation in fundamental topics from trigonometry and elementary functions, circular trigonometric functions and their graphs, sums and differences formulas and related reduction identities, trigonometric equations, inverses of trigonometric functions, trigonometric solutions of triangles, complex numbers, and introductions to limits.This course will receive honors credit.
MAT409 1.0 credit Prerequisite:See chart on pages 42-44
Statistics and Trigonometry 410
This year-long course covers two distinct topics. One semester serves as an introduction to statistics. Topics covered include summarizing and presentation of numerical data, probability and their distributions, the normal distribution and linear regression. The other semester spotlights trigonometry. Some topics include a study of the six trigonometric functions and their graphs, Law of Sines, Law of Cosines, trigonometric identities and inverse trig functions.
MAT410 1.0 credit Prerequisite:See chart on pages 42-44
SATPrep Course 412
TheSATPrep Course, open to sophomores, juniors and seniors, is designed to help students improve theirSATscores by familiarizing students with various test taking strategies and test content. Ideally, students should register for this course prior to taking theSATfor the final time. Students will be able to identify their weaknesses by pre-testing and take a series of actualSATpractice tests. Students will also learn time-saving techniques and short-cuts to apply to theSATproblems. Students will complete a nine week session of Mathematics and a nine week session of Reading Comprehension/Essay writing to prepare them for the newSATexamination. This course is graded on a pass or fail basis.
MAT412 0.5 credit Prerequisite:Completed Grade 9
Statistics II 413
This semester course is designed as extensions of Statistics I. Topics include probability, distribution, Central Limit theorem, and inferential statistics.
MAT413 0.5 credit Prerequisite:See chart on pages 42-44
Pre-Calculus/Calculus 414
This course will explore functions and their graphs and exponential functions, logarithmic functions and their graphs. This course is for the college-bound student who has already taken Statistics and Trigonometry. Topics include analysis of graphs, limits of a function, and derivatives. A graphing calculator will be used consistently in this course.
MAT414 1.0 credit Prerequisite:See chart on pages 42-44
Calculus 416
This year-long course is designed for college-bound students and is intended to be rigorous and challenging. Topics include analysis of graphs, limits of functions, understanding the derivative graphically, numerically, analytically and verbally as a rate of change, the definite integral as a limit of Riemann sums, integrals, differential equations, and representations of differential equations with slope fields, and applications to modeling. A TI-89 graphing calculator will be used consistently.
MAT416 1.0 credit Prerequisite:See chart on pages 42-44
Financial Math 427
This practical mathematics course is designed to provide an understanding of typical mathematics calculations in the business world. Emphasis will be placed on the calculation process as well as the analysis of the calculation. In addition to the computation, students will utilize spreadsheet technology applicable to the various topics covered throughout the course.
MAT427 1.0 credit Prerequisite: See chart on pages 42-44
Building Mathematical Foundations I 285
A one semester mathematical foundations class will be required for all freshmen who scored Basic or Below Basic on the 8thgrade PSSA Assessment in math. The class will help to provide students with strong mathematical foundations. This course will include a semester of mathematical strategies and concepts presented through mini lessons and through a computerized mathematical program. The course will focus on strengthening students' skills needed to become more competent mathematicians.
MAT285 0.25credit Prerequisite: Score of Basic or Below Basic on the 8thgrade PSSA in math
Building Mathematical Foundations II 286
The Building Mathematical Foundations II course is a nine-week course that is required for all seniors who scored basic or below basic on the 11thgrade PSSA Assessment in math. The class will utilize both technology and teacher led instruction focusing on the Pennsylvania Academic Standards for Mathematics. Student progress will be tracked using a series of formative and summative assessments.
MAT286.25 creditPrerequisite:Score of Basic or Below Basic on 11thgrade PSSA in math
AP Statistics/Basic Applied Statistics (CHS) 905
This is an introductory college-level course in statistics and probability. The use of statistical methods in the modern world makes it imperative that students understand the fundamental ideas that underlie decisions that are reached by these methods. Probability will help students understand the kinds of regularity that occur amid mathematical models in the real world. Mathematical problems with computer solutions will be emphasized. This course is aimed at students who plan to enter such fields as economics, business, education, psychology, biology, medicine, mathematics, and engineering which now require statistics for their effective pursuit.(Fourcredits from the University of Pittsburgh can be earned when taken as a College in High School course).AP credit will be given.
MAT905 1.0 credit Prerequisite:See chart on pages 42-44
AP Calculus/Calculus with Analytic Geometry (CHS)906
This course is designed for accelerated students who plan to take the AP exam. It is intended to be rigorous and challenging. Topics included are analysis of graphs, limits of a function, understanding the derivative graphically, numerically, analytically, and verbally and as a rate of change, the definite integral as a limit of Riemann sums, integrals, differential equations, and representations of differentiated equations with slope fields, and applications and modeling. ATI-89graphing calculator will be consistently used in class.AP credit will be given.(Fourcredits from Seton Hill University can be earned when taken as a College in High School course).
MAT906 1.0 credit Prerequisite:See chart on pages 42-44
Calculus II/Calculus 2 with Analytic Geometry (CHS) 916
This course is designed for the serious Math student who has completed AP Calculus 906. It is taught as a second year college-level course focusing on all the topics of AP Calculus AB and beyond. Topics include: Logarithmic, Exponential and other Transcendental Functions; Differential Equations; Applications of Integration; Integration Techniques, L'Hopital's Rule, Improper Integrals; and Infinite Series. This course is an excellent option for students who plan to focus on mathematics and/or Engineering in college. Graphing calculator applications are included.AP credit given.(Fourcredits fromSetonHillUniversitycan be earned when taken as a College in High School course).
MAT916 1.0 credit Prerequisite:See chart on pages 42-44
CalculusIII/Calculus 3 with Analytic Geometry (CHS) 917
This course is designed for the serious math student who has completed AP Statistics 905, AP Calculus 906 and Honors Calculus II 916. It is taught as a third semester college-level course focusing on all the topics of AP Calculus AB and beyond. Topics include: Conics, Parametric Equations and Polar Coordinates, Vectors and the Geometry of Space, Vector-Valued Functions, Functions of Several Variables, Multiple Integration and Vector Analysis. This course is an excellent option for students who plan to focus on mathematics and/or engineering in college. Graphing calculator applications are included.AP credit given.(Fourcredits from Seton Hill University can be earned when taken as a College in High School course).This course is only offered online.
MAT917 1.0 credit Prerequisite: See chart on pages 42-44
Functional Math 9 (421), 10 (422), 11 (423), 12 (424)
These courses focus on providing students with a modified math curriculum to address the student's specific Individual Education Plan goals. These courses are designed to accommodate students who are working significantly below grade level who would not be successful meeting the course requirements of the general curriculum without extensive supports. The courses will address individual student needs to enhance math computations, problem solving, measurement, telling time and money concepts and will address math skills to build a solid foundation through extensive skills practice, real-life connections and functional daily living math skills. These courses are aligned to state standards. | 677.169 | 1 |
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Step 4: Solving a System of Linear Equations in three variables. calculator
what are the rules for adding, subtracting,multiplying and dividing in scientific notation?
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howis doing operation (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations fraction? can understandinghow to work with onekind of problem help unstand how to work another type? when might you use this skill in real life? | 677.169 | 1 |
I'm starting an undergrad. course in Mathematical Physics in September and I'm gonna want to study some extra maths in the mean time I think. I figure it might as well be something useful, so my question is basically whether or not studying the old Edexcel "pure" units would be useful/helpful come September?
I'm asking about the old pure units and not more mechanics/further pure units (I've only done M1 and FP1 at A-level o: ) or some such because these are the textbooks that I'll be able to keep. My school was getting rid of a load of old textbooks recently so I figured I might as well take a few off their hands, but I've only managed to get P1-5 so far. I'm hoping to get P6 and if I'm lucky I might be able to get some of the older application textbooks as well, but I really don't know.
So yeah, would studying this stuff be a good idea or is there something else that'd be more worthwhile?
Thanks
EDIT: I just realised it sounds like I've stolen the textbooks haha. I asked first!
(Original post by TenOfThem)
Depending on your board more FP might be good
AQA have downloadable FP2 and FP3 books on their website
Their FP3 is all about differential equations which may be of use
I'm not actually going to be taking any exams so the board only matters if the textbooks will assume I know stuff that I don't know e.g. if AQA FP2 assumes I know stuff from AQA FP1 that isn't in Edexcel FP1. I'll have a look on the website, thank you downloadable textbooks sound perfect haha!
But yeah, do you reckon more pure would be more useful than more mechanics then? | 677.169 | 1 |
Algebra at Cool math .com Hundreds of free Algebra 1, Algebra 2 and Precalcus Algebra lessons. Great to share with students and serve as extra information. Some contain some great animation related to the topics presented. Bored with Algebra? Confused by Algebra? Hate Algebra? We can fix that. Coolmath Algebra has hundreds of really easy to follow lessons and examples. Algebra 1, Algebra 2 and Precalculus Algebra. with system:unfiledby 2 users
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Math Foundation Math Foundation is an award-winning program which features interactive e-learning tools to help you master the concepts of mathematics quickly and easily. The courseware is highly effective for adult learners, homeschool and traditional students. with foundationhomelearningmathtutorial | 677.169 | 1 |
Friday, May 25, 2012
A Mathematical Orchard and the End of May Sale
A collection of 208 challenging, original problems with carefully worked solutions. In addition to problems from The Wohascum County Problem Book, there are about 80 new problems, many of which involve experimentation and pattern finding.
The problems are intended for undergraduates; although some knowledge of linear or abstract algebra is needed for a few of the problems, most require nothing beyond calculus. In fact, many of the problems should be accessible to high school students. On the other hand, some of the problems require considerable mathematical maturity, and most students will find few of the problems routine.
Over four-fifths of the book is devoted to presenting instructive, clear, and often elegant solutions. For many problems, multiple solutions are given. Appendices list the prerequisites for individual problems and arrange them by topic. This should be helpful to classes on problem solving and to individuals or teams preparing for contests such as the Putnam. The index can help, as well, in finding problems with a specific theme, or in recovering a half-remembered problem. | 677.169 | 1 |
Normal 0 false false false Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps students explore key concepts and push their understanding to new heig...
Normal 0 false false false For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet... | 677.169 | 1 |
Discovering Geometry Intro
Discovering Geometry began in my classroom over 35 years ago. During my first ten years of teaching I did not use a textbook, but created my own daily lesson plans and classroom management system. I believe students learn with greater depth of understanding when they are actively engaged in the process of discovering concepts and we should delay the introduction of proof in geometry until students are ready. Until Discovering Geometry, no textbook followed that philosophy.
I was also involved in a Research In Industry grant where I repeatedly heard that the skills valued in all working environments were the ability to express ideas verbally and in writing, and the ability to work as part of a team. I wanted my students to be engaged daily in doing mathematics and exchanging ideas in small cooperative groups.
The fourth edition of Discovering Geometry includes new hands-on techniques, curriculum research, and technologies that enhance my vision of the ideal geometry class. I send my heartfelt appreciation to the many teachers who contributed their feedback during classroom use. Their students and future students will help continue the evolution of Discovering Geometry. | 677.169 | 1 |
Calculus - an Introduction
By M. Bourne
Founders
of Calculus
Sir Isaac Newton
Gottfried
Leibniz
The volume of wine
barrels was one of the problems solved using the
techniques of calculus. See a solution at Volumes by Integration.
Calculus is concerned with comparing quantities which
vary in a non-linear way. It is used extensively in
science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit)
do not behave in a simple, linear fashion. If quantities are continually changing, we need calculus to study what is going on.
Calculus was developed independently by the Englishman, Sir
Isaac Newton, and by the German, Gottfried Leibniz. They were both working on problems of motion towards
the end of the 17th century. There was a bitter dispute between the men over who developed calculus first.
Because of this independent development, we have an unfortunate mix of notation and vocabulary that is used in calculus.
From Leibniz we get the dy/dx and ∫ signs.
The development of an accurate clock in the 17th century led to significant developments in science and mathematics, and amongst the greatest of these was the calculus.
For scientists, it was very important to be able to predict the
positions of the stars, to help in maritime navigation. The greatest challenge was to determine longitude when a ship was at sea.
Whichever nation could send ships to the New World and
successfully bring them back laden with goods, would become a
rich country.
Newton and Leibniz built on the algebraic and geometric work
of Rene Descartes, who developed the Cartesian co-ordinate system, which we met before.
There are two main branches of calculus.
The first is differentiation (or derivatives), which helps us to find a rate of change of one quantity compared to another.
The second is integration, which is the reverse of differentiation.
We may be given a rate of change and we need to work backwards to find the original relationship (or equation) between the two quantities.
Calculus in Action 1
Solar Two sustainable energy project in
California.
A power tower produces electricity from sunlight
by focusing thousands of sun-tracking mirrors, called
heliostats, on a single receiver sitting on top of a
tower. The receiver captures the thermal energy of the
sun and stores it in tanks of molten salt (to the right
of the tower) at temperatures greater than 500 degrees
centigrade.
When
electricity is needed, the energy in the molten salt is used
to create steam, which drives a conventional electricity-generating
turbine (to the left of the tower).
Calculus (in this case, differentiation) is used to maximise
the efficiency of the process.
Calculus in Action 2
Calculus is used to improve the efficiency of hard drives and other computer components.
Differentiation
The 3 sections on differentiation in Interactive Mathematics are as follows:
Differentiation, which introduces the concept of the derivative and gives examples of the basic techniques for differentiating. | 677.169 | 1 |
UA preparatory math goes virtual
Apr 26, 2011 By La Monica Everett-Haynes
Is this what flashes across your mental screen when you think about math? The UA's mathematics department is piloting a new course, Math 100, which is designed to help students who struggle with university-level math. The course provides personalized instruction with a heavy emphasis on tutoring, peer support and the use of technology.
The University of Arizona's math department is experimenting with a novel approach to early math instruction – one with a heavy emphasis on technology and peer-to-peer tutoring.
Arguably, few other required college-level courses elicit the same frustration or the intimidation factor as mathematics.
Some commonly talk about holding a hatred for math, believe they are no good at it or think up strategies to avoid it all together.
But one University of Arizona team is working to unravel the enigmatic nature of math for the very students who struggle the most with it – those who do not test into college-level math.
Math 100, now in the second semester of its pilot phase, has a heavy emphasis on both self-paced progress and peer-to-peer support while being offered through Elluminate, a web-conferencing system.
"Students are so used to being online. We thought that if we put the course online we could interact more," said Michelle Woodward, who coordinates the pilot course being offered by the UA mathematics department.
The number of section offerings will be expanded during the fall to accommodate more UA students who do not test into algebra-level mathematics.
Woodward said the course is being emphasized and expanded because it is especially important for new students to grasp college math, especially algebra – a curricular core – early.
Algebraic skills have long been associated with giving students the ability to think in more complex ways. A student's ability to comprehend algebra has long been upheld as an indication of college-readiness, particularly for study in science and engineering-related disciplines.
"It's the foundational material they need to be prepared for college algebra," Woodward said.
"My whole goal in this is to make an online environment that is as close to what students would do in person. I want the environment to be as interactive as possible," Woodward said, adding that another program, the ALEKS Learning Module, provides both structure and flexibility while also offering the course content.
"I have done a lot of work with students who needed individualized plans. ALEKS does that for me," she said. "I could not do that for 300 students, it doesn't replace me – it frees me up to work with students individually, the kind of work I didn't have time to do before."
Over the course of the semester, the 300 students currently enrolled in one dozen Math 100 sections meet three hours weekly, receiving self-paced instruction mediated by Elluminate. Students complete assignments, learning to master algebraic expressions and graphing techniques and, all the while, ALEKS tracks their progress.
"We are able to personalize the lessons much better than we have. It's been wonderful," said Cheryl Ekstrom, a mathematics lecturer who initiated the idea to incorporate Elluminate. "You aren't stuck listening to a lecture on things you already know or breezing by things you don't understand."
This is in direct contrast to more established and traditional ways of teaching math.
"In a traditional class, it doesn't matter if it's hard for you," said Shailendra Simkhada, an electrical engineering senior also studying math.
"Each day in a regular class, you might get a new chapter or deadline to meet but, here, they can work at their own pace," he said.
"It's not that they do less work, but if you don't understand something you get more information and one-on-one help so that they stay on track," he added.
If fact, students designate their goals at the start of the class, deciding what sections they want to master and what math class they hope to test into at the end of the term.
Students also engage in weekly virtual classroom meetings, sharing their computer screens and conversing online with student leads and support staff – UA students who are advanced in math and receive more than 15 hours of training.
Kirandeed Banga, a UA sophomore studying biology, is a member of the student lead and support staff.
Each week, Banga joins the other leads and support staff members in a classroom in the Math Building where they each log online to tutor and monitor student work.
"With it being completely online, it's hard to get their trust. But we try to talk to them as much as possible," said Banga who, like others on the team, also offer office hours.
"And we put them into virtual groups, so they are also able to help one another," she added. "They obviously are used to the technology, so they can adapt to it."
Also built into the design of the course is extensive support to the UA students facilitating the class.
Ivvette Rios, a UA math and French major, observes the virtual sessions and conducts weekly meetings with all of the students offering tutoring and support. Her role is to ensure that the leads and support staff have everything they need to appropriately help the hundreds of students enrolled.
Rios said the time for self-evaluation and self-reflection is critical for those involved, and helps to ensure that the structure is working well for all involved.
"We are always thinking of ways we can do this better; to make it more and more like our everyday experience," Rios said. "It's work out way better than we thought it would."
Leo Shmuylovich knows a lot about how tutoring can take a student from confused to confident. The Washington University graduate student has worked as a tutor for several test preparatory companies over the years, helping ...
(PhysOrg.com) -- New research from the University of Notre Dame suggests that even though adults tend to think in more advanced ways than children do, those advanced ways of thinking don't always override old, incorrect"Considering how many fools can calculate, it is surprising that it should be thought either a difficult or tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the text-books of advanced mathematics-and they are mostly clever fools-seldom take the trouble to show you how easy the calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way." Calculus Made Easy, Silvanus P. Thompson, Prologue, 1910 Diet | 677.169 | 1 |
Math Content Standard A: Content of Math
Key Element 2. Measurement
A student who meets the content standard should select
and use appropriate systems, units and tools of measurement,
including estimation.
Measurement For All
Students make measurement decision such as which units
are most appropriate for the context, what degree of accuracy
should be measured, and how much confidence can be put
into interpretations about variations of measurement.
The same measurement concepts that are learned as primary
students apply throughout our mathematical education in
high school, college, and the work place.
Measurement extends beyond length, area, volume, temperature,
and weights as attributes of objects. It includes brightness,
relations, pulse, speed, radioactivity, sound, pressure
and many other attributes. It can be expressed as a direct
physical measurement or as a rate. Technology (probe-ware
and computer based labs) helps extend the concepts of
measurement to complex interactions and abstract measurements,
all requiring an understanding of measurement concepts
above and beyond the old-fashioned skills of using non-technical
measuring tools. | 677.169 | 1 |
Griffin, GA CalRadicals Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals. Polynomials We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials | 677.169 | 1 |
Sharp3D.Math contains fundemental classes to dealing with numerics on the .NET platform. It contains various mathematical structures such as vectors, matrices, complex numbers and contains methods for numerical integration, random numbers generation and other object-oriented n... | 677.169 | 1 |
Mathematics - Algebra (356 results)
Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college. Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinar processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers. The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value. Webster Wells. Boston, 1886.
In the selection of materials, those articles liave been taken which have a practical application, and which are preparatory to succeeding parts of the mathematics, philosophy, and astronomy. Tlie object has not been to introduce original matler. In the mathematics, which have been cultivated with success from the days of Pythagoras, and in which the principles already established are sufficient to occupy the most active mind for years, the parts to which the student ought first to attend, are not those recently discovered. Free use has been made of the works of Newton, Maclaurin, Saunderspn, Simpson, Euler, Emerson, Lacroix, and others, but in a way that rendered it inconvenient to refer to them, in particular instances. The proper field for the display of mathematical genius is in the region of invention. But what is requisite for an elementary work, is to collect, arrange and illustrate, materials already provided. However humble this employment, he ought patiently to submit to it, whose object is to instruct, not those who have made considerable progress in the mathematics, but those who are just commencing the study. Original discoveries are not for the benefit of beginners though they may be of great importance to the advancement of science. The arrangement of the parts is such, that the explanation of one is not made to depend on another which is to follow. The addition, multiplication, and division of powers for instance, is placed after involution. In the statement of general rules, if they are reduced to a small number, their applications to particular cases may not, always, be readily understood. On the other hand, if they are very numerous, they become tedious and burdensome to the memory. The rules given in this introduction, are most of them comprehensive; but they are explained and applied, in subordinate articles. A particular demonstration is sometimes substituted for a general one, Avhen the application of the principle to other cases is obvious. The examples are not often taken fi om philosophical subjects, as the learner is supposed to be familiar with none of the sciences except arithmetic. In treating of negative quantities, frequent references are made to mercantile concerns, to debt, and credit, c.These are merely for the purpose of illustration.
This text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics Avhich the engineer must emphasize, such as numerical com)utations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid. The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject. The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytical geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of eii ort. The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest.
They feel themselves continually handicapped by this ignorance. Their critical faculty is eager to submit, alike old established beliefs and revolutionary doctrines, to the test of science. But they lack the necessary knowledge. Equally serious is the fact that another generation is at this moment growing up to a similar ignorance. The child, between the ages of six and twelve, lives in a wonderland of discovery; he is for ever asking questions, seeking explanations of natural phenomena. It is because many parents have resorted to sentimental evasion in their replies to these questionings, and because children are often allowed either to blunder on natural truths for themselves or to remain unenlightened, that there exists the body of men and women already described. On all sides intelligent people are demanding something more concrete than theory; on all sides they are turning to science for proof and guidance. To meet this double need the need of the man who would teach himself the elements of science, and the need of the child who shows himself every day eager to have them taught him is the aim of the Thresholds of Science series. This series consists of short, simply written monographs by competent authorities, dealing with every branch of science mathematics, zoology, chemistry and the like. They are well illustrated, and issued at the cheapest possible price.
Advantage has been taken of the issue of a new edition of the Intermediate Algebra to revise the text and to make a number of changes., To meet the wishes of teachers who have used, or propose to use, the book in the advanced classes of the secondary schools, additions have been made in order that the prescribed courses may be formally covered. To the chapter on equations there have been added exercises bearing on or developing further the theory. A chapter on Scales of Notation has been introduced. The note on Annuities, incidental to the Geometrical Progression, has been expanded to constitute a chapter in which are considered the simpler problems of finance related to annuities, and the use of the fundamental tables of Interest and Annuities provided for and explained. The Miscellaneous Examples that were given in the earlier edition have been retained in the hope that the more adventurous students, in particular candidates for Honours at Matriculation, may find in them a help and a stimulus. The chapter on Exponential and Logarithmic Series has been enlarged in order to give prominence to the concrete problem of the construction of tables of logarithmics, it being felt that in this way the significance of the theory is best brought out. Alfred T.DeLURY. Toronto, July 15,
In preparing this second edition the earlier portions of the book have been partly re-written, while the chapters on recent mathematics are greatly enlarged and almost wholly new. The desirability of having a reliable one-volume history for the use of readers who cannot devote themselves to an intensive study of the history of mathematics is generally recognized. On the other hand, it is a difficult task to give an adequate bird s-eye-view of the development of mathematics from its earliest beginnings to the present time. In compiling this history the endeavor has been to use only the most reliable sources. Nevertheless, in covering such a wide territory, mistakes are sure to have crept in. References to the sources used in the revision are given as fully as the limitations of space would permit. These references will assist the reader in following into greater detail the history of any special subject. Frequent use without acknowledgment has been made of the following publications: Annuario Biografico del Circolo MaknuUico di Palermo 1914; Jakrhuch uber die Fortschritte der Mathematiky Berlin;. C.Poggendorffs Biographisch-Literarisckes Handworterbuch, Leipzig; Gedenkkigebuch fur McUhenuUikeTf von Felix Miiller, 3. Aufl., Leipzig und Berlin, i()i 2 Revue SemestrieUe des Publications MathinuUigues, Amsterdam. The author is indebted to Miss Falka M.Gibson of Oakland, Cal. for assistance in the reading of the proofs. Floman Cajori. University of California March, 1919.
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as wellinformed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large safety factor of deud wood in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing. The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
El Preface This book is the result of twenty years of patient experiment in actual teaching. It is intended to be completed in the first year of the high school. It presents algebraic equations primarily as a device for the solution of problems stated in words, and gives a complete treatment of numerical equations such as are usually included in high-school algebra one-letter and two-letter equations, integral and fractional, including one-letter quadratics and the linear-quadratic pair. So much of algebraic manipulation is included as is necessary for the treatment of these equations. The arithmetic in the book is presented from a new point of view that of approximate computation and is utilized in the evaluation of formulas and in the solution of equations throughout the succeeding pages. Geometrical facts are introduced as the basis of many algebraic and arithmetic problems, and wherever they are not intuitively accepted by the pupils they are accompanied by adequate logical demonstration. Proofs, and parts of proofs, are avoided when they seem to the pupils of an unnecessary and hair-splitting kind. Ah problems are carefully graded, for it is by means of problems that each successive algebraic difficulty is introduced. A great deal of pains has been taken to present new topics clearly and concretely, often dividing them into sub-topics each of which is separately illustrated and apphed to practice. Definitions are generally prepared for by such advance work as will cause the student to feel the need of them; and where no need exists, they are omittedIx this text the authors have endeavored to present a course in algebra for the first year of high school which shall be simple, comprehensible to the students, and of high educational and mathematical value. They have made the solution of equations and problems the core of the course; they have emphasized the essentials, avoiding little-used complexities of algebra; they have taught new ideas inductively; they have emphasized thoughtful rather than mechanical solutions of exercises; they have tried to make the course maintain and increase the students efficiency in arithmetic; they have tried to make the course interesting by including varied problem material and historical notes, and valuable by including practical applications. The essential features of the course have been tried out in the classroom by many teachers. The text contains sufficient material to meet the needs of schools whose pupils have studied algebra before entering the high school; the topics have been arranged, however, so that a class may easily cover the essentials of the course in one school year. Attention is directed to the following devices that have been employed to attain the desired ends: Each topic that is taken up is used in the solution of equations. (See 9, 10, 12, 41, 51, 60, 107, etc.) This makes the study of the various topics purposeful, allows for good gradation in the book as a whole, and emphasizes the equation. Problems are introduced at short intervals. Informational, geometric, and physics problems in reasonable number are used. New types of problems are introduced gradually, appearing first in classified lists, are taught with extreme care, and are used thereafter in miscellaneous lists. Experimental verification is suggested for some of the facts from geometry and physics that are used. (See Exercises 7, 25, 28, 29, 38, 39, 49, 106; 13, 142, 143, 190, etc.
The main object in preparing this new Algebra has been to simplify principles and give them interest, by showmg niunbers. Each successive process is taken up for the sake of the economy or new power which it gives as compared with previous processes. This treatment should not only make each principle clearer to the pupil, but should give increased unity to the subject as a whole. We believe also that this treatment of algebra is better adapted to the practical American spirit, and gives the study of the subject a larger educational value. Among the special features of this Introductory Algebra, the following may be mentioned: A large nmnber of written problems are given in the early part of the book, and these are grouped in types which correspond in a measure to the groups used in treating original exercises in the authors Geometry. Many informational facts are used in the written problems. The central and permanent numerical facts in various departments of knowledge have been collected and tabulated on pages280-286 for use in niaking problems.
Thi 8 work was commenced sixteen years ago at the earnest solicitation of numerous teachers, who were dissatisfied with the textbooks then in use. That they were not alone in their opinion is evidenced by the number of new treatises, or revisions of old ones, printed since that time, and now used in the schools of this country. The crudeness of even the best Algebras of a quarter-century ago was mainly owing to the fact that, as a rule, mathematicians neglected the elementary branches for the more attractive fields of Higher and Applied Mathematics; hence blunders and inconsistencies were allowed which otherwise would not have been tolerated. The wonderful progress made in the Natural Sciences, and the extended use of Algebra in the treatment of Geometrical Magnitudes, have finally called the attention of educators to the necessity of improving the elementary treatises, and more rigidly limiting the meaning of the signs. That this agitation comes none too soon is evident to every thoughtful teacher, and can be readily seen by auy one who compares the various text-books used in our schools. Note the following inconsistencies: In some text-books now before me, 6 : 7 equals f;in others, 6 : 7 equals. In some, 6 -f 4 X 2 = 20;in others, 6 -- 4 X 2 = 14.Of course, the meaning and use of a sign depend upon agi eement, but it is of extreme importance that we do agree in such matters. In the same work, too, statements incompatible with each other are made; thus, a -i-bc and a -i-b Xc are said to have different values, and yet be and bXc are, in all woi ks, said to have one and the same meaning. Since a-h be and a -ib Xe differ only in She use of bXc for be, it is plainly necessary that one or the other of these two statements be changed. One of the objects in writing this book is to urge the adoption of the following law for Numerical Values; viz.,(l) Find the value of each term separately; thus, 6-f-4X 2 = 6 -f8= 14. (2)In finding the m, lue of a term, begin at the Right and use the signs in their oi der; thus, 6-f-4x 2 = 6-r-8= f.In other words, the jm tion of the term to the left of the division sign is the Dividend, and the part to the right is the divisor.
The main object in preparing this new Algebra has been to simplify principles This treatment should not only make each principle dearer to the pupil, but should give increased unity to the subject as a whole. We beheve also that this treatment of algebra is better adapted to the practical American spirit, and gives the study of the subject a larger educational value. Among the special features of this Introductory Algebra, the following may be mentioned: A large nimiber of written problems are given in the early part of the book, and these are grouped in types which correspond in a measure to the groups used in treating original exercises in the authors Geometry. Many informational facts are used in the written problems. The central and permanent niunerical facts in various departments of knowledge have been collected and tabulated on pages280-286 for use in making problems.
There are two classes of men who might be benefited by a work of this kind, viz., teachers of the elements, who have hitherto confined their pupils to the working of rules, without demonstration, and students, who, having acquired some knowledge under this system, find their further progress checked by the insufficiency of their previous methods and attainments. To such it must be an irksome task to recommence their studies entirely; I have therefore placed before them, by itself, the part which has been omitted in their mathematical education, presuming throughout in my reader such a knowledge of the rules of algebra, and the theorems of Euclid, as is usually obtained in schools. It is needless to say that those who have the advantage of University education will not find more in this treatise than a little thought would enable them to collect from the best works now in use 1831, both at Cambridge and Oxford. Nordo I pretend to settle the many disputed points on which I have necessarily been obliged to treat. The perusal of the opinions of an individual, offered simply as such, may excite many to become inquirers, who would otherwise have been workers of rules and followers of dogmas. They may not ultimately coincide in the views promulgated by the work which first drew their attention, but the benefit which they will derive from it is not the less on that account. I am not.
The present volume contains a Second Course in Algebra adapted to the latter part of the high school curriculum. It covers the topics usually included in Interme Idiate and Advanced Algebra in secondary schools. Hence pupils who have completed it will be prepared in algebra vfor scientific and engineering schools as well as for the rx ordinary academic college. The methods which are characteristic of the authors Algebra, Book One are here continued and developed. The chief aim is to simplify principles and give them interest, by showing more plainly, if possible, than has been done heretofore, the practical or common-sense reason for each step or process. Each new process, for instance, is introduced by what may be termed the efficiency-inductive method. In the Exercises also there are special examples which cause the pupil to realize the efficiency meaning of processes from various points of view. As in the authors other mathematical texts, pivotal and permanently valuable number facts and laws from other branches of study are introduced in various ways. This gives a correlation of algebra with geography, history, and other subjects. A further correlation with physics and engineering is obtained by the use of some of the most important formulas in these branches, and also by familiarizing the pupil with their fundamental concepts and number facts.
The present book is an enlargement of the authors Elements of Algebra. To the end of Chapter XXVIII. it is identical with the latter and the School Algebra. Some revision of the later chapters in the Elements has been incorporated in this book, and a number of new chapters have been added. The scope of the books, amply justified by their successful use in high and normal schools and colleges, is stated in the preface to the Elements: The aim has been to make the transition from ordinary Arithmetic to Algebra natural and easy. Ko efforts.have been spared to present the subject in a simple and clear manner. Yet nothing has been slighted or evaded, and all difficulties have been honestly faced and explained. New terms and ideas have been introduced only when the development of the subject made them necessary. Special attention has been paid to making clear the reason for every step taken. Each principle is first illustrated by particular examples, thus preparing the mind of the student to grasp the meaning of a formal statement of the principle and its proof. Directions for performing the different operations are, as a rule, given after these operations have been illustrated by particular examples. The importance of mental discipline to every student of mathematics has also been fully recognized.
Colleges and Scientific Schools. The first part is simply a review of the principles of Algebra preceding Quadratic Equations, with just enough examples to illustrate and enforce these principles. By this brief treatment of the first chapters, sufficient space is allowed, without making the book cumbersome, for a full discussion of Quadratic Equations, The Binomial Theorem, Choice, Chance, Series, Determinants, and The General Properties of Equations. Every effort has been made to present in the clearest light each subject discussed, and to give in matter and methods the best training in algebraic analysis at present attainable. The work is designed for a full-year course. Sections and problems marked with a star can be omitted, if necessary; and for a half-year course many chapters must be omitted. The author gratefully acknowledges his obligation to Mr. G.W. Sawin of Harvard College, who has contributed the excellent chapter on Determinants, and been of invaluable assistance in revising every chapter of the book. Answers to the problems are bound separately in paper covers, and will be furnished free to pupils when teachers apply to the publishers for them. Any corrections or suggestions relating to the work will be thankfully received. G.A. Wentworth. Phillips Exeter Academy, September, 1888.
The present volume contains a second course in algebra adapted to the latter part of the High School curriculum. The book is divided into two parts, Part One being meant for use in such classes as give only a half year to the second course in algebra, while the entire volume is to be used by classes giving a whole year to the second course. In half-year classes, Part Two will constitute a reservoir of extra work for bright pupils. The features which characterize the authors First Book in Algebra are continued and dievelopediuible numbers, facts and laws from other branches of study are introduced in various ways. This gives a correlation of algebra with geography, history, economics, and other school studies.
The present volume contains a First Course in Algebra adapted to the early part of the high school curriculum. The main purpose in writing the book has been to simplify prinr Among the special features of this Algebra, the following may be mentioned: A large number of written problems are given in the ben collected and tabulated on pages387-390 for use in making problems. Similariy the most important formulas in arithmetic, geometry, physics, and engineering have been tabulated for use by teacher and pupil (pp. 385, 386).
TlHE following manual was prepared for the use- of the students of Columbia College, and in its original form it has been employed as a text-book, not only in that institution, but in various Colleges, Academies, High Schools, and other institutions of learning. The flattering manner in which it has been received by our most successful teachers of Mathematics, has induced the Author to publish it in its present revised form. In preparing it anew for the press, such alterations and improvements have been made as have been suggested by the authors practical experience in its use as a college text-book. The opening chapters have been somewhat simplified, the chapter on logarithms has been extended, a section on inequalities has been added, and the whole has been carefully corrected and revised.
As regards the method of teaching algebra, I would make it, in the earlier stages, as much a generalized arithmetic as possible. Results obtained by algebra would be verified by arithmetical instances; and the use of a formula would be indicated as including any number of instances. Elaborate (and to my mind wearisome) processes, useful for solving artificial combinations of difiiculties, would be at least deferred. With a comparative beginner, progress towards new ideas or new stages of old ideas can, I think, best be made by the simplest instances, and it is on this account that I would build algebra entirely on arithmetical foundations so far as concerns the teaching of beginners. Professor Forsyth, M.A,, D, Sc,, F.Rs., Cambridge. It is assumed that pupils will be required throughout the course to solve numerous problems which involve putting questions into equations. Some oJE these problems should be chosen from mensuration, from physics, and from commercial life. The use of graphical methods and illustrations, particularly in connection with the solution of equations, is also expected. Extract from the Report of the American Mathematical Society,
The present volume contains a First Course in Algebra adapted to the early part of the high school curriculum. The main purpose in writing the book has been to simplify pririr jwwer which it gives as compared with previous processes. Among the special features of this Algebra, the following may be mentioned: A large number of written problems are given in tjije been collected and tabulated on pages387-390 for use in making problems. Similarly the most important formulas in arithmetic, geometry, physics, and engineering have been tabulated for use by teacher and pupil (pp. 385, 386).
The aim of this little book is to provide an introductory course as a foundation to elementary algebra. A minimum number of definitions, an early introduction of the literal symbol in its simplest form, a clear conception of the opposition of positive and negative quantity, and a gradual introduction to the early processes are believed to be the first essentials to successful later work. New elements are introduced as the result of some natural process, the exponent, for example, not being mentioned or used until, in multiplication, the pupil meets the operation that produces it. Certain important topics are given a more extended treatment than is customary in most books prepared for beginners. The application of the equation to the problem is made in a form that experience has shown to give excellent results, and the reasoning powers developed by the limited classifications have been equal to the demands of the general problem. Substitution has a much more important position than is usual in elementary teaching, and its constant applications are designed to meet an actual need felt by teachers in higher grades of work.
The present volume contains a second course in algebra adapted to the latter part of the High School curriculum. Many schools give only one half year to the study of the second course in algebra,, and it is the object of this book to supply material adapted to the needs of such schools. In different parts of the country, tentative syllabi have recently. been worked out for such a briefer study, and these syllabi have been carefully considered by the authors in writing the present volume. The features which characterize the authors First Book in Algebra are continued and developediLable number facts, and laws from other branches of study are introduced in various ways. | 677.169 | 1 |
Try to complete this by our next meeting. You do NOT need to memorize the material. Just take
in what you can.
1 - Read and complete pages 24 - 35 of the REA College Algebra. Take notes as you work on the sample problems. If you need
help use the EZ-101 study keys book. Remember, this is college material and we have plenty of time.
Do not worry if you do not understand it all. We will review the problems
at the next class.
At our next meeting we will:
-review the problems from the first two weeks assignments
-will answer your own questions
-will view some of the video tapes
Email me with any final questions you may have about the material
or the exam and we'll find the answers together!
Please feel free to make a donation towards our effort of providing you with a well thought
out lesson plan for passing the CLEP. Please use the link above to spread the word about this site. Thank
you! | 677.169 | 1 |
new. We distribute directly for the publisher. Just published, an Expanded Edition of a popular
[...]
Brand new. We distribute directly for the publisher. Just published, an Expanded Edition of a popular book. Ideal for a broad spectrum of audiences, including students in math history courses at the late high school or early college level, pre-service or in-service teachers, and casual readers who just want to know a little more about the origins of mathematics. Can be used a History of Mathematics text, as a Liberal Arts Mathematics Text, or as part of the preparation of future mathematics teachers. Where did math come from? Who thought up all those algebra symbols, and why? What's the story behind? Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today | 677.169 | 1 |
Short details of Horizontal Tank Add-on for MathU Pro: Given the diameter, and length of the horizontal cylindrical tank, calculate the volume of the tank for a given depth of liquid = x.. Creative Creek: Calculators, Software and Consulting for Palm OS, Windows Mobile and MATLAB. Calculators, Software and consulting for Palm OS, iPhone, Windows...
Calendar functions for MathU Pro similar to those available on an HP-12C and similar calculators.. Creative Creek: Calculators, Software and Consulting for Palm OS, Windows Mobile and MATLAB. Calculators, Software and consulting for Palm OS, iPhone, Windows Mobile, and MATLAB. Makers of professional calculators for Palm OS, iPhone and Windows Mobile. Our Palm OS, iPhone and Windows Mobile calculators turn your PDA into a advanced scientific,...Program to allow calculation of predictive values and post-test probabilities given input in one of three methods: 1. Data from study (true positive, false positive, true negative, false negative) 2. Sensitivity, Specificity, Pre-test probability 3. Likelihood ratios, Pre-test probability Includes an RTF file that explains Bayesian analysis along with the formulas used, reference to an online calculator as well as instructions for the...
Provides conversions/calculations (add, subtract, multiply and divide) with decimals of a foot to feet, inches, sixteenths and visa versa. Also includes a RISE, RUN, SLOPE, PITCH program to calculate the three sides of a triangle (in Ft.In16 format) and the angle of slope (degrees or Ft.In16 on 12" pitch) with input of any two items. Includes comprehensive PDF-based documentation.. Creative Creek: Calculators, Software and Consulting for...
Provides conversions/calculations (add, subtract, multiply and divide) with decimals of a foot to feet, inches, sixteenths and visa versa. Also includes an "area" program to calculate the "area of squares/rectangles" in Ft.In format input or in Dc.Ft format input. It will calculate the area of ONE square/rectangle OR run an accumulative total of areas of squares/rectangles (add or subtract feature included here). Includes | 677.169 | 1 |
Mathematics and Statistics Courses
Mathematics and statistics courses are designed (1) to provide mathematics courses
in the core curriculum of undergraduate study, (2) to serve the requirements of undergraduate
students pursuing a curriculum in business, education, engineering, etc. (3) to provide
undergraduate students majoring in mathematics or statistics a thorough preparation
for graduate mathematics or employment in industry or education, (4) to provide M.S.
or Ph.D. students mathematics or statistics courses needed for their respective majoring
field.
Courses are numbered as follows:
100 level -- freshmen,
200 level -- sophomores,
300 level -- juniors,
400 level -- seniors, and
500 & 600 levels -- graduate students.
Certain 300-, 400- level courses may be taken by graduate students for graduate credit, in such cases,
graduate students complete additional research assignments to bring the courses up
to graduate level rigor. | 677.169 | 1 |
With over a million users around the world, the Mathematica software system created by Stephen Wolfram has defined the direction of technical computing for the past decade. The enhanced text and hypertext processing and state-of-the-art numerical computation features ensure that Mathematica 4 takes scientific computing into the next century. New to this version: visual tour of key features, practical tutorial introduction, full descriptions of 1100 built-in functions, a thousand illustrative examples, easy-to-follow descriptive tables, essays highlighting key concepts, examples of data import and export, award-winning gallery of Mathematica graphics, gallery of mathematical typesetting, dictionary of 700 special characters, a complete guide to the MathLink API, notes on internal implementation, and an index with over 10,000 entries copublished with Wolfram Media. [via]
This book covers the use of Mathematica as programming language. Various programming paradigms are explained in a uniform manner, with fully worked out examples that are useful tools in their own right. The floppy disk contains numerous Mathematica notebooks and packages, valuable tools for applying each of the methods discussed. [via]
Physics and computer science genius Stephen Wolfram, whose Mathematica computer language launched a multimillion-dollar company, now sets his sights on a more daunting goal: understanding the universe. A New Kind of Science is a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modelling complex systems.
On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple non-mathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day.
Wolfram wrote the book in a distinct style meant to make it easy to read, even for non-techies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton[via] | 677.169 | 1 |
Intended Outcomes for the course
1. Use quadratic, rational and radical models in academic and nnon-academic environments.
2. Recognize connections between graphical and algebraic representations in academic and non-academic settings.
3. Interpret graphs in academic and non-academic contexts.
4. Be prepared in future coursework that requires the use of algebraic concepts and an understanding of functions.
Outcome Assessment Strategies
Assessment shall include:
The following topics must be assessed in a closed-book, no-note, no-calculator setting:
a.finding the equation of the linear function given two ordered pairs stated using function notation
b.solving rational equations
c.solving radical equations
d.determining the domain of rational and radical functions
e.evaluating algebraic expressions that include function notation
At least two proctored closed-book, no-note examinations, one of which is the comprehensive final. These exams must consist primarily of free response questions although a limited number of multiple choice and/or fill in the blank questions may be used where appropriate.
Assessment must include evaluation of the student's ability to arrive at correct and appropriate conclusions using proper mathematical procedures and proper mathematical notation. Additionally, each student must be assessed on their ability to use appropriate organizational strategies and their ability to write conclusions appropriate to the problem.
2.1.3.Represent the domain in both interval and set notation, where appropriate
2.1.4.Apply unions and intersections ("and" and "or") when finding and stating the domain of functions
2.1.5.Understand how the context of a function used as a model can limit the domain
2.2. Range
2.2.1.Understand the definition of range (set of all possible outputs)
2.2.2.Determine the range of functions represented graphically, numerically and verbally
2.2.3.Represent the range in interval and set notation, where appropriate
2.3. Function notation
2.3.1.Evaluate functions with given inputs using function notation where functions are represented graphically, algebraically, numerically and verbally (e.g. evaluate )
2.3.2.Interpret in the appropriate context e.g. interpret where models a real-world function
2.3.3.Solve function equations where functions are represented graphically, algebraically, numerically and verbally (i.e. solve for and solve for where and gshould include but not be limited to linear functions, rational functions, radical functions and quadratic functions)
2.3.4.Solve function inequalities algebraically (i.e. , , and where and are linear functions and and where is an absolute value function)
2.3.5.Solve function inequalities graphically (i.e. , , and where and should include but not be limited to linear functions, and for quadratic and absolute value functions)
2.4. Graphs of functions
2.4.1.Use the language of graphs and understand how to present answers to questions based on the graph (i.e. read the value of an intersection to solve an equation and understand that is a number not a point)
2.4.2.Determine function values, solve equations and inequalities, and find domain and range given a graph
3.Rational Functions (continued from MTH 91)
3.1. Solve rational equations
3.1.1.Check solutions algebraically
3.2. Solve literal rational equations for a specified variable
3.2.1.Introduce variables with subscripts
3.3. Applications
3.3.1.Solve distance, rate and time problems involving rational terms using well defined variables and stating conclusions in complete sentences including appropriate units
3.3.2.Solve problems involving work rates using well defined variables and stating conclusions in complete sentences including appropriate units
4.Quadratics
4.1.Recognize a quadratic equation given in standard form, vertex form and factored form
4.2. Solve quadratic equations by completing the square
4.3.Find complex solutions to quadratic equations by the quadratic formula or by completing the square
4.3.1.Understand the graphical implications (i.e. when there is a complex number as a solution to a quadratic equation)
4.3.2.Interpret the meaning in the context of an application
4.4. Quadratic functions in vertex form
4.4.1.Graph a parabola after obtaining the vertex form of the equation by completing the square
4.4.2.Given a quadratic function in vertex form or as a graph, observe the vertical shift and horizontal shift of the graph
5.8.2.Understand that extraneous solutions found algebraically do not appear as solutions on the graph
5.8.3.Solve literal radical equations for a specified variable
5.10.Calculator
5.10.1. Approximate radicals as powers with rational exponents
5.10.2. Find the domain and range of radical functions
5.10.3. Solve radical equations graphically
5.10.4. Use graphical solutions to check the validity of algebraic solutions
Addendum
·Functions should be studied symbolically, graphically, numerically and verbally.
·As much as possible, instructors should present functions that model real-world problems and relationships to address the content outlined on this CCOG.
·Function notation is emphasized and should be used whenever it is appropriate in the course.
·Students should be required to use proper mathematical language and notation. This includes using equal signs appropriately, labeling and scaling the axes of graphs appropriately, using correct units throughout the problem solving process, conveying answers in complete sentences when appropriate, and in general, using the required symbols correctly.
·Students should understand the fundamental differences between expressions and equations including their definitions and proper notations.
·All mathematical work should be organized so that it is clear and obvious what techniques the student employed to find his answer. Showing scratch work in the middle of a problem is not acceptable.
·Since technology is used throughout the course, there is a required calculator packet for students that gives directions for several graphing calculators. The students should understand the limitations of calculator—i.e. when the calculator gives misleading information. Examples of the calculator's limitations include the following: when finding horizontal intercepts, the calculator sometimes gives something like y = 3E-13; the calculator rounds to 12 or fewer decimal places; some calculators appear to show vertical asymptotes on the graphs of rational functions; it appears that the graph of touches the x axis; the calculator does not show holes on rational function graphs; the calculator cannot handle very large numbers, e.g. etc.
·Exploration of difficult rational exponents, as in 4.5, should be limited. Basic understanding is essential and a deep understanding takes more than one course to develop. Examples should be limited to one or two variables, keeping things as simple as possible while covering all possibilities. E.g. , , , .
·As much as possible, instructors should present functions that model real-world problems and relationships to address the content outlined on this CCOG.
·In 3.3.1, when solving applications of quadratic equations, a complex solution should be interpreted as the graph never reaching a particular real world y-value. | 677.169 | 1 |
WEEK OF MAY 20th
Created on Saturday, 18 May 2013 10:33
Written by Joe Chamberlin
ONLY THREE MORE WEEKS TO GO! This week we cover the highlights of Chapters 9 and 10. MONDAY: Shapes and Formulas of conics, including circles, ellipses, and hyperbolas. We will also start our next project... cutting shapes with stained glass. TUESDAY: We go 3-D again, with cones and spheres, along with distances and midpoints in x-y-z space. Watch out for a quiz sometime! WEDNESDAY: Polar coordinates (another way to locate a point) and polar equations, along with some honors level engineering math. And we will try to finish up our projects. THURSDAY: Multi-chapter review, and TEST.
The following WEEK OF MAY 27: We will just do Chapter 11, more thoroughly, because it contains the two basic ideas of calculus. And we will have gone thru the major ideas of the book. So the final week will be preparing for the class final!
WEEK OF MAY 13
Created on Friday, 10 May 2013 12:48
Written by Joe Chamberlin
Six chapters down, six more to go! Again, we are just skimming the highlights of functions, reviewing your algebra and introducing some new formulas and notations.
MONDAY: In the AM, a little Ch.6 review on vectors, and then a Ch. 4-6 REVIEW TEST. For the PM, Chapter 7.1 and 7.2 on solving systems, and a brief look at how matrices do it. And maybe we will try to float our boats again. TUESDAY: Jump into Chapter 8, which is more "beginning calculus" oriented... 8.1 thru 8.3 are on series, and introduce summation notation. Expect a pop quiz in there somewhere. WEDNESDAY: Sections 8.5 thru 8.7 are on counting and probability, which will be a fun way to challenge your lovely brains. And THURSDAY: will be, as usual, Chapter review and TEST.
SPECIAL NOTE FOR HAYDEN, LEVI AND STEPHEN: Make sure you get a worksheet for Chapter 9 before you leave for Israel. Have fun! Maseltov!
3RD WEEK OF PRECAL: MORE TRIG
Created on Wednesday, 08 May 2013 11:51
Written by Joe Chamberlin
Monday we will do Chapter 4, part of 5, Review and TEST. Tuesday we have solemn assembly, but we will still do Law of Sines and Cosines at start of Chapter 6. We will also look at waves (heart, brain, and tidal), and start building our boats. Wednesday we will review Law of Sines and Cosines, and throw in Herons rule for figuring out area, before we have more boats and a special afternoon chapel. Thursday we finish up Chapter 6 with Vectors, another Trig TEST, and hopefully, float our boats! | 677.169 | 1 |
Features
MATHEMATICS A GOOD BEGINNING 7th EDITION
Here is a more complete list of the 7th edition's features that illustrate why it is such a valuable teaching tool:
MGB has fully integrated the new Common Core State Standards for Mathematics (CCSSM) into the text and supporting activities.
MGB includes a learning trajectoryfor every content chapter. Learning trajectories constitute a specific mathematics goal, the developmental path (progression) students follow to achieve that goal, and the instructional tasks necessary to facilitate students' learning along that path (i.e., Clements & Sarama, 2009; Fuson, Caroll & Drueck, 2000). Learning trajectories are foundational to the CCSSM, and no other mathematics methods text integrates them into all content topics.
MGB places heavy emphasis on pedagogical content knowledge (PCK) within every content chapter. Research has shown that teachers in the U.S. suffer from weak mathematical PCK (Ma, 2000), a deficiency this text will help to overcome.
MGB includes a chapter on number theory, a topic critical to the development of algebraic concepts yet missing from all other elementary mathematics methods texts.
MGB'scomputational algorithms have been reformulated to support student's number sense, place value understanding, estimation skills, and mental mathematics.
MGB is written using informal language that is non-threatening to pre-service teachers with math anxiety. At the same time, the authors carefully build the reader's conceptual understanding of precise mathematical vocabulary.
MGB includes a booklet of full-size reproducible Resource Sheets (RS) that support sensory input for activities that develop key mathematical concepts.The resources in this booklet can sensitize teachers to the kinds of materials that are appropriate mathematics teaching and learning aids.
MGB incorporates the authors' years of research on diagnosis of student misconceptions into an assessment section in every content chapter. For every major concept covered in each chapter, an explanation of students' typical conceptual difficulties is provided.
MGB's authors have a wealth of experience in preparing teachers to teach mathematics, experience that has informed the content, presentation of concepts, and book length (200 pages shorter than the typical methods text).
MGB provides a Study Guide for each chapter to help pre-service teachers gain maximum benefit from the content and to provide teacher educators with a wealth of meaningful activities they can assign for coursework.
MGB's authors believe that classroom teachers must recognize that they are teachers of children, as much as they are teachers of mathematics. They must know the mathematics they teach and must be competent to communicate content in a way that children can understand.
For every content chapter, MGB presents a list of essential learning expectationsthat illustrates how children's learning will progress.
Within every content chapter, MGB Spotlights authors and articles that will help pre-service and in-service teachers enhance their knowledge.
MGB's companion website will keep readers informed of current topics in mathematics education.
See it for yourself! Simply register and log in to view samples from our text and resources on the Evaluate the Book page! This page is only available to logged-in registered users. | 677.169 | 1 |
Mathematics Departmental Page
The Broughton Mathematics department strives to provide high-quality instruction to enable high school students to solve problems creatively and resourcefully, to compute fluently, and to prepare them to fulfill personal ambitions and career goals in an ever-changing world. It is based on a philosophy of teaching and learning mathematics that is consistent with the current research, exemplary practices, and national standards. The North Carolina Standard Course of Study describes the mathematical concepts, skills, operations, and relationships that are the significant mathematics that all North Carolina students should learn and understand.
All students are now required to complete four years of high school mathematics, including Algebra I and Geometry or Algebra II, and pass the Algebra I EOC. Broughton offers a wide variety of math courses, including Advanced Placement and International Baccalaureate courses. All courses emphasize the use of technology and the development of mathematical literacy | 677.169 | 1 |
Mathematics is one of the oldest and most universal means of creating, communicating, connecting and applying structural and quantitative ideas. The discipline of Mathematics allows the formulation and solution of real-world problems as well as the creation of new mathematical ideas, both as an intellectual end in itself, but also as a means to increase the success and generality of mathematical applications. This success can be measured by the quantum leap that occurs in the progress made in other traditional disciplines, once mathematics is introduced to describe and analyses the problems studied.
It is therefore essential that as many persons as possible be taught not only to be able to use mathematics, but also to understand it.
Students doing this syllabus will have been already exposed to Mathematics in some form mainly through courses that emphasise skills in using mathematics as a tool, rather than giving insight into the underlying concepts. To enable students to gain access to mathematics training at the tertiary level, to equip them with the ability to expand their mathematical knowledge and to make proper use of it, it is, therefore, necessary that a mathematics course at this level should not only provide them with more advanced mathematical ideas, skills and techniques, but encourage them to understand the concepts involved, why and how they "work" and how they are interconnected. It is also to be hoped that, in this way, students will lose the fear associated with having to learn a multiplicity of seemingly unconnected facts, procedures and formulae. In addition, the course should show that that mathematical concepts lend themselves to generalisations, and that there is enormous scope for applications to the solving of real problems.
Mathematics covers extremely wide areas. However, students can gain more from a study of carefully selected, representative areas of Mathematics, for a "mathematical" understanding of these areas, rather than to provide them with only a superficial overview of a much wider field. While proper exposure to a mathematical topic does not immediately make students into experts in it, that proper exposure will certainly give the students the kind of attitude which will allow them to become experts in other mathematical areas to which they have not been previously exposed. The course is, therefore, intended to provide quality in selected areas, rather than a large area of topics.
To optimise the competing claims of spread of syllabus and the depth of treatment intended, all items in the proposed syllabus are required to achieve the aims of the course. None of the Modules of the two Units making up the whole course will, therefore, be optimal. However, Unit 1, representing the basics of the syllabus, is assessed separately, can stand on its own, can be combined with other Units, such as Statistical Analysis, and can be separately certified. Unit 2, which will also be separately assessed and certified, will also be accessible on its own by students who have already adequately covered the material contained in Unit 1.
While there will be a great deal of attention to the application of mathematics to solving problems arising in other areas, including mechanics and statistics, it is not the intention to develop a general account of these subjects; there is, therefore, no section on statistics or mechanics; these are expected to be specifically addressed in other courses.
Through a development of understanding of these areas, it is expected that the course will enable students to:
Develop mathematical thinking, understanding and creativity;
Develop skills in using mathematics as a tool for other disciplines;
Develop the ability to communicate through the use of mathematics;
Develop the ability to use mathematics to model and solve real world problems; | 677.169 | 1 |
Applied Mathematics is the application of Mathematics to the modeling and solving of practical, real world problems. It is at the core of many disciplines, ranging from Business, Finance, and Economics, through Geography and Geology to all branches of Engineering and the Sciences. The First Year course in Arts assumes no previous knowledge of Applied Mathematics and there is extensive tutorial support available throughout the year | 677.169 | 1 |
098 Developmental Arithmetic (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is less than 15 or COMPASS Math score of 30 or less. Fundamental topics in arithmetic, geometry, and pre-algebra.
099 Developmental Algebra (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is at least 15 but less than 19 or COMPASS Math score of 31 to 58. Fundamental topics in algebra for students with insufficient knowledge of high school level mathematics. PR: ACT Mathematics Main score of 15 or grade of "S" in MATH 098.
109 Algebra (3-0-3). Real numbers, exponents, roots and radicals; polynomials, first and second degree equations and inequalities; functions and graphs. PR: ACT Mathematics main score of 19 or grade of "S" in MATH 099.
211 Informal Geometry (3-0-3). Theorems are motivated by using experiences with physical objects or pictures and most of them are stated without proof. Point approach is used with space as the set of all points; review elementary geometry, measurement, observation, intuition and inductive reasoning, distance, coordinate systems, convexitivity, separation, angles, and polygons. No field credit for math majors/minors. PR: MATH 101 or higher.
220 Calculus I (4-0-4). A study of elements of plane analytical geometry, including polar coordinates, the derivative of a function with applications, integrals and applications, differentiation of transcendental functions, and methods of integration. PR: MATH 109 and MATH 110, or GNET 116, or ACT Mathematics main score of 26 or COMPASS Trigonometry score of 46 or above.
250 Discrete Mathematics (3-0-3). Treats a variety of themes in discrete mathematics: logic and proof, to develop students' ability to think abstractly; induction and recursion, the use of smaller cases to solve larger cases of problems; combinatorics, mathematics of counting and arranging objects; algorithms and their analysis, the sequence of instructions; discrete structures, e.g., graphs, trees, sets; and mathematical models, applying one theory to many different problems. PR: MATH 109 and MATH 110 or GNET 116.
290 Topics in Mathematics (1-4 hours credit). Formal course in diverse areas of mathematics. Course may be repeated for different topics. Specific topics will be announced and indicated by subtitle on the student transcript. PR: Consent of instructor.
400 Introduction to Topology (3-0-3). A study of set theory; topological spaces, cartesian products, connectedness; separation axioms; convergences; compactness. Special attention will be given to the interpretation of the above ideas in terms of the real line and other metric spaces. PR: MATH 240.
490 Topics in Mathematics (1-4 hours credit per semester). Advanced formal courses in diverse areas of mathematics. Courses may be repeated for different topics. Specific topics will be announced and indicated by subtitle on transcript. PR: Consent of instructor. | 677.169 | 1 |
The study of mathematics is not only exciting, but important. Mathematicians contribute to society by helping to solve problems in such diverse fields as medicine, business, industry, government, computer science, physics, psychology, engineering, and social science. Mathematics is often done in conjunction with another field: biology, physics, economics, or a host of others. Mathematical modeling is used to solve real problems in a variety of fields. Statistics is a growing field, particularly in those fields dealing with human behavior. Many topics in
"pure math" have important applications in computer science. There is a national shortage of teachers in all the mathematical science (pure math, applied math, statistics, and computer science) at all levels, so any of these fields goes well with teaching and/or research. | 677.169 | 1 |
Quick Overview
Details
Practice and application characterize LIFEPAC's Mathematics series, focusing on the mastery of basic concepts and skills as well as advanced concepts of mathematics. The major content strands are as follows:
Grade 10: A Geometry course, which includes Proofs, Congruency, Similar Polygons, Circles, Constructions, Area & Volume, and Coordinate Geometry | 677.169 | 1 |
Variables, Constants, and Real Numbers
Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses variables, constants, and real numbers. By the end of the module students should be able to distinguish between variables and constants, be able to recognize a real number and particular subsets of the real numbers and understand the ordering of the real numbers.
Links
Supplemental links
Section Overview
Variables and Constants
Real Numbers
Subsets of Real Numbers
Ordering Real Numbers
Variables and Constants
A basic distinction between algebra and arithmetic is the use of symbols (usually letters) in algebra to represent numbers. So, algebra is a generalization of arithmetic. Let us look at two examples of situations in which letters are substituted for numbers:
Suppose that a student is taking four college classes, and each class can have at most 1 exam per week. In any 1-week period, the student may have 0, 1, 2, 3, or 4 exams. In algebra, we can let the letter
xx size 12{x} {} represent the number of exams this student may have in a 1-week period. The letter
xx size 12{x} {} may assume any of the various values 0, 1, 2, 3, 4.
Suppose that in writing a term paper for a biology class a student needs to specify the average lifetime, in days, of a male housefly. If she does not know this number off the top of her head, she might represent it (at least temporarily) on her paper with the letter
tt size 12{t} {} (which reminds her of time). Later, she could look up the average time in a reference book and find it to be 17 days. The letter
tt size 12{t} {} can assume only the one value, 17, and no other values. The value
tt size 12{t} {} is constant.
Variable, Constant
A letter or symbol that represents any member of a collection of two or more numbers is called a variable.
A letter or symbol that represents one specific number, known or unknown, is called a constant.
In example 1, the letter
xx size 12{x} {} is a variable since it can represent any of the numbers 0, 1, 2, 3, 4. The letter
tt size 12{t} {}example 2 is a constant since it can only have the value 17.
Real Numbers
Real Number Line
The study of mathematics requires the use of several collections of numbers. The real number line allows us to visually display (graph) the numbers in which we are interested.
A line is composed of infinitely many points. To each point we can associate a unique number, and with each number, we can associate a particular point.
Coordinate
The number associated with a point on the number line is called the coordinate of the point.
Graph
The point on a number line that is associated with a particular number is called the graph of that number.
Constructing a Real Number Line
We construct a real number line as follows:
Draw a horizontal line.
Origin
Choose any point on the line and label it 0. This point is called the origin.
Choose a convenient length. Starting at 0, mark this length off in both directions, being careful to have the lengths look like they are about the same.
We now define a real number.
Real Number
A real number is any number that is the coordinate of a point on the real number line.
Positive Numbers, Negative Numbers
Real numbers whose graphs are to the right of 0 are called positive real numbers, or more simply, positive numbers. Real numbers whose graphs appear to the left of 0 are called negative real numbers, or more simply, negative numbers.
The number 0 is neither positive nor negative.
Subsets of Real Numbers
The set of real numbers has many subsets. Some of the subsets that are of interest in the study of algebra are listed below along with their notations and graphs.
Natural Numbers, Counting Numbers
Whole Numbers
Integers
The integers (ZZ): . . . -3, -2, -1, 0, 1, 2, 3, . . .
Notice that every whole number is an integer.
Rational Numbers (Fractions)
The rational numbers (QQ): Rational numbers are sometimes called fractions. They are numbers that can be written as the quotient of two integers. They have decimal representations that either terminate or do not terminate but contain a repeating block of digits. Some examples are
Notice that there are still a great many points on the number line that have not yet been assigned a type of number. We will not examine these other types of numbers in this text. They are examined in detail in algebra. An example of these numbers is the number ππ, whose decimal representation does not terminate nor contain a repeating block of digits. An approximation for ππ is 3.14.
Exercise 4
Solution
Exercise 5
Solution
Ordering Real Numbers
Ordering Real Numbers
A real number
bb size 12{b} {} is said to be greater than a real number
aa size 12{a} {}, denoted
b>ab>a size 12{b>a} {}, if
bb size 12{b} {} is to the right of
aa size 12{a} {} on the number line. Thus, as we would expect,
5>25>2 size 12{5>2} {} since 5 is to the right of 2 on the number line. Also,
-2>-5-2>-5 size 12{"- 2 ">"-5"} {} since -2 is to the right of -5 on the number line.
If we let
aa size 12{a} {} and
bb size 12{b} {} represent two numbers, then
aa size 12{a} {} and
bb size 12{b} {} are related in exactly one of three ways: Either
Equality Symbol
a=ba and b are equal(8=8)a=ba and b are equal(8=8)
Inequality Symbols
Sample Set B
Example 4
What integers can replace xx so that the following statement is true?
-3≤ x< 2-3≤ x< 2 size 12{"-3" <= " x"<" 2"} {}
The integers are -3, -2, -1, 0, 1.
Example 5
Draw a number line that extends from -3 to 5. Place points at all whole numbers between and including -1 and 3.
Exercise 7
Solution
Exercises
For the following 8problems, next to each real number, note all collections to which it belongs by writing
NN size 12{N} {} for natural number,
WW size 12{W} {} for whole number, or
ZZ size 12{Z} {} for integer. Some numbers may belong to more than one collection | 677.169 | 1 |
## DESCRIPTION
## Matrix Algebra
## ENDDESCRIPTION
## KEYWORDS('Algebra' 'Matrix' 'Matrices' 'True' 'False')
## Tagged by tda2d
## DBsubject('Algebra')
## DBchapter('Systems of Equations and Inequalities')
## DBsection('The Algebra of Matrices')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
DOCUMENT();
loadMacros("PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
);
TEXT(beginproblem(), $BR,$BBOLD, "True False Problem", $EBOLD, $BR,$BR);
# Since this is a true questions, we do not usually wish to tell students which
# parts of the matching question have been answered correctly and which are
# incorrect. That is too easy. To accomplish this we set the following flag to
# zero.
$showPartialCorrectAnswers = 0;
# True false questions are a special case of a "select list"
# Make a new select list
$tf = new_select_list();
# $tf now "contains" the select list object.
# Insert some questions and whether or not they are true.
$tf -> qa ( # each entry has to end with a comma
"If A and B are both square matrices such that AB equals BA equals the identity matrix, then B is the inverse matrix of A.",
"T",
"If A is a square matrix, then there exists a matrix B such that AB equals the identity matrix.",
"F",
"If \( AX = B \) represents a system of linear equations and \( A^{-1} \) exists, then the product \( A^{-1}B \) gives the solution to the system.",
"T",
); # every statement has to end with a semi-colon.
# Choose two of the question and answer pairs at random.
$tf ->choose(2);
# Now print the text using $ml->print_q for the questions
# and $ml->print_a to print the answers.
BEGIN_TEXT
$PAR
Enter T or F depending on whether the statement is true or false.
(You must enter T or F -- True and False will not work.)$BR
\{ $tf-> print_q \}
$PAR
END_TEXT
# Enter the correct answers to be checked against the answers to the students.
ANS(str_cmp( $tf->ra_correct_ans ) ) ;
ENDDOCUMENT(); # This should be the last executable | 677.169 | 1 |
Course Description: An investigation of topics, including the history of mathematics, number systems, geometry, logic, probability, and statistics. There is an emphasis throughout on problem solving. Recommended for general education requirements, B.S. degree.
Text: Mathematics in Our World, by Bluman (McGraw-Hill, 2005)
CORE SKILL OBJECTIVES:
These skills are related to the General Education core abilities document. They are also written to refer to the various INTASC standards for the purposes of the Elementary Education program.
Thinking Skills: The students will engage in the process of inquiry and problem solving that involves both critical and creative thinking.
Students will
(a) ... explore writing numbers and performing calculations in various numeration systems. (INTASC 1)
(b) ... solve simple linear algebraic equations. (INTASC 1)
(c) ... explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models. (INTASC 1)
(d) ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system. (INTASC 1)
(e) ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms. (INTASC 1)
(f) ... explore the basics of probability. (INTASC 1)
(g) ... learn descriptive statistics, including making the connection between probability and the normal distribution table. (INTASC 1)
(h) ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations. (INTASC 1)
(i) ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course. (INTASC 1)
Life Value Skills: The students will analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
Students will
(a) ... develop an appreciation for the intellectual honesty of deductive reasoning. (INTASC 9)
(b) ... understand the need to do one's own work, to honestly challenge oneself to master the material. (INTASC 1)
Communication Skills: The students will communicate orally and in writing in an appropriate manner both personally and professionally.
Student will
(a) ... write a mathematical autobiography. (INTASC 9)
(b) ... do group work (labs and practice exams), involving both written and oral communication. (INTASC 4)
(c) ... turn in written solutions to occasional problems. (INTASC 1)
Cultural Skills: The students will understand their own and other cultural traditions and respect the diversity of the human experience.
Student will
(a) ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples. (INTASC 1)
(b) ... develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages". (INTASC 1)
(c) ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry. (INTASC 1)
It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course:
The students shall develop an appreciation of mathematics, its history and its applications.
The students shall become confident in their own ability to do mathematics.
The students shall become mathematical problem solvers.
The students shall learn to communicate mathematical content.
The students shall learn to reason mathematically.
FURTHER COURSE NOTES: This course is aimed at the needs of elementary education majors and as such is the first part of a three-course, 12-credit sequence (MATH 155-255-355). This is a "content" course rather than a "methods" course (teaching methods are addressed in the latter two courses in the above sequence). This is what people generally call a "Liberal Arts Mathematics Course", meaning that it covers a wide variety of topics, has an emphasis on problem solving, and uses a historical and humanistic approach. Consequently, the course is considered appropriate for the general education requirements and is open to all students.
Homework questions 100 pts.
(Full credit is given for each completed assignment)
Homework will be due one class week after it has been assigned. Any questions regarding how to do particular homework problems will be welcomed in the intervening class meetings or in my office but not in class on the day that the homework is due. Late homework will be penalized by a deduction of 20% of the assigned grade for each schoolday -- including schooldays on which class does not meet – that the work is late, so that, if the work is one week late, it will not receive any points. You may, however, still hand the work in so that you can benefit from corrections and be certain you know how to do a question that could well appear on an exam
Examinations 400 pts
There will be four in class exams worth 100 pts apiece, and lasting 50 minutes each.
Participation 50 pts
Participation points are easy to acquire and you probably already know how to get them; don't chat to your neighbors when I'm lecturing (asking a neighbor to help if you didn't understand what I said is, however, always acceptable). General politeness counts. Cheerfulness, engagement, willingness to push buttons on your calculator, asking me to clarify if you are stuck, taking advantage of my office hours, these are all, to quote the Sound of Music, a few of my favorite things.
Labs 150 pts
Cumulative Final Examination 200 pts
Total 900 pts
Attendance Policy: You can afford to miss no more than the equivalent of one week of class. Any more absences are a dangerous loss of classtime percentage. Once you have had 3 unexcused absences, every unexcused absence from that point onward will incur a penalty of 10 pts from your participation and attendance score.
Make up exams situations will be considered on a case-by-case basis, but invariably they require as much forewarning as possible -- and documentation. You know when the exams are; please do not book flights home, or your wedding, etc, etc on those dates. If your, or your best friend's, or your uncle's hairdresser's poodle's (if you're from the Coast) wedding is already booked for any of those dates, please let me know ASAP. I will not give make up tests without good reason, and if you should miss a test that is not made up, your score for that test will be zero.
The sad fact is that it is a rare semester when some student doesn't have to rush home to tend a family crisis, or bury a loved one. Often this interferes with exams. Should such sadness happen to you, I will need to ask you for some sort of verification (obituary, hospital record, etc) and then we will try to get your semester moving again.
RESOURCES: Tutoring is available in the Learning Center - third floor, Murphy Center. I also want you to consider coming to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. I don't resent your coming – it's part of my job! I want your success as much as you do.
FINAL COMMENTS: I believe firmly that you as the student are the learner, and that "to learn" is an active verb; you must be actively engaged in the learning process, and this is best accomplished by your DOING mathematics. I am not here to show you how much I know - I am here to be "a guide on the side, not a sage on the stage". Please feel free to ask questions in class, either of me or of your group-mates. Please feel free to come to my office to discuss problems you might be having. Please feel free to go visit the learning center for tutoring help if necessary. The bottom line is that you must take responsibility for your own learning. Please believe that "Mathematics is not a spectator sport!" | 677.169 | 1 |
Credit: 0.5 units Lessons: 8 lessons, 8 submitted Exams: 2 exams Grading: Computer and Faculty Evaluated Prerequisites: Full credit for Geometry and Precalculus or Trigonometry (C or better) Description: This course provides students with a college-level foundation in calculus. Coursework emphasizes the relationship between the various forms of a function: graphs, equations, tables, and verbal expressions. Calculus has two main topics: rate of change and area under a curve. The fall semester focuses on finding rates of change, i.e. differentiation. Students will review familiar functions and explore the concept of limits and differentiation.
Gifted: This course is academically challenging. Any student who has an interest in the subject and has met the prerequisites (if any), may enroll.
Special Instructions:
The course content will be viewable prior to the start date. Read more about our online Advanced Placement courses. Our AP courses follow a specific calendar, and the normal 9-month completion policy does not apply to these courses. Therefore, students who have not completed all work by the due date for the course final (listed on the course calendar) will automatically be withdrawn from the course. Students who choose to take the AP exam will need to make their own arrangements. Contact the College Board for assistance in locating a testing site, or contact a local high school to determine whether it administers the test.
Lesson assignments need to be created in Microsoft Word or another word processor that saves files as .doc (Word 97–2003 document) or .rtf (Rich Text format).
Materials Note: Students will need access to a graphing calculator (e.g. TI-83+ or newer). The same textbook is also used for the fall semester.
Preview This Course — A preview includes general information about the course and, if available, one lesson and one progress evaluation. | 677.169 | 1 |
Unit specification
Aims
The programme unit aims to introduce the basic ideas of real analysis (continuity, differentiability and Riemann
integration) and their rigorous treatment, and then to introduce the basic elements of complex analysis, with
particular emphasis on Cauchy's Theorem and the calculus of residues.
Brief description
The first half of the course describes how the basic ideas of the calculus of real functions of a real variable
(continuity, differentiation and integration) can be made precise and how the basic properties can be developed
from the definitions. It builds on the treatment of sequences and series in MT1242. Important results are the
Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the
Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration.
The second half of the course extends these ideas to complex functions of a complex variable. It turns out
that complex differentiability is a very strong condition and differentiable functions behave very well.
Integration is along paths in the complex plane. The central result of this spectacularly beautiful part
of mathematics is Cauchy's Theorem guaranteeing that certain integrals along closed paths are zero. This
striking result leads to useful techniques for evaluating real integrals based on the `calculus of residues'.
Intended learning outcomes
On completion of this unit successful students will be able to:
understand the concept of limit for real functions and be able to calculate limits of standard functions and construct simple proofs involving this concept;
understand the concept of continuity and be familiar with the statements and proofs of the standard results about continuous real functions;
understand the concept of the differentiability of a real valued function and be familiar with the statements and proofs of the standard results about differentiable real functions;
appreciate the definition of the Riemann integral, and be familiar with the statements and proofs of the standard results about the Riemann integral including the Fundamental Theorem of Calculus;
understand the significance of differentiability for complex functions and be familiar with the Cauchy-Riemann equations;
evaluate integrals along a path in the complex plane and understand the statement of Cauchy's Theorem and have seen an outline of the proof;
compute the Taylor and Laurent expansions of simple functions, determining the nature of the singularities and calculating residues;
use the Cauchy Residue Theorem to evaluate integrals and sum series.
Future topics requiring this course unit
Real analysis is needed in more advanced courses in analysis, functional analysis and topology and some
courses in numerical analysis.
Complex analysis is needed for advanced analysis, geometry and topology, but also has applications
in differential equations, potential theory, fluid mechanics, asymptotics and wave analysis. | 677.169 | 1 |
This textbook entitled Trigonometry (Notes) is a complete and detailed account of trigonometry, including numerous solved problems and formula derivations with each and every step included. Furthermore, the textbook presents the development of trigonometry in a logical manner, starting with the definitions of the six trigonometric ratios on a right-triangle, and later generalizing these definitions for the rectangular coordinate system. Finally, the six trigonometric functions are abstracted from the six trigonometric functions. The textbook is essentially divided into two parts:
Trigonometry developed from the right-triangle, and
Trigonometry derived from the rectangular coordinate system.
Trigonometry (Notes) is intended for the student who wants to learn trigonometry completely and thoroughly, with a complete understanding of the concepts and their relationships to one another.
Except for the Table of Contents, the textbook is hand-written as opposed to typed; thus the word Notes in parentheses in the title.
Originally formulated for the home-schooled student, this five hundred page text and study guide provides extremely detailed explanations in simple English with numerous example problems accompanied by narrative explanations for each topic presented. Reader friendly and logically organized, this volume serves as an all-inclusive high-school algebra text for the college bound student or as an excellent study guide to accompany any serious algebra or trigonometry course. Hundreds of practice problems complete with solutions are included in the text, covering every aspect of a high school or introductory level college algebra course. Also, it is perfect as summer reading for the student who wishes to get ahead or for adults participating in continuing education courses. | 677.169 | 1 |
Prerequisite: MAT 076 (min grade C) or 1 year of high school geometry (min grade C), and MAT 080 (min grade C), or 2 years of high school algebra (min grade C) or appropriate Placement score or ACT score of 21-22
30220
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3
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11:00-12:40
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CR. Conderman
0
MAT115 Principles of Modern Math
Prerequisite: MAT 076 (min grade C) or 1 year high school geometry (min grade C), and MAT 080 (min grade C) or 2 years of high school algebra (min grade C) or appropriate Placement score or ACT score of 21-22
IAI#: M1904
30153
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3
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3G06
CR. Conderman
13
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11:00-12:15
2M05
JL. Horn
0
MAT121 College Algebra
Prerequisite: MAT 076 (min grade C) or 1 year of high school geometry (min grade C) and MAT 080 (min grade C) or 2 years of high school algebra (min grade C) or appropriate Placement or ACT score of 21-22
30155
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$10
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12:30-2:15
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$10
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4
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EA. Etter
15
$10
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$10
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Staff
23
$10
MAT122 Trigonometry
Prerequisite: MAT 121 (min grade C) or appropriate Placement score or 4 years of college preparatory high school mathematics (min grade C) and apprpriate placement score or ACT score of 23-25
30158
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3
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6:00-7:15
2H14
SP. McPherson
13
$10
MAT203 Calculus & Analytic Geometry I
Prerequisite: MAT 122 (min grade C) or appropriate Placement score or 4 years of college preparatory high school mathematics (min grade C) and appropriate Placement score or ACT score of 23-25 | 677.169 | 1 |
Vectors: Grade 10 Grade 10: Vectors. Are vectors physics? No, vectors themselves are not physics. Physics is just a description of the world around us. To describe something we need to use a language. The most common language used to describe physics is mathematics. Vectors form a very important part of the mathematical description of physics, so much so that it is absolutely essential to master the use of vectors. Author(s): Creator not set
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Rights not setCK-12 Geometry (CA Textbook) CK-12's Geometry delivers a full course of study in the mathematics of shape and space for the high school student, relating the ancient logic and modern applications of measurement and description to its essential elements, processes of reasoning and proof, parallel and perpendicular lines, congruence and similarity, relationships within triangles and among quadrilaterals, trigonometry of right triangles, circles, perimeter, area, surface area, volume, and geometric transformations.
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Rights not setEmpirical Research Methods Regression analysis is an enormously popular and powerful tool, used ubiquitously in the social and behavioral sciences. Most courses on the subject immediately dive into the mathematical aspects of the subject and illustrate the technique on problems that are already highly structured. As a result, most students come away with little idea of the wide range of problems to which regression analysis can be applied and how to represent those problems in a way that cleverly utilizes readily availabl Author(s): Creator not set
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Rights not setAlgorithms The design of algorithms is studied, according to methodology and application. Methodologies include: divide and conquer, dynamic programming, and greedy strategies. Applications involve: sorting, ordering and searching, graph algorithms, geometric algorithms, mathematical (number theory, algebra and linear algebra) algorithms, and string matching algorithms. Analysis of algorithms is studied - worst case, average case, and amortized - with an emphasis on the close connection between the time coPersonalisation Services for Self e-Learning Networks This paper describes the personalisation services designed for self e-learning networks in the SeLeNe project. A self e-learning network consists of web-based learning objects that have been made available to the network by its users, along with metadata descriptions of these learning objects and of the network's users. The proposed personalisation facilities include: querying learning object descriptions to return results tailored towards users' individual goals and preferences; the ability to Author(s): Keenoy Kevin,Poulovassilis Alexandra,Christophides
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Darden MBA International Community and Opportunities Marie Skjold-Joergensen, Class of 2011, talks about the international student community at the University of Virginia Darden School of Business, as well as international opportunities offered through the Full-Time MBA program. Author(s): No creator set
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Bill of Rights On 12 September 1787, during the final days of the Constitutional Convention, George Mason of Virginia expressed the desire that the Constitution be prefaced by a Bill of Rights. Elbridge Gerry of Massachusetts proposed a motion to form a committee to incorporate such a declaration of rights; however the motion was defeated. This lesson examines the First Congress's addition of a Bill of Rights as the first ten amendments to the Constitution. Author(s): No creator set
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7.60 Cell Biology: Structure and Functions of the Nucleus (MIT) The goal of this course is to teach both the fundamentals of nuclear cell biology as well as the methodological and experimental approaches upon which they are based. Lectures and class discussions will cover the background and fundamental findings in a particular area of nuclear cell biology. The assigned readings will provide concrete examples of the experimental approaches and logic used to establish these findings. Some examples of topics include genome and systems biology, transcription, an Author(s): Sharp, Phillip,Young=B This book is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks. Author(s): No creator set
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Greetings from Kingan & Company, Ltd. The company's logo is in the upper left corner of the card. It shows a man at the wheel of a ship. In the center is a drawing of the Kingan & Company Indianapolis facility. It is near a river and has railroad tracks next to it. Some of the buildings are labeled, such as the canning factory and the curing warehouse. Above the picture of the plant, pigs are holding a banner that says "Greetings." Beneath the plant picture a family of pigs is playing on the ice. The father pig is helping the mother Author(s): Creator not set | 677.169 | 1 |
Euclidean plane geometry is one of the oldest and most beautiful of subjects in mathematics, and Methods for Euclidean Geometry explores the application of a broad range of mathematical techniques to the solution of Euclidean problems.
The book presents numerous problems of varying difficulty and diverse methods for solving them. More than a third of the book is devoted to problem statements, hints, and complete solutions. Some exercises are repeated in several chapters so that students can understand that there are various ways to solve them.
The book offers a unique and refreshing approach to teaching Euclidean geometry, which can serve to enhance students' understanding of mathematics as a whole.
Having completed a survey of lines, polygons, circles, and angles, we come to another collection of well-known figures in the plane: ellipses, parabolas, and hyperbolas. In what situations do these figures appear? What is our motivation for studying them?
One way in which these figures arise quite naturally is when we try to find answers to questions of the type, "What is the set of all points (loci) of a plane that satisfy a given property?" Another is when we wish to understand the trajectory of a moving point. Yet a third situation occurs when we seek to describe the intersection of two surfaces in space. | 677.169 | 1 |
The Coffeecup Caustic - Roy Williams
You are drinking from a cylindrical cup in the sunshine. Sometimes, when the sun shines into the cup, you can see a crescent of light as the sunshine reflects from the inside of the cup onto the surface of the drink. This Java applet illustrates the optics
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Colégio de Gaia, Grupo de Matematica
Math resources in Portuguese: Galeria de Sketches - a gallery of JavaSketchpad and Geometer's Sketchpad problems and sketches including the Pythagorean theorem (o Teorema de Pitágoras), Vector Addition (Adicao de Vectores), cutting a cube/parallelepiped
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College Entrance Exam Math Prep - EduCAD
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Complex Numbers and the Distributive Law for Complex Numbers, offering a short way to reach and explain trigonometry, the Pythagorean theorem, trig formulas for dot- and cross-products, the cosine law, and a converse to the Pythagorean theorem. A geometricnexions - Rice University
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Constructor animates and edits two-dimensional models made out of masses and springs. The springs can be controlled by a wave to make pulsing muscles, and you can construct models that bounce, roll, walk, etc. Try some of the ready-made models or build
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An applet that demonstrates some algorithms for computing the convex hull of points in three dimensions. See the points from different viewpoints; see how the Incremental algorithm constructs the hull, face by face; while it's playing, look at it from
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Shockwave whiteboard movies on algebra, geometry, probability, statistics, the mathematics of finance, and more. A whiteboard movie (WM) is a multimedia screen recording of writing on an electronic whiteboard (real or virtual) with or without voice and/or
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A Java game that revolves around replicating a picture created by several patterned faces of a solid object (like a cube), challenging the mind to understand complex geometrical structures and symmetry. To do well at the game, the player must first become
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A good physics book besides Giancoli?
A good physics book besides Giancoli?
Hey!
I'm a junior in high school who's curious and determined to figure and (and retain the knowledge afterwards) how the world works. I'm enrolled in AP physics (i think it was B) but i don't really like how things are explained in our Giancoli book. By no means is it a bad book but I think he focuses too much emphasis on algebraic proofs than explanations (i don't think memorizing formulas is a good way to understanding physics). So what are your recommendations? I'm taking calculus A right now and am proficient in that course.
is conceptual physics by Hewitt any good? I only have enough money to buy 1 book right now. Thanks for your input.A good physics book besides Giancoli?
Quote by Kwally3Feynman uses intuition and philosophy, it is not very mathematically emphasized. It would let you "understand" physics.
there's philosophy in physics??
I'm now super hyped. Unless no one else suggests anything by this afternoon, I'm going to purchase them.
When you say it's not mathematically emphasized, do you mean he provides you with the knowledge to derive formulas yourself?
And, just to suppress a side thought, it's definitely not one of those books that you have a great time reading but have no idea how
to apply the knowledge afterwards right? | 677.169 | 1 |
Attributes
Additional Constraints
Description
An equation is a formal mathematical equation (with an optional rather than a required title).
If the MathML Module is used, equation can also contain the mml:math element.
Processing expectations
Formatted as a displayed block. For an inline equation, use inlineequation.
Processing systems that number equations or build a table of equations at the beginning of a document may have difficulty correctly formatting documents that contain both equations with titles and equations without titles. You are advised to use informalequation for equations without titles. | 677.169 | 1 |
Riverside, RI Precalculus...I ...It's not unusual for some courses to include solid geometry and advanced algebra, such as synthetic division, sequences, and series. These subjects form the foundations of calculus, and not mastering these topics will haunt students when they get into calculus, particularly integral calculus and... | 677.169 | 1 |
How long does it take on avg. to finish Spivak's Calculus book?
How long does it take on avg. to finish Spivak's Calculus book?
i would like to gain a deeper understanding of Calculus so i'm planning on self-studying more on the side. i will do majority of my studies during winter break but i'd like to know long it takes a student who has already taken Calculus 2 to finish his book?
i know it's dependent on the person, but i'm committed and would just like to know.
Why not just get a regular analysis book like Pugh? He explains things very well. I don't think Spivak covers metric spaces or topology. Spivak is more like a half calculus/ half analysis book. In my opinion, it is pretty overrated.Here is the book.
It's not something you really want to do for speed...figure first pass over the course of a few months, maybe? Not full time, obviously. You don't want to do it as a block, anyway, you need time to digest & rest. | 677.169 | 1 |
This course is designed to provide a study in mathematical ideas suitable for education majors and those needing course work for teacher re-certification. The topics covered will include number sense, concepts and operations, measurement, geometry and spatial sense, algebraic thinking, data analysis and probability. The topics are in alignment with the National Council of Teachers of Mathematics standards, the Sunshine State Standards, math curriculum of Marion, Citrus and Levy counties, and the FCAT. | 677.169 | 1 |
QAX - The Complete Mathematics Solution
What is QAX?
QAX Mathematics can be used for your school's entire mathematics program. It covers the secondary curriculum for each Australian state, negating the need for other teaching resources. Each topic within the curriculum has a supply of questions and an introduction including examples of questions with full working out.
Teachers can create work programs or question sets (called Q Sets) for each topic from the 50,000 available questions.
Students complete questions online or as printed worksheets.
The program assists students by providing example questions, hints and solutions.
A fully worked solution is shown to students once they have answered the question correctly or made two incorrect attempts.
Students who have answered incorrectly are shown the correct solution and then given similar questions to answer. | 677.169 | 1 |
College Algebra and Trigonometry
Study Guide with Student Solution Manual for Aufmann/Barker/Nation's College Algebra and Trigonometry, 7th
Summary
Accessible to students and flexible for instructors, COLLEGE ALGEBRA AND TRIGONOMETRY, Seventh Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Seventh Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts. | 677.169 | 1 |
You will be completing math assignments pertaining to the probability and statistics. Tasks will include watching videos, playing math games online, writing journals, completing discussions, and performing math computation and application skill problems. | 677.169 | 1 |
Related Products
Without a basic understanding of maths, students of any science discipline are ill-equipped to tackle new problems or to apply themselves to novel situations. This book covers essential topics that will help encourage an understanding of... | 677.169 | 1 |
CCEA Foundation GCSE Mathematics
Neill Hamilton, Rosi MacCrea
Summary: This book covers the complete Foundation GCSE Mathematics course for years 11 and 12. Each chapter begins with Learning Objectives and pre-requisite knowledge. There are worked examples and full and clear explanations as well as teaching and learning tips throughout. Non-calculator and calculator questions are clearly indicated. Each chapter ends with a 'You should know' list of what has been covered in that chapter, and a summary exercise, as well as past exam questions.
Written especially by Northern Ireland authors to match the 2010 GCSE Mathematics specification from CCEA.
Complete coverage of the Foundation tier modules and completion paper. | 677.169 | 1 |
Discrete Mathematics with Proof 2nd Edition
0470457937
9780470457931 Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications.The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include:An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofsNew sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distributionImportant examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databasesNumerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theoremExtensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercisesCombinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems.Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics. «Show less... Show more»
Rent Discrete Mathematics with Proof 2nd Edition today, or search our site for other Gossett | 677.169 | 1 |
Lecture: Parallel Preconditioning Techniques for Linear Systems
Description:
The term preconditioning comprises as set of
techniques to modify a given system of linear equations such
that its iterative solution is easier than the solution of
the original system. Traditional algorithms for
preconditioning are often inherently sequential. When
designing parallel preconditioning algorithms, it is
crucial to make sure that increasing the level of
parallelism does not lead to a slower convergence behavior.
Audience:
This interdisciplinary course is offered to students from
computer science, mathematics, natural sciences, and engineering
disciplines. | 677.169 | 1 |
Math Club
The Math Club is organized to encourage
interest in mathematics, support students in mathematics classes, and
provide an informal setting for students to share ideas and participate in
mathematical activities. This is accomplished through regular meetings. At
these meetings, invited speakers (UM students, UM faculty, and guests from
other institutions) present colloquia, films are shown, problems are
presented, and students socialize over refreshments, asking questions and
discussing their thoughts and concerns. | 677.169 | 1 |
link below is the entry point to a Pomona College undergraduate course that uses mathematical processes, ranging from difference and differential equations to probability, to address topics in biological systems.
Introduces the fundamentals of machine tool and computer tool use. Students work with a variety of machine tools including the bandsaw, milling machine, and lathe. Instruction given on the use of the Athena network and Athena-based software packages including MATLABĺ¨, MAPLEĺ¨, XESSĺ¨, and CAD. Emphasis on problem solving, not programming or algorithmic development. Assignments are project-oriented relating to mechanical engineering topics. It is recommended that students take this subject in the first IAP after declaring the major in Mechanical Engineering. From the course home page: This course was co-created by Prof. Douglas Hart and Dr. Kevin Otto.
Numerical Computing with MATLAB is a textbook for an introductory course in numerical methods, MATLAB, and technical computing. It emphasizes the informed use of mathematical software. Topics include matrix computation, interpolation and zero finding, differential equations, random numbers, and Fourier analysis.
Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLABĺ¨ computing environment.
Most books that use MATLAB are aimed at readers who know how to program. This book is for people who have never programmed before. As a result, the order of presentation is unusual. The book starts with scalar values and works up to vectors and matrices very gradually. This approach is good for beginning programmers, because it is hard to understand composite objects until you understand basic programming semantics. | 677.169 | 1 |
Welcome to Algebra 1! Every student in the state is required to take this course in order to graduate from high school. We will cover all basic algebra topics: data analysis, solving equations, graphing lines, simplifying expressions, and exponents. These topics will be applied to real-world situations. I look forward to working with each one of you! | 677.169 | 1 |
Courses: Non-FL Students
Course Name:
Algebra II
Course Code:
1200330
Honors Course Code:
1200340
AP Course Code:
Description:
This course allows students to learn while having fun. Interactive examples help guide students' journey through customized feedback and praise. Mathematical concepts are applied to everyday occurrences such as earthquakes, stadium seating, and purchasing movie tickets. Students investigate the effects of an equation on its graph through the use of technology. Students have opportunities to work with their peers on specific lessons.
Algebra II is an advanced course using hands-on activities, applications, group interactions, and the latest technology | 677.169 | 1 |
Ages: 10+ Grade Levels: 5-12 Availability:Sold out and no longer available from Timberdoodle Co. Product Code:345-500
Sold Out!
Timberdoodle's review
Introduce your students to algebra in simple terms. KeyAbout the Key To... series: The Key To... series was developed by the same folks who produce Miquon Math. Though not manipulative dependent, there are scads of illustrations to make the concepts crystal clear. There is also a lot of white space, large type, and only one concept is presented per page.
The Key to ... books are not only easy to learn from, but also to follow along with if you, the teacher, are a little foggy on these topics! These books are self-directed, which means your child works independently at his own pace. What will you do with all your spare time?!?
Answer books are included in each pack, and the answers are clearly worked out, in case you need to bluff your way through!! More than 5 million of these workbooks have been bought since their creation over 30 years ago! Most workbooks are printed on recycled paper. | 677.169 | 1 |
I am happy to see that others besides myself have tried to use GAP as
a pedagogical aid in teaching abstract algebra. I am currently teaching
an undergraduate course, using Gallian's book, which I find to be an
excellent text. My students are primarily computer programming majors,
who take abstract algebra because they have to. Thus, one would think
that my class is an ideal laboratory for introducing GAP to students.
However, I can only report limited success. Perhaps some of you in the
forum can give me some suggestions.
I am reluctant to make assignments involving GAP, because I am fairly
new to it myself. I would not know how to evaluate the results. Hence,
the projects I suggest in class are "extra credit". I find the students'
intellectual curiousity is insufficient to cause them to play with GAP
on their own. A manual should include a section telling us mathematicians
how to evaluate computer homework.
I think the GAP manual is pretty intimidating to undergraduates. My students
are struggling with concepts like "isomorphism" and "coset". Even at this
level, they could benefit from some of GAP's capabilities, if they just
ignore all the stuff about character tables, representation theory, etc.
There is a much more user-friendly and simple program called "An Introduction
to Groups / A Computer Illustrated Text" (comes with a disc) by D. Asche,
available from IOP Publihsing for about $40. It does calculations in S_4,
mainly. Even with this, you have to wait until Chapter 5 (in Gallian's text)
before the students can use it. In my class, this is more than halfway through
the first semester. I might consider doing Chapter 5 sooner just so I can
use this software. Still, it seems that programmers ought to be more
interested in GAP. There is a saying, "You can lead a student to a computer,
but you can't make him think." Can we? At the undergraduate level? And with
non-math majors? After I tackle this, I will work on making them like it! | 677.169 | 1 |
Educational level
Academic level (A-D)
Subject area
Grade scale
Learning outcomes
Basic laws of nature are typically expressed in the form of partial differential equations (PDE), such as Navier's equations of elasticity, Maxwell's equations of electromagnetics, Navier-Stokes equations of fluid flow, and Schrödinger's equations of quantum mechanics. The Finite element method (FEM) has emerged as a universal tool for the computational solution of PDEs with a multitude of applications in engineering and science. Adaptivity is an important computational technology where the FEM algorithm is automatically tailored to compute a user specified output of interest to a chosen accuracy, to a minimal computational cost.
This FEM course aims to provide the student both with theoretical and practical skills, including the ability to formulate and implement adaptive FEM algorithms for an important family of PDEs.
The theoretical part of this course deals mainly with scalar linear PDE, for which the student should be able to:
derive the weak formulation.
formulate a corresponding FEM approximation.
estimate the stability of a given linear PDE and it's FEM approximation.
derive a priori and a posteriori error estimates in the energy norm, the L2-norm, and linear functionals of the solution.
state and use the Lax-Milgram theorem for a given variational problem.
In the practical part of the course the student should be able to:
modify an existing FEM program to solve a new scalar linear PDE.
implement an adaptive mesh refinement algorithm, based on an a posteriori error estimate derived in the theoretical part. | 677.169 | 1 |
Introduction: This page is a brief outline for Intermediate Algebra with Mr. Hoven.
Attendance: In nearly three decades of teaching, good attendance is one of the most important things that a student can have to help him/her be successful. If a class is missed, it is important to get caught up as soon as possible….math builds one day upon the previous.
Daily Work: In class work and homework are essential for success. Homework counts as 25% of the class grade. Work is due at the start of the next class period. Late work is given half credit, if turned in by the end of the current chapter.
Tests and Quizzes: Tests and quizzes account for 75% of the class grade. Retests are not given.
Office Hours and Extra Help: Mr. Hoven encourages all students to come in for extra help when needed. Office hours are available every morning before school that there is not a meeting (every Wednesday has a meeting). Students are kept informed as soon as possible when Mr. Hoven learns of a scheduled meeting. After school hours Monday through Thursday until 3:30 p.m. are available when there are no meetings.
Contact: Mr. Hoven checks voice mail and email each school day (unless out of the building for meeting or illness). Voice and email are not checked evenings or weekends. Every attempt will be made to respond within 24 hours. Voice mail is 768 – 5438 and email is [email protected]
Behavior: Appropriate behavior is expected from all students. If a student is not able to improve behavior, or if improper behavior is significant, parents/ guardians/ administration will possibly become involved.
Calculators: It is very helpful if your student has a scientific calculator. A graphing calculator is not necessary, but will be helpful (I lend out some graphing calculators during class time so all students can keep up with the graphing, when necessary). If purchasing a graphing calculator, the TI 83 and 84 series is the preferred calculator.
Books: Books are new and should be cared well cared for. The entire textbook is online and available for all students/ parents/ guardians… my.hrw.com with username and password both being : WHSINTALG.
Monday, April 1 - review for big quiz tuesday and .....see bottom of this page for quiz review copy
Tuesday, April 2 - big quiz...after quiz homework p. 740 #1-22
Wednesday, April 3 - p 747 #2-12
Thursday, April 4 - a day of learning...and no HW. absent should either read all of section 10-7 or watch the Dr. Berger videos from the my.hrw.com website...either way is acceptable.
Friday, April 5 - On the Packet (three hole punched...given to students last week...the first page says "Lesson 14" on it....Read example #1 on page 90...only pay attention to Mean, Median, Mode, and Range on all these problems. HW from page 92-93 is #1-4,8,9,24,25 Those in class will be doing a coin and card experimental probability.
Monday, April 8 - Finally grade p.747. Learn about combinations and permutations. p. 764 #1-12. Absent students must also, read their packets on lesson 19 and 20, and if they haven't already, do p.93 (in packet) #23 and 24. Also, below the Friday lesson plan...do the combination and permutation practice worksheet......UPDATE: YIKES, the lecture took too long...we did not get to the homework today.
Tuesday, April 9 - All day practice problems from the chapter worksheet....UPDATE....today we will do the combination and permutation practice worksheet listed below Friday April 12. Also, you will get the first page of the "pretend" test. Also, learn how to do Combinations and Permutations the long way, and the short way. HW page 764 #1-11.
Tuesday (period 4 and 6) Wednesday (period 3): Learn about compound interest...and the formula A = P (1 + r/n)^(nt)...no homework due to testing.
Thursday, April 18- Period 2 learn the A = formula along with the following:
All classes, graphs of exponentials. Homework for period 2 is p. 800 #5,8,10 and page 808 #2,3,5,16. For period 3,4,6 the homework is p.800 #3,4,5,9,18 and page 808 #2,3,4,5,14,15,16
Friday, April 19 - learn how to see if it's an exponential graph from a table. Homework is practice worksheets 11-2,11-3
Showing work, or what you did, can help you earn potential partial credit.
Forumlas: C = ( F – 32)
Probability of Independent Events: P (A and B) = P(A) * P(B)
Probability of Dependent Events: P (A and B) = P(A) * P(B after A)
1.The following are degrees in Fahrenheit. 55, 66, 66, 67, 84. Convert them to Celsius to the nearest tenth of a degree. Write them down. Calculate and/or state the mean, median, and range of these degrees.
2.How many committees (all members being equal) can be formed with 8 people choosing 4 people.
3.7 people out of 10 are going to line up. How many ways might this happen?
4.Calculate 5. Calculate
5.In faction form, what is the probability of rolling a number cube twice, and four showing up both times?
6.In fraction form, from a standard deck of cards without replacement (52 total cards, 4 of them are eights) what is the probability that you choose an eight, then your next pick you get another eight.
7.There is a class of 17 girls and 13 boys. Each day the teacher randomly gives one lucky student a Safety Sucker. Assuming no absences, in percent form, what is the probability that a girls is the lucky student two days in a row? | 677.169 | 1 |
Basic Geometry (5 periods, 5 credits)
Prerequisite: Algebra I
This course is designed for those students who are non-college bound and need additional support in mathematics. Basic concepts from geometry will be covered including properties from geometric figures and concepts of congruence and similarity. Students will work with parallel lines, triangles, polygons and circles. Perimeter, volume and area will be computed for plans and solid figures. Students will also review basic algebraic concepts.
Algebra II, College Prep (5 periods, 5 credits)
Prerequisites: Algebra I, Geometry and Teacher Recommendation
Algebra II is the third year of sequential mathematics for college bound students. This course stresses the relationship between concepts and skills and emphasizes analytical thinking skills and problem solving strategies that are essential to the mastery of advanced high school and college mathematics. | 677.169 | 1 |
MEL3E Grade 11 Mathematics for Work & Everyday Life
MEL3E Grade 11 Math Course Description
This MEL3E grade 11 math course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their thinking | 677.169 | 1 |
Damon Prealgebra hel...A branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. | 677.169 | 1 |
Online course materials are available through the MATH34042 page in Blackboard
Specification
Aims
To introduce nonlinear
discrete time dynamical systems and study some of their properties, in
particular the kinds of dynamics they can exhibit.
Brief Description of the unit
This course introduces
discrete time dynamical systems (iterated mappings) and analyses them
using the sort of qualitative approaches developed for continuous time
systems in MATH10202 or MATH10232. Mappings of the interval [0, 1] to
itself are studied in detail; these are simple examples of discrete time
systems but they can show remarkably complex dynamical behaviour,
including chaotic dynamics. The existence of fixed points and
periodic points is explored, and the way these change as the system
changes (bifurcation theory) is investigated. The basic ideas of
symbolic dynamics as a way of analysing dynamical systems is introduced,
and the method is used to show some simple maps have chaotic
behaviour.
Learning Outcomes
On successful completion of this course unit students will
have acquired a basic understanding of
discrete time dynamical systems on the interval;
be able to find the fixed and periodic
points of simple dynamical systems on the interval, and determine their stability;
have some familiarity with some of the
simpler bifurcations that fixed and periodic points can undergo;
have some familiarity with the notion of
self-similar fractals, and how they arise as attractors. | 677.169 | 1 |
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues.
In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems.
Included are
• an overview of computational methods together with their properties and advantages
• topics from statistical regression analysis that help readers to understand and evaluate the computed solutions
• many examples that illustrate the techniques and algorithms
Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.
This book aims to illustrate with practical examples the applications of linear optimization techniques. It is written in simple and easy to understand language and has put together a useful and comprehensive set of worked examples based on real life problems.
Mel Gibson teaching Euclidean geometry, Meg Ryan and Tim Robbins acting out Zeno's paradox, Michael Jackson proving in three different ways that 7 x 13 = 28. These are just a few of the intriguing mathematical snippets that occur in hundreds of movies. Burkard Polster and Marty Ross have pored through the cinematic calculus and here offer a thorough and entertaining survey of the quirky, fun, and beautiful mathematics to be found on the big screen.
Math Goes to the Movies is based on the authors' own collection of more than 700 mathematical movies and their many years using movie clips to inject moments of fun into their courses. With more than 200 illustrations, many of them screenshots from the movies themselves, this book provides an inviting way to explore math, featuring such movies as
• Good Will Hunting
• A Beautiful Mind
• Stand and Deliver
• Pi
• Die Hard
• The Mirror Has Two Faces
The authors use these iconic movies to introduce and explain important and famous mathematical ideas: higher dimensions, the golden ratio, infinity, and much more. Not all math in movies makes sense, however, and Polster and Ross talk about Hollywood's most absurd blunders and outrageous mathematical scenes. They round out this engaging journey into the realm of mathematics by conducting interviews with mathematical consultants to movies.
This fascinating behind-the-scenes look at movie math shows how fun and illuminating equations can be.
This magisterial annotated bibliography of the earliest mathematical works to be printed in the New World challenges long-held assumptions about the earliest examples of American mathematical endeavor. Bruce Stanley Burdick brings together mathematical writings from Mexico, Lima, and the English colonies of Massachusetts, Pennsylvania, and New York. The book provides important information such as author, printer, place of publication, and location of original copies of each of the works discussed.
Burdick's exhaustive research has unearthed numerous examples of books not previously cataloged as mathematical. While it was thought that no mathematical writings in English were printed in the Americas before 1703, Burdick gives scholars one of their first chances to discover Jacob Taylor's 1697 Tenebrae, a treatise on solving triangles and other figures using basic trigonometry. He also goes beyond the English language to discuss works in Spanish and Latin, such as Alonso de la Vera Cruz's 1554 logic text, the Recognitio Summularum; a book on astrology by Enrico Martínez; books on the nature of comets by Carlos de Sigüenza y Góngora and Eusebio Francisco Kino; and a 1676 almanac by Feliciana Ruiz, the first woman to produce a mathematical work in the Americas.
Those fascinated by mathematics, its history, and its culture will note with interest that many of these works, including all of the earliest ones, are from Mexico, not from what is now the United States. As such, the book will challenge us to rethink the history of mathematics on the American continents.
In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices.
The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world's population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness?
In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders.
These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry | 677.169 | 1 |
MATLAB for Engineers, 3e, is ideal for Freshman or Introductory courses in Engineering and Computer Science. With a hands-on approach and focus on problem solving, this introduction to the powerful MATLAB computing language is designed for students with only a basic college algebra background. Numerous examples are drawn from a range of engineering disciplines, demonstrating MATLAB's applications to a broad variety of problems. This book is included in Prentice Hall's ESource series. ESource allows professors to select the content appropriate for their freshman/first-year engineering course. Professors can adopt the published manuals as is or use ESource's website to view and select the chapters they need, in the sequence they want. The option to add their own material or copyrighted material from other publishers also exists.
You can earn a 5% commission by selling MATLAB for Engineers | 677.169 | 1 |
When Less Is More
Claudi Alsina and Roger Nelsen
Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often, especially in secondary and collegiate mathematics, the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they donít possess the richness and variety that one finds with inequalities.
The objective of this book is to illustrate how the use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and the authors will convince you that the same is true when working with inequalities. They show how to produce figures in a systematic way for the illustration of inequalities and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument cannot only show two things unequal, but also help the observer see just how unequal they are.
The concentration on geometric inequalities is partially motivated by the hope that secondary and collegiate teachers might use these pictures with their students. Teachers may wish to use one of the drawings when an inequality arises in the course. Alternatively, When Less Is More might serve as a guide for devoting some time to inequalities and problem solving techniques, or even as part of a course on inequalities. | 677.169 | 1 |
Description
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Practice Makes Perfect: Algebra, provides students with the same clear, concise approach and extensive exercises to key fields they've come to expect from the series-but now within mathematics. This book presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations. Practice Makes Perfect: Algebra is not focused on any particular test or exam, but complementary to most algebra curricula. Because of this approach, the book can be used by struggling students needing extra help, readers who need to firm up skills for an exam, or those who are returning to the subject years after they first studied algebra.
Recommendations:
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Welcome Back!!! updated January 8, 2012
Welcome to my class! I am so excited about this year. We are going to learn a lot and have fun doing so. In order for this to happen, I need you to do a few things for...
CCGPS Coordinate Algebra
This is the first course in a sequence of courses designed to provide students with a rigorous
program of study in mathematics. It includes radical, polynomial and rational expressions, basic
functions and their graphs, simple equations, complex numbers; quadratic and piecewise
functions, sample statistics, and curve fitting.
I have scheduled weekly help sessions for Coordinate Algebra on Monday afternoons, Wednesday mornings, and Thursday afternoons. I will be available on these days and times unless I have a department meeting, faculty meeting, or parent conference.
This is the second in a sequence of mathematics courses designed to prepare students to take AB or BC Advanced Placement Calculus. It includes right triangle trigonometry; exponential, logarithmic, and higher degree polynomial functions; matrices; linear programming; vertex-edge graphs; conic sections; planes and spheres; population means, standard deviations, and normal distributions.
I have scheduled weekly help sessions for Accelerated Math 2 on Tuesday mornings, Tuesday afternoons, and Thursday mornings. I will be available on these days and times unless I have a department meeting, faculty meeting, or parent conference. | 677.169 | 1 |
A calculator that shows how it got its answer! It supports variables (X, Y, Z etc.) and many pre-defined constants such as Pi etc. It also has most if not all the functions of a Scientific calculator.
It was coded in VB6 but was updated and is now VB.NE
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and moreFuniter (FUNction ITERation) is developed for educational purposes, generating graphs of several types for iteration of real and complex functions with comfortable switching between related types of graphs.
An efficient 2D Simple Graphing program for windows, perfect for plotting collected data incorporating features of cricket graph which allow you to apply a function to all your data.
Regression Lines for data.
The algorithm allows any kind of weights (costs, frequencies), including non-numerical ones. The {0, 1, ..., n-1} alphabet is used to encode message. Built tree is n-ary one.The algorithm is based on a set of template classes : Cell(SYMBOL, WEIGHT), Node(
GeoCalculator, the new latest thing in geometrical math. GeoCalculator is your one stop for solving any geometry-related equations. Features such as Triangle Solvers, Polygon Finders, and TONS of equations lets you solve ALL equations that you need.
This is an attempt to make a portable, efficient, and abstract set of C++ classes which manipulate algebraic expressions. I wrote it to explore C++ inheritance and polymorphism and it's extremely likely this project is the wrong solution for you. | 677.169 | 1 |
Based on recent research on the adolescent brain, Active Algebra presents a living, working example of how teachers can use active learning techniques to make linear relationships more meaningful for students. In addition to the 10 reproducible, sequenced lessons, this award-winning resource offers seven chapters of guidance in teaching algebra.
Review by Kay Gilliland, from the the 2010 NCSM Spring Newsletter.
After describing a hilarious incident in his classroom, Dan Brutlag comments in Active Algebra: Strategies for Successfully Teaching Linear Relationships ". . . the truth is that the mathematical logic often makes no sense at all to these students. That is why textbook presentations consisting of clear, logical examples and explanations, although necessary, usually are not sufficient to teach mathematics to adolescents." How true, and how often we as mathematics leaders have tried to say this! Active Algebra does this for us, helping teachers build awareness of adolescents' thinking and behavior. Brutleg explains what he considers to be active learning in algebra involving the whole brain: listening, reading, writing, speaking, movement, social interaction, visualizing, and imagining. He includes lessons designed to build connections across large areas of the brain, mental mathematics exercises designed to stretch students' memory and recall, and a 10-lesson unit that focuses on understanding linear functions numerically, graphically, and symbolically. A CD of the 10 lessons comes with the book. Brutleg carefully explains the teacher's role in the lessons and peppers the text with real incidents from his own classroom.
2010 Winner Distinguished Achievement Award:
Professional Development: Learning Styles
The Association of Educational Publishers (AEP) Awards seal is recognized by teachers and parents as a mark of excellence in education. Finalist or winner status in the awards tells readers that the product has met rigorous standards for quality, professional content for education. | 677.169 | 1 |
Problem Solving
9780759342644
0759342644
Summary: Problem Solving provides students with a general approach and strategies to solve problems in real life. The text is easy to read and geared mainly for students who dislike math. Problems throughout the book range from easy to difficult, and require minimal mathematical experience. While possessing knowledge is one important requirement to solving problems, there are many others. Problem Solving focuses on providing ...strategies to help students become proactive, successful, and confident problem solvers.[read more] | 677.169 | 1 |
Mathematics for Physicists
9780534379971
ISBN:
0534379974
Pub Date: 2003 Publisher: Thomson Learning
Summary: This essential new text by Dr. Susan Lea will help physics undergraduate and graduate student hone their mathematical skills. Ideal for the one-semester course, MATHEMATICS FOR PHYSICISTS has been extensively class-tested at San Francisco State University--and the response has been enthusiastic from students and instructors alike. Because physics students are often uncomfortable using the mathematical tools that they... learned in their undergraduate courses, MATHEMATICS FOR PHYSICISTS provides students with the necessary tools to hone those skills. Lea designed the text specifically for physics students by using physics problems to teach mathematical concepts.[read more] | 677.169 | 1 |
GCSE Mathematics
Content of Course
The GCSE in Mathematics gives students the opportunity to develop the ability to acquire and use problem-solving strategies, select and apply mathematical techniques and methods in mathematical, every day and real-world situations. It also allows you to be able to reason mathematically, make deductions and inferences and draw conclusions and interpret and communicate mathematical information in a variety of forms.
Teaching of this Mathematics GCSE began in 2010 (first examination is in June 2012) and it still has its focus on number, algebra, geometry, measures, statistics and probability but also allows you to apply the functional elements and problem solving strategies required to use mathematics in everyday life. Within the department there is a Co-ordinator of Mathematics and a member of staff in charge of each key stage.
The course has 2 examinations of 1 hour 45 minutes per paper (Higher tier – Grades A* to C) and 1 hour 30 minutes per paper (Foundation tier – Grades C to G). One paper is non-calculator, the other a calculator is allowed. There is no coursework or controlled assessment.
3 good reasons why a good grade in maths is so important:
A vast array of potential future careers will be opened up to you, for example: | 677.169 | 1 |
Mathematics for the Trades : A Guided Basic Math, Math for the Trades, Occupational Math, and similar basic math skills courses servicing trade or technical programs at the undergraduate/graduate level.THE leader in trades and occupational mathematics,Mathematics for the Trades: A Guided Approach focuses on fundamental concepts of arithmetic, algebra, geometry, and trigonometry. It supports these concepts with practical applications in a variety of technical and career vocations, including automotive, allied health, welding, plumbing, machine tool, carpentry, auto mechanics, HV... MOREAC, and many other fields. The workbook format of this text makes it appropriate for use in the traditional classroom as well as in self-paced or lab settings. For this revision, the authors have added over 150 new applications, new chapter summaries for quick review, and a new chapter on basic statistics. Student will find success in this clear and easy to follow format which provides immediate feedback for each step the student takes to ensure understanding and continued attention.
MATHEMATICS FOR THE TRADES: A GUIDED APPROACH, 9/e focuses on the fundamental concepts of arithmetic, algebra, geometry and trigonometry needed by learners in technical trade programs.
The authors interviewed trades workers, apprentices, teachers, and training program directors to ensure realistic problems and applications and added over 100 new exercises to this edition. Geometry, triangle trigonometry, and advanced algebra. For individuals who will need technical math skills to succeed in a wide variety of trades. | 677.169 | 1 |
Using the Spreadsheet to Develop an Intuitive Understanding of the Limit Concept
Phyllis Brudney, Marilyn Keir and Mary Viruleg
Abstract
Students who have successfully completed algebra and have studied some geometry should have success with this module. The purpose is to lead the student to an intuitive understanding of the limit concept. It includes three activities which may be used independently or sequentially. The activities take the student from the discreet to the continuous beginning with a geometric model which is easily visualized and culminating with the more theoretical case of the limit of a function.
Technology
This module requires the use of a spreadsheet program such as Excel or Microsoft WORKS. Students should be familiar with basic spreadsheet capabilities, including the use of formulas and replication.
Teacher Notes
The three activities which accompany this module may be used independently. Each involves the use of the spreadsheet to observe and draw conclusions based on patterns in a sequence. Activity 0 is a geometry activity. Activity 1 should be introduced once students have studied and discussed different kinds of sequences and their behavior. Activity 2 gives students who understand sequences an opportunity to explore infinite geometric series and to discover the conditions under which they have a sum. Activity 3 allows students to examine the classic - definition of the limit of a function and to work toward an intuitive understanding of this fundamental idea.
Activity 0 : Using Spreadsheets to Study Circle Measurements
Use your spreadsheet to find a relationship between regular polygons and circles. If we consider regular polygons with radius, r, and n sides, beginning with n = 3 and watch what happens to the perimeter of the polygon as the number of sides increases, we will discover a relationship between the sequence of perimeters and the circumference of the circle with the same radius. A similar relationship exists between polygonal areas and the area of the circle.
To set up your worksheet:
Col A number of sides, n
Col B perimeter of polygon with n sides
Col C area of polygon with n sides.
Set aside cells for the value of r, and for the circumference and area of the circle with radius, r.
To calculate the perimeter of an n-sides polygon with radius, r:, (Column C)
= = x =
s = 2 r sin (/n)
perimeter = n s
= 2 n r sin(/n)
To calculate the area of each regular polygon: (Column D)
Area = .5 a p (perimeter is in Col C)
= .5 (r cos (/n) p
Calculate the circumference of the circle with radius, r. Compare your result with the sequence of perimeters. What do you find?
Calculate the area of the circle with radius, r. Compare it with the sequence of areas. What do you find?
Activity 0: Circumference and area of a circle using limits
You must enter the radius of your polygon.
Circle with radius r:
radius =
4
Perimeter =
Area =
25.1327412
50.2654825
Number of sides
Perimeter
Area
3
20.7846
20.7846
4
22.6274
32.0000
5
23.5114
38.0423
6
24.0000
41.5692
7
24.2975
43.7826
8
24.4917
45.2548
9
24.6255
46.2807
10
24.7214
47.0228
11
24.7925
47.5764
12
24.8466
48.0000
13
24.8888
48.3312
14
24.9223
48.5950
A
C B
D
Formulas for spreadsheet
Number of sides
Perimeter
Area
3
=A8*2*C$4*SIN(PI()/A8)
=C8/2*C$4*COS(PI()/A8)
=A8+1
=A9*2*C$4*SIN(PI()/A9)
=C9/2*C$4*COS(PI()/A9)
=A9+1
=A10*2*C$4*SIN(PI()/A10)
=C10/2*C$4*COS(PI()/A10)
Activity 1: Infinite Geometric Sequence and Iteration
INSTRUCTIONS:
1. Set up spreadsheet to find N(R) = .
2. Label columns N, N(R), and N(N(R)).
3. Off to the side, label entry R and put a constant value in for R.
4. Start N at 0 counting by increases of 1 for the first experiment.
5. Increment N by more than 1 for following trials in each experiment.
EXPERIMENT #1:
1. Set an arbitrary R in a cell off to the right.
2. Fill in down columns labeled N, R, N(R), and N(N(R)).
3. Record observations about N(R) & N(N(R)).
4. Reset increments of N. Record observations.
5. Reset values for R 20 times. Record observations each time.
6. Answer questions: For which values of R do N(R) and N(N(R)) have limits?
Does incrementing N differently make any difference?
Are there different limits for N(R) and N(N(R))?
EXPERIMENT #2:
1. Now try N(R) = K *.
2. Set up a cell off to the right for K and enter a value.
3. Repeat process in experiment #1 for different values of R and K.
4. Record observations.
5. Answer the same questions as #6 in experiment #1.
EXPERIMENT #3:
1. Now try N(R) = K*+C where C is a constant.
2. Set up a cell off to the right for C and enter a value.
3. Repeat process in experiments #1 and #2 for different values of R, K, and C.
4. Record observations.
5. Answer the same set of questions as before.
CONCLUSION:
1. Do you see any overall patterns? Explain.
2. Do any specific R's produce different results? Explain.
3. Do any specific K's produce different results? Explain.
4. Do any specific C's produce different results? Explain.
5. Do any of your observations suggest that N(R) approaches a limit?
6. Do any of your observations suggest that N(N(R)) approaches a limit?
7. Is this a discrete or a continuous model?
8. What can you say overall for N(R) = K* + C?
INFINITE SEQUENCE
N(R)=R^N
N(N(R))=PREVIOUS N(R)^N
REMEMBER TO NOTE OBSERVATIONS OF THE CHANGE IN N(R) & N(N(R))
PERFORM THE EXPERIMENT WITH ONE R; RECORD OBSERVATIONS;
CHANGE R; REPEAT TRIAL; USE R>1 & 0<R<1
N
N(R)
N(N(R))
R
0
1
1
0.01
1
0.01
0.01
2
0.0001
1E-08
3
0.000001
1E-18
4
0.00000001
1E-32
5
1E-10
1E-50
6
1E-12
1E-72
7
1E-14
1E-98
8
1E-16
1E-128
9
1E-18
1E-162
10
1E-20
1E-200
11
1E-22
1E-242
12
1E-24
1E-288
13
1E-26
0
14
1E-28
0
15
1E-30
0
16
1E-32
0
17
1E-34
0
18
1E-36
0
19
1E-38
0
20
1E-40
0
21
1E-42
0
22
1E-44
0
23
1E-46
0
24
1E-48
0
EXPERIMENT #1
Trial#
R2
Trial#
R
K3
Trial#
R
K
CInvestigating the Sum of an Infinite Geometric Series
Technology: This activity requires the use of a spreadsheet program such as Excel or Microsoft WORKS. Students should be familiar with basic spreadsheet capabilities, including the use of formulas and replication.
Teacher notes: Introduce this activity once students have studied the behavior of different kinds of sequences and have been introduced to series.
Series: If you add the terms of a sequence, the sum is called a series. For example, the sequence: 3, 7, 11, 15,... yields the series: 3 + 7 + 11 + 15 + ...
The n-th partial sum of a series is the sum of the first n terms of that series and is represented by Sn . For the example above,
S1 = 3
S2 = 3 + 7 = 10
S3 = 3 + 7 + 11 = 21
S4 = 3 + 7 + 11 + 15 = 36
Notice that the partial sums also form a sequence: 3, 10, 21, 36, ... A partial sum is often represented using "sigma" notation. If t k represents the k-th term of the sequence, the n-th partial sum can be represented:
Sn =
If the series is infinite, it may or may not be useful to study the behavior of the sequence of its partial sums. For example, the series: 1 + 6 + 11 + 16 + 21 + ... has partial sums that just keep getting bigger as n increases. Examining the partial sums of infinite geometric series leads to more interesting conclusions.
Consider the infinite geometric series:5 + + + + ...
The first few partial sums are: S1 = 5
S2 =5 + = 7
S3 = 5 + + = 8
S4 =5 + + + = 9
S5 =5 + + + + = 9
The partial sums are increasing, but they seem to be getting closer (converging) to 10. We say that series converges to a number, S, if its sequence of partial sums, Sn , converges to that number, S.
Exploring Infinite Series on the Spreadsheet
Use your spreadsheet to construct the following:
Col A The value of n (the number of the term).
Col B The terms of the sequence from 1 to n.
Col C The sequence of partial sums.
For each sequence, list an approximation for the i-th term requested and for the i-th partial sum. Also, give the limit of the sequence, if it exists, and the limit of the sequence of partial sums. Generate at least twenty terms of each sequence and associated series.
1. The geometric sequence with first term: 4 and r =
t18 = __________________ S10 = __________________________
limit tn = ______________ limit Sn = ______________________
2. The geometric sequence with first term: .4 and r = -1.2
t14 = __________________ S14 = _________________________
limit tn = ______________ limit Sn = _____________________
3. The geometric sequence with first term: 1.75 and r =
t19 = __________________ S13= _________________________
limit tn = ______________ limit Sn = _____________________
4. The geometric sequence with first term: 4 and r =
t9 = __________________ S14 = _________________________
limit tn = ______________ limit Sn = _____________________
5. The geometric sequence with first term: 100 and r = .8
t12= __________________ S20 = _________________________
limit tn = ______________ limit Sn = _____________________
Conjecture: An infinite geometric series converges to a number, S, when the value
Bouncing Ball Problem. Suppose that you drop a ball from a window 18 meters above the ground. The ball bounces up to 80% of its previous height with each bounce. How far does the ball travel between the first and second bounce? Between the second and third bounce? Between the third and fourth bounce?
If the ball continues to bounce this way until coming to rest, how far has it traveled from the time it was dropped from the window?
Nested Squares Problem. A set of nested squares is drawn inside a square of edge 1 unit. The corners of the next square are the midpoints of the sides of the preceding square.
Set up four columns on your spreadsheet:
Col A The level of your drawing. Let the original square be level 1.
Col B The length of a side of each new square in the figure.
Col C The area of each new square formed.
Col D The cumulative sum of all the squares starting with square 1.
Use your worksheet to answer the following:
1. What is the length of the side of the 11th square formed by this process? _______
2. How is the length of the sides of the squares changing? ____________________
3. What is the area of the fourth square? _____ ...of the eighth square? _________
4. How is the area of the squares changing? ________________________________
5. What is the sum of the areas of the first 6 squares? _____ ...of the first 7? _____
6. What finite number does this area sum seem to be approaching?______________
7. Does the sum of the perimeters seem to be approaching a finite number? _______
Activity 3: Informal Investigation of the Limit of a Function
Technology: This activity requires the use of a spreadsheet program such as Excel. The students should have enough familiarity with spreadsheet use to put the appropriate formulas in the spreadsheet.
Teacher notes:The teacher should set up the spreadsheet in advance. The formulas used are listed here: (Thanks to David Bannard for the spreadsheet layout.)
C D E F G H
Right
Left
x
y =
x
y =
=B11
=SIN(C11)/C11
=$B$12-($B$11-$B$12)
=SIN(E11)/E11
=$B$14+$B$15
=$B$14-$B$15
=(C11+$B$12)/2
=SIN(C12)/C12
=(E11+$B$12)/2
=SIN(E12)/E12
=$B$14+$B$15
=$B$14-$B$15
=(C12+$B$12)/2
=SIN(C13)/C13
=(E12+$B$12)/2
=SIN(E13)/E13
=$B$14+$B$15
=$B$14-$B$15
Setting up the graph chart takes a bit of doing. To get both left and right limits on the same graph, you must begin with the , , [add series] commands after you have the initial graph. To set it up for the right, chart C to D for the function, C to G and C to H for the epsilon line. On the left for the same lines, chart E to F, E to G and E to H.
The student screen should be so that the chart shows as well as the spreadsheet. The students should be encouraged to play around with it awhile and get comfortable with what each of the columns is showing, and how to tell what the limit is and when you have selected a good epsilon for a given delta.
Student Activity Sheet on the Limit of a Function
Idea of a limit: The mathematical statement of a limit is written : f(x) = L
The intuitive idea of a function approaching a limit says that as x gets close to some value, a the value of the function f(x) gets close to some limit, L. You can generally get a good idea of what limit a function is approaching by using your graphing calculator.
A more formal definition of a limit:
f(x) = L means that for any small epsilon (e) you select, you can find a delta ( ) such that whenever 0<|x-a| < then 0<|f(x)-L|< e.
Instructions: Enter each function on the spreadsheet in both column D and F using column C and column E as the x value, respectively. Be certain to copy the formula down in the column. For each, pick an x start value near the a value and try to determine the limit of the function. When you have determined the limit, find a delta which will give you an epsilon < .001. When you have succeeded, your graph on the spread sheet should `fill' the area between the two lines of the epsilon. Like this:
If the function crosses the epsilon line, then your delta is too large. If it doesn't `fill' the area, it is too small. | 677.169 | 1 |
Algebra 1
Class.com algebra courses provide the rigorous curriculum of a traditional classroom, with ample opportunities to practice concepts, refine skills, learn new material, and build math vocabulary. Among many cutting-edge and interactive features, our algebra courses include the following:
Contextualized content that connects algebra to real life
Simulated blackboard that presents step-by-step examples
Interactive geometry software that allows students to manipulate variables and graph points with immediate feedback
Writing assignments and discussion groups
Computer-graded self-checks, quizzes, and final exam
Algebra 1A
Algebra 1A, designed as the first semester of a middle- or high school math course, introduces students to algebra and illustrates its relevance in today's world. Students evaluate expressions, graph and solve linear functions and inequalities, and learn problem-solving strategies. Scope and Sequence
Algebra 1B
Algebra 1B is the second semester of a middle- or high school math course. Students continue their progression through algebraic concepts, expanding their knowledge of functions and relations, simplifying rational and radical expressions, solving and graphing radical and quadratic equations and inequalities, and analyzing data and making predictions. Students are introduced to graphing calculators in this course. Scope and Sequence | 677.169 | 1 |
What is Calculus About?
W. W. Sawyer
What is Calculus About? gives students the big picture of calculus. It should be read by prospective and current calculus students and by their teachers. Even someone who has completely mastered the technical side of the subject can benefit from being reminded of the essentially simple ideas and the calculational needs that led mathematicians to develop the rather complex machinery of calculus. Sawyer deals with it all, from what background a student needs to begin, to the study of speed and acceleration, to graphing (slope and curvature), to areas, volumes, and the integral. | 677.169 | 1 |
Welcome to the Orange High School
Math Department
The Mathematics Department offers a variety of courses to help students acquire prerequisite skills needed for future careers. The number of units a student needs for graduation depends upon the course of study chosen at the high school level. Please refer to the State of North Carolina Department of Public Instruction web site about graduation requirements at:
The use of calculators is required in all math classes at Orange High School. Many upper-level math classes assume that a student has access to a graphing calculator at home. Consistently paced practice of mathematics is a necessity and thus students will usually have homework daily. Mathematics is the language for many subjects and applications allow students to use mathematics. Students will be expected to solve problems allowing them to see to power of mathematics in their daily lives. Having students become better problem solvers is a goal of the mathematics department. | 677.169 | 1 |
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