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We will provide students with experiences that will enhance their ability to understand mathematics and the mathematical procedures necessary to make informed judgments on issues, to act as wise consumers, and to come to logical determinations as they pertain to personal and professional endeavors.
The purpose of the mathematics curriculum at Assabet Valley is to:
Provide a rigorous and relevant course of studies to meet the needs of all students Prepare all students for all graduation requirements of the Commonwealth of Massachusetts and of Assabet Valley Regional Technical High School Instruct students in how to reason, solve problems and to produce a level of competence required for their high school years and their adult lives Provide a rigorous and relevant course of studies to meet the needs of all students
Our curriculum provides students with the opportunities to develop a foundation from which they can pursue a profession and/or further their education at a higher level, such as two or four year colleges. | 677.169 | 1 |
Major Features of the Text
A Balanced Approach: Form, Function, and Fluency
Form follows function. The form of a wing follows from the function of flight. Similarly, the form of an algebraic expression or equation reflects its function. To use algebra in later courses, students need not only manipulative skill, but fluency in the language of algebra, including an ability to recognize algebraic form and an understanding of the purpose of different forms.
Restoring Meaning to Expressions and Equations
After introducing each type of function — linear, power, quadratic, exponential, polynomial — the text encourages students to pause and examine the basic forms of expressions for that function, see how they are constructed, and consider the different properties of the function that the different forms reveal. Students also study the types of equations that arise from each function.
Maintaining Manipulative Skills: Review and Practice
Acquiring the skills to perform basic algebraic manipulations is as important as recognizing algebraic forms. Algebra: Form and Function provides sections reviewing the rules of algebra, and the reasons for them, throughout the book, numerous exercises to reinforce skills in each chapter, and a section of drill problems on solving equations at the end of the chapters on linear, power, and quadratic functions.
Students with Varying Backgrounds
Algebra: Form and Function is thought-provoking for well-prepared students while still accessible to students with weaker backgrounds, making it understandable to students of all ability levels. By emphasizing the basic ideas of algebra, the book provides a conceptual basis to help students master the material. After completing this course, students will be well-prepared for Precalculus, Calculus, and other subsequent courses in mathematics and other disciplines.
Changes Since The Preliminary Edition
NEW — four new chapters on summation notation, sequences and series, matrices, and probability and statistics.
The initial chapter reviewing basic skills is now three shorter chapters on rules and the reasons for them, placed throughout the book.
NEW — Focus on Practice sections at the end of the chapters on linear, power, and quadratic functions. These sections provide practice solving linear, power, and quadratic equations.
NEW material on radical expressions in Chapter 6, the chapter on the exponent rules.
NEW material on solving inequalities, and absolute value equations and inequalities, in Chapter 3, the chapter on rules for equations. | 677.169 | 1 |
This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition.
Table of Contents for The Origins of Cauchy's Rigorous Calculus
1. Cauchy and the Nineteenth-Century Revolution in Calculus
2. The Status of Foundations in Eighteenth-Century Calculus
3. The Algebraic Background of Cauchy's New Analysis
4. The Origins of the Basic Concepts of Cauchy's Analysis: Limit, Continuity, Convergence | 677.169 | 1 |
Student Solutions Manual for Cohen/Lee/Sklar's Precalculus, 7th
Book Description: Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. | 677.169 | 1 |
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Self taught mechanical drawing and elementary machine design
SELF TAUGHT MECHANICAL DRAWING AND ELEMENTARY MACHINE DESIGN
A Treatise Comprising the First Principles of Geometric and Mechanical Drawings Workshop Mathematics, Mechanics, Strength of Materials, and the Design of Machine Details, including Cams, Sprockets, Gearing, Shafts, Pulleys, Belting, Couplings, Screws and Bolts, Clutches, Flywheels, etc. Prepared for the Use of Practical Mechanics and Young Draftsmen.
The demand for an elementary treatise on mechanical drawing, including the first principles of machine design, and presented in such a way as to meet, in particular, the needs of the student whose previous theoretical knowledge is limited, has caused the author to prepare the present volume. It has been the author's aim to adapt this treatise to the requirements of the practical mechanic and young draftsman, and to present the matter in as clear and concise a manner as possible, so as to make "self-study" easy. In order to meet the demands of this class of students, practically all the important elements of machine design have been dealt with, and, besides, algebraic formulas have been explained and the elements of trigonometry have been treated in a manner suited to the needs of the practical man.
In arranging the material, the author has first devoted himself to mechanical drawing, pure and simple, because a thorough understanding of the principles of representing objects greatly facilitates further study of mechanical subjects; then, attention has been given to the mathematics necessary for the solution of the problems in machine design presented later, and to a practical introduction to theoretical mechanics and strength of materials; and, finally, the various elements entering in machine design, such as cams, gears, sprocket wheels, cone pulleys, bolts, screws, couplings, clutches, shafting, flywheels, etc., have been treated. This arrangement makes it possible to present a continuous course of study which is easily comprehended and assimilated even by students of limited previous training.
Portions of the section on mechanical drawing was published by the author in The Patternmaker several years ago. These articles have, however, been carefully revised to harmonize with the present treatise, and in some sections amplified. In the preparation of the material, the author has also consulted the works of various authors on machine design, and credit has been given in the text wherever use has been made of material from such sources.
General Principles. In designing machinery it is frequently desirable to give to some part of the mechanism an irregular motion. This is often done by the use of cams, which are made of such form that when they receive motion, either rotary or reciprocating, they impart to a follower the desired irregular motion.
The follower is sometimes flat, and sometimes round. When the follower is round it is usually made in the form of a wheel or roller, so as to lessen the wear and the friction. The follower may work upon the edge of the cam, or if round, it may work in a groove formed either on the face or on the side of the cam.
The working surfaces of cams with round followers are laid out from a pitch line, so called, which passes through the center of the follower. The shape of this pitch line determines the work which the cam will do. The working surface of the cam is at a distance from the follower equal to one-half the diameter of the follower. This principle of a pitch line holds good whether the cam works only upon its edge like the one shown in Fig. 139, or whether it has an outer portion to insure the positive return of the follower. This outer portion is frequently made in the form of a rim of uniform thickness around the groove.
Design a Cam Having a Straight Follower Which Moves Toward or From the Axis of the Cam, as Shown in Fig. 136. Let it be required that the follower shall advance at a uniform rate from a to b as the cam makes a half revolution, this advance being preceded and followed by a period of rest of
a twelfth of a revolution of the cam.
Divide that half of the cam during the revolution of which the follower is to be raised from a to b, in this case the half at the right of the vertical center line, into a number of equal angles, and divide the distance from a to b into the same number of equal spaces. Mark off the points so obtained onto the successive radial lines as indicated by the dotted lines, and at the points where these dotted lines intersect the radial lines draw lines at right angles to the radial lines to represent the position of the follower when these radial lines become vertical as the cam revolves.
A period of rest in a cam is represented by a circular portion, having the axis of the cam as its center. In order, therefore, to obtain the required periods of rest, the distances of a and b from the center are marked off upon the radial lines c and d, these lines being made a twelfth of a revolution from the vertical center line, and lines representing the follower are drawn at these points as before. To get the return of the follower the space from c to d is divided into a number of equal angles, and the distance from e to f is divided off to represent the desired rate of return of the follower. In this case the rate of return is made uniform, so the distance ef is spaced off equally. The distance of these points from the axis is marked off upon the radial lines between c and d, and lines representing the follower are drawn.
A curved line, which may be made with the aid of the irregular curves, which is tangent to all of the lines representing the follower, gives the shape of the cam.
Fig. 137 shows a cam having the conditions as to the rise, rest and return of the follower the same as the one shown in Fig. 136, the follower, however, being pivoted at one end.
Draw the arc ab representing the path of a point in the follower at the vertical center line, and divide that part of the arc through which the follower rises into the same number of equal spaces as the half circle at the right of the vertical center line is divided into angles. Through these points draw lines, as shown, representing consecutive positions of the working face of the follower. The various distances of the follower from the axis of the cam are now marked off upon the corresponding radial lines as before. Lines to represent the follower are now drawn across each of these radial lines, at the same angle to them that the follower makes with the vertical center line when at that part of its stroke corresponding to the particular radial line across which the line representing the follower is being drawn. A curved line passing along tangent to all of these lines gives the shape of the cam as before.
Design a Cam with a Round Follower Rising Vertically. In Fig. 138 the follower has the same uniform rise, and the same periods of rest as before.
A cam with a round follower is less limited in its capabilities than one with a straight follower; in the one here shown the follower on its return drops below the position in which it is shown. That part of the cam during which the conditions are the same as in the others is divided off and the position of the center of the follower upon the radial lines is obtained in the same manner as before. That part of the cam representing the return of the follower is divided into such angles as desired, and the distance through which the follower is to drop as the cam revolves through each of these angles is marked off upon the proper radial line. A curved line which is now made to pass through all of the points so obtained gives the pitch line of the cam.
In drawing such a cam it is not always necessary to fully draw the working faces. The pitch line and the method of obtaining it being shown, a number of circles representing consecutive positions of the follower may be drawn. This will usually be sufficient. The side view of the cam, which in a case like this would naturally be made in section, will give opportunity to show any further detail that may be desired.
Design a Cam with a Round Follower Mounted on a Swinging Arm. Fig. 139 shows such a cam, all of the conditions as to rise, rest and return of the follower being the same as in the cam shown in Fig. 138. The cam is divided into the same angles as before, and the position of the follower is laid out on these radial lines as though it moved vertically. | 677.169 | 1 |
The class meets six times a week: four times in lecture, once in conference,
and once in the computer laboratory. You are responsible for any and all
material discussed in lecture, conference, and lab.
Aside from the 6 hours that you spend in class each week, you should devote
at least another 8-10 hours to studying on your
own: reading the book, reading and organizing your notes, solving problems.
Conferences:
In the Friday conference sessions, you will meet with the Peer Learning
Assistant (PLA) for the class. You will be able to ask the PLA questions on the material
covered and homework. The PLA may lso give you in-class assignments and
review course material.
Homework: Written Homework: Problems will be assigned for each section of the
book covered and will be posted on the class web page. It is necessary to do,
at a minimum, the assigned problems so that you can learn and understand
the mathematics. You should do additional problems for further practice.
Working the exercises will help you learn, and give you some perspective
on your progress. You are welcome to
discuss homework problems with one another but you must write up your homework
solutions on your own. Be mindful of your academic integrity.
Your homework will be collected at the beginning of each Monday's class.
Late homework will not be accepted.
If you must miss Monday's class, you should have your work turned in before class time in order for it to be graded.
Do not wait until the weekend to start your homework.
Work on the problems daily.
Your work should be very legible and done neatly. If the work is not
presentable, and is illegible, you will not receive credit for it. Please staple
the sheets of your assignment together. Do not use paper torn out of spiral
bound notebooks. In the upper right hand corner of your assignment you
should write your name, the class section number, and the list
of book sections for the assignment.
Discipline yourself to write clear readable solutions,
they will be of great value as review.
You
need to show both your answer and the work leading to it. Merely having
the right answer gets no credit - we can all look them up in the back of the
book.
Online Homework: There will be homework using the online tool
WebWork. This is the same software that you used for the Math Placement Exam
that you took during the summer. There will occasionally be 7-15 questions
on WebWork that must be done. Go to
Do not use the WebWork system to email for help on problems; such an
email will be sent to all the professors and assistants for all the sections of
MA1022! Instead, see Prof. Weekes or your PLA as soon as possible.
Quizzes:
Each Monday, there will be a 15-20 minute in-class quiz emphasizing the
most recently covered topics. If you miss a quiz for any reason (illness, travel,
etc.), you will receive a score of zero. However, don't worry, the lowest quiz
score will be dropped. Make-up quizzes will, thus, never be given.
Labs:
Each week, students will meet in the computer lab (SH003) with the
Instructor's Assistant (IA) who is Jane Bouchard. We will use the computer
algebra system, Maple V, as a visual and computational aid to help you explore
the mathematical theory and ideas of the calculus. You will not be given
credit for a lab report if you did not attend the lab.
There are no make-up labs.
The first lab will be on Oct. 31st/Nov. 1st.
The final lab will be on Dec. 5th/Dec. 6th.
Final Exam/Basic Skills Test:
On Wednesday 12th December from 7-9 pm, you will have a 2 hour comprehensive final examination. Make arrangements now so that there are no
con
flicts with the final exam.
The Final Assessment will consist of two parts. The first part is the Final
Exam which is used in determining your course average score as detailed before.
The other part is the Basic Skills Exam. You cannot pass the course if you do not pass the
Basic Skills Exam.
Students with failing averages in the course are given grades of NR, whether
or not they passed the Basic Skills exam.
If you pass the Basic Skills component, then your course average will be used
by the professor to determine your grade for the course.
If you fail the Basic Skills Exam, yet have what the instructor determines
to be a course average high enough to pass the course, you will be given a
grade of I (incomplete). You will be given the opportunity to re-take the
Basic Skills exam at a later date; if you pass it, you will receive the grade
that is based on your course average.
Mathematics Tutoring Center:
The Mathematics Tutoring Center is available for any WPI student taking a
course in calculus, differential equations, statistics, and linear algebra.
Stratton Hall 002A
Monday-Thursday 10am-8pm and Friday 10am-4pm.
No appointment needed - drop in any time!
Academic Dishonesty
Please read WPI's
Academic Honesty Policy
and all its pages. Make note of the examples of
academic dishonesty; i.e. acts that interfere with the process of evaluation
by misrepresentation
of the relation between the work being evaluated (or the resulting evaluation)
and the student's actual state of knowledge.
Each student is responsible for familiarizing him/herself with
academic integrity issues and policies at WPI.
All suspected cases of dishonesty will be fully investigated.
Ask Prof. Weekes if you are in any way unsure whether your proposed actions/collaborations will be considered academically honest or not.
Students with Disabilities
Students with disabilities who believe that they may need accommodations in this class are encouraged to contact the Disability Services Office (DSO), as soon as possible to ensure that such accommodations are implemented in a timely fashion. The DSO is located in the Student Development and Counseling Center and the phone number is 508-831-4908,
e-mail is DSO@WPI.
If you are eligible for course adaptations or accommodations because of a disability (whether or not you choose to use these accommodations), or if you have medical information that I should know about please make an appointment with me immediately. | 677.169 | 1 |
In Pursuit of the Unknown: 17 Equations That Changed the World
by Ian Stewart Publisher Comments
Most people are familiar with historys great equations: Newtons Law of Gravity, for instance, or Einsteins theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the...Cartoon Guide to Statistics
by Larry Gonick Publisher Comments... (read more)
Trigonometry (Homework Helpers)
by Denise Szecsei Publisher Comments
Homework Helpers: Algebra emphasizes the role that arithmetic plays in the development of Algebra and covers all of the topics in a typical Algebra 1 class, including: * Solving linear equalities and inequalities * Solving systems of linear equations... (read more)
The King of Infinite Space: Euclid and His Elements
by David Berlinski Publisher Comments
Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclids Elements, arguably the most influential book in | 677.169 | 1 |
This workbook is written as an aid to learn the skills necessary for
success in college level Algebra classes. You may use a single lesson to help
review a particular topic, or you may want to work your way through the
entire workbook. Topics presented here are at the level of Math 091
(Elementary Algebra), as taught in the UW Colleges, but the workbook does not
include all topics that would be covered in the course. For the best
preparation for Intermediate Algebra (Math 105), you should take and complete
the Math 091 course (or one of its equivalents).
Whether you are reviewing previously learned material or studying Algebra
for the first time, this material should help you build a mathematical
foundation for any further studies. The concepts presented here are not
intended to cover all possible course topics, but rather only to strengthen
foundations. You should strive for a mastery of all topics in this workbook,
for later successes will depend on these basic skills. By 'mastery', I expect
that you can not only do most of the exercises correctly, but also that you
can recognize mistakes in your own work.
The single most important factor for success will be your own personal
effort. Math is not a mystical subject; rather it is based on common sense.
With practice and guidance, you should soon be able to judge your own work
for correctness. Indeed, one of the best signs of mathematical mastery is the
ability to find and correct your own errors.
A final few words of advice will get you off to a good start in learning
Algebra: Take responsibility for your own learning by working carefully
through the entire workbook. Ask questions whenever you do not understand a
concept. Attend classes regularly. Remember, at all times, that learning is
an active process that requires your participation. | 677.169 | 1 |
Computational Introduction To Number Theory And Algebra - 05 edition
Summary: Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus...show more is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students | 677.169 | 1 |
A student may NOT take this course
for credit if he/she already has credit for a college algebra or calculus
course.
General:
Math 167 is a preparatory
course for calculus. Students interested in taking calculus but feel that
they are not ready for it should take this class. For a few majors
Math 167 is the prefered mathematics course. To check which majors require
calculus or precalculus, go to "List of Majors by
Math Course requirement".
Prerequisite:
None.
Description:
The study of elementary functions, their
analysis and application. Included are investigations of polynomial, rational,
exponential, and trigonometric functions. | 677.169 | 1 |
MTH:160B COLLEGE ALGEBRA WITH CALCULATOR TI-83: NON-TECHNICAL MAJORS
MATHEMATICS DEPARTMENT'S STUDENT OBJECTIVES AND ASSIGNMENTS
A Student Should Be Able To:
Introduction to Graphs and the Graphing Calculator { REVIEW }* · Plot points by hand and using a grapher
· Graph equations by hand and using a grapher
· Find the point(s) of intersection of two graphs
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
Chapter R Basic Concepts of Algebra { REVIEW }
R.1 The Real-Number System · Identify various kinds of real numbers
· Use interval notation to write a set of numbers
· Identify the properties of real numbers
· Find the absolute value of a real number
FINISH THE ASSIGNMENT OF: (ask your professor)
R.2 Integer Exponents, Scientific Notation, and Order of Operations · Simplify expressions with integer exponents
· Solve problems using scientific notation
· Use the rules for order of operations
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
1.1 Functions, Graphs, and Graphers · Determine whether a correspondence or relation is a function
· Find function values, or outputs, using a formula
· Find the domain and the range of a function
· Determine whether a graph is that of a functions
· Solve applied problems using functions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression · Analyze a set of data to determine whether it can be modeled
by a linear function
· Fit a regression line to a set of data; then use the linear model
to make predictions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
1.4 More on Functions · Graph functions, looking for intervals on which the function
is increasing, decreasing, or constant, and determine
relative maxima and minima
· Given an application, find a function formula that models the
application; find the domain of the function and function values, and then graph the function
· Graph functions defined piecewise
· Find the sum, the difference, the product, and the quotient
of two functions, and
determine their domains
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
1.5 Symmetry and Transformations · Determine whether a graph is symmetric with respect to
the x-axis, the y-axis, and the origin
· Determine whether a function is even, odd, or neither
even nor odd
· Given the graph of a function, graph its transformation
under translations, reflections, stretchings, and shrinkings
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
1.7 Distance, Midpoints, and Circles · Find the distance between two points in the plane and find
the midpoint of a segment
· Find an equation of a circle with a given center and radius, and
given an equation of a circle, find the center and the radius
· Graph equations of circles
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
2.3 Zeros of Quadratic Functions and Models · Find zeros of quadratic functions and solve quadratic
equations by completing the square and by using
the quadratic formula
· Solve equations that are reducible to quadratic
· Solve applied problems
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
2.4 Analyzing Graphs of Quadratic Functions · Find the vertex, the line of symmetry, and the maximum
or minimum value of a quadratic function using the
method of completing the square
· Graph quadratic functions
· Solve applied problems involving maximum and minimum
function values
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
3.1 Polynomial Functions and Modeling · Use a grapher to graph a polynomial function and find its
real-number zeros relative maximum and minimum
values, and domain and range
· Solve applied problems using polynomial models
· Fit linear, quadratic, power, cubic, and quartic polynomial
functions to date and make predictions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
3.2 Polynomial Division; The Remainder and Factor Theorems · Perform long division with polynomials and determine whether one polynomial is a factor of another
· Use synthetic division to divide a polynomial by (x - c)
· Use the remainder theorem to find a function value f(c)
· Use the factor theorem to determine whether (x - c) is a factor of f(x)
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
3.3 Theorems about Zeros of Polynomial Functions · Factor polynomial functions and find the zeros of their multiplicities
· Find a polynomial with specified zeros
· Find a polynomial function with integer coefficients, find the rational
zeros and the other zeros, if possible with this level of algebra
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
4.1 Composite and Inverse Functions · Find the composition of two functions and the domain of the
composition; decompose a function as a composition
of two functions
· Determine whether a function is one-to-one, and if it is, find a
formula for its inverse
· Simplify expressions of the type (f • f -1)(x) and (f -1 • f)(x)
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
4.3 Logarithmic Functions and Graphs · Graph logarithmic functions
· Convert between exponential and logarithmic equations
· Find common and natural logarithms using a grapher
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
4.4 Properties of Logarithmic Functions · Convert from logarithms of products, powers, and quotients to
expressions in terms of individual logarithms, and conversely
· Simplify expressions of the type loga(ax) and alogax FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
5.1 Systems of Equations in Two Variables · Solve a system of two linear equations in two variables by graphing
· Solve a system of two linear equations in two variables by using
the substitution and the elimination methods
· Use systems of two linear equations to solve applied problems
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
5.2 Systems of Equations in Three Variables · Solve systems of linear equations in three variables
· Use systems of three equations to solve applied problems
· Model a situation using a quadratic function
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
5.3 Matrices and Systems of Equations · Solve systems of equations using matrices
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
5.4 Matrix Operations · Add, subtract, and multiply matrices when possible
· Write a matrix equation equivalent to a systems of equations
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
5.5 Inverses of Matrices · Find the inverse of a square matrix, if it exists
· Use inverses of matrices to solve systems of equations
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
6.1 The Parabola · Given an equation of a parabola, complete the square, if necessary,
and then find the vertex, the focus, and the directrix and
graph the parabola
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
6.2 The Circle (and the Ellipse [ OPTIONAL ]) · Given an equation of a circle, complete the square, if necessary,
and then find the center and the radius and graph the circle
· Given an equation of an ellipse, complete the square, if necessary,
and then find the center, the vertices, and the foci and graph
the ellipse
FINISH THE ASSIGNMENT OF: (ask your professor)
6.3 The Hyperbola [ OPTIONAL ] · Given an equation of a hyperbola, complete the square, if necessary,
and then find the center, the vertices, and the foci and graph
the hyperbola
FINISH THE ASSIGNMENT OF: (ask your professor)
6.4 Nonlinear Systems of Equations · Solve a nonlinear system of equations
· Use nonlinear systems of equations to solve applied problems
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
Chapter 7 Sequences, Series, and Combinatorics
7.1 Sequences and Series · Find terms of sequences given the nth term
· Look for a pattern in a sequence and try to determine a general term
· Convert between sigma notation and other notation for a series
· Construct the terms of a recursively defined sequence
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
7.2 Arithmetic Sequences and Series · For any arithmetic sequences, find the nth term when n is given
and n when the nth term is given, and given two terms,
find the common difference and construct the sequence
· Find the sum of the first n terms of an arithmetic sequence
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
7.3 Geometric Sequences and Series · Identify the common ratio of a geometric sequence, and find
a given term and the sum of the first n terms
· Find the sum of an infinite geometric series, if it exists
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
PROJECT #7
7.4 Mathematical Induction [ OPTIONAL ] · List the statements of an infinite sequence that is defined by a formula
· Do proofs by mathematical induction
FINISH THE ASSIGNMENT OF: (ask your professor)
7.7 The Binomial Theorem · Expand a power of a binomial using Pascal's triangle or factorial notation
· Find a specific term of a binomial expansion
· Find the total number of subsets of a set of n objects
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES
A Descartes' Rule of Signs · Use Descartes' rule of signs to find information about the number
of real zeros of a polynomial function with real coefficients
FINISH THE ASSIGNMENT OF: (ASK YOUR PROFESSOR)
* { REVIEW } topics covered in prerequisite courses and skills needed for this course. Students are expected to brush up on these topics to the point of knowing the concepts at a problem solving conversational level every day of the course.
** [ OPTIONAL ] means your professor will determine the need for covering this OPTIONAL topic based on the types of projects selected in your professor's syllabus. | 677.169 | 1 |
Product Details
Uncommon Mathematical Excursions by Dan Kalman
This book presents an assortment of topics that extend the standard algebra-geometry-calculus curriculum of advanced secondary school and introductory college mathematics. It is intended as enrichment reading for anyone familiar with the standard curriculum, including teachers, scientists, engineers, analysts, and advanced students of mathematics. The book is divided into three parts each with a specific theme. In the first part, all of the topics are related to polynomials: properties and applications of Horner form, reverse and palindromic polynomials, identities linking roots and coefficients, among others. Topics in the second part are all connected in some way with maxima and minima. They include a new idea about an old approach to Lagrange multipliers, optimization as a method of proof, and some unusual max/min problems. In the final part calculus is the focus. Here the reader will find a limit-free development of differentiation, visually appealing treatment of envelopes and asymptotes, a rumination on the subject's surprising power and simplicity, and other topics. The book is particularly recommended for professional development and continuing education of secondary and college mathematics teachers. For more information, visit | 677.169 | 1 |
...ractice Problems Involving Computation 1 Assume you have a black hole of initial mass M0 and some specified initial spin and that it accretes matter at the innermost stable circular orbit Write a computer program to calculate the dimensionless spin parameter j a M J M 2 of the hole as a function...
...omputability and Modeling Computation What are some really impressive things that computers can do Land the space shuttle and other aircraft from the ground Automatically track the location of a space or land vehicle Beat a grandmaster at chess Are there any things that computers can t do Yes...
...omputation Calculators and Common Sense A Position of the National Council of Teachers of Mathematics Question Is there a place for both computation and calculators in the math classroom NCTM Position School mathematics programs should provide students with a range of knowledge skills and tools...
1 0 1 Sample Computational Problems Factoring a polynomial To factor a polynomial place the insertion point inside or to the right of the polynomial select Factor from the Compute menu Example 1 5x5 5x4 1 0 2 10x3 10x2 5x 5 5 x 2 3 1 x 1 Finding the roots of a polynomial To nd the roots of a polynomial place the insertion point inside or to the rig...
...age 1 of 4 Models of computation indicates problems that have been selected for discussion in section time permitting Problem 1 In lecture we saw an enumeration of FSMs having the property that every FSM that can be built is equivalent to some FSM in that enumeration A We didn t deal with FSMs... | 677.169 | 1 |
Mathematics is a compulsory subject until the end of Year 11 and is one of the few subjects taught banded, with high-expectation groups extended and accelerated. Students with needs in numeracy are also targeted with extra support.
Homework
Students will receive homework on a daily basis except on assessment days; this is checked and feedback is given. Homework has a tremendous impact on student achievement and thus gets taken very seriously.
Assessment
Year 9 and 10 students study the units from the 3 strands of the New Zealand Mathematics Curriculum over their schooling. Assessment is aligned as closely to the structure of NCEA as possible. So a unit may be assessed as "Internal" (a project style assessment assessed during the year) or "External" (assessed at the end of the year in an examination).
Senior courses are entered in a combination of Unit Standards (best grade is achieved) and Achievement Standards (can also achieve with Merit and Excellence)
Structure
Year 9
Four Bands. Students are assessed in term 1 and placed appropriately in 1 of these 4 bands.
Year 10
Four Bands. Students are placed according to their final results in Year 9.
Year 11
Four courses to cater for the different needs of all students. The content and assessed standards in these courses is carefully selected to be give each student the chance to achieve well and be challenged.
Year 12
Three different courses to cater for the needs of all students - regular holiday workshops
Year 13
Mathematics with Statistics : Two courses
Mathematics with Calculus : Two courses
More information about each course can be found in the student handouts that all students receive at the beginning of their course.
Maths Publication
Maths Uncensored is a delightful read, put together entirely by students and aimed at introducing Maths at Springs to the community. | 677.169 | 1 |
AP Calculus AB Curriculum Map
Freeport Public Schools
Time Topics Skills
Line (Use of graphing calculator is required on a regular basis)
Students will:
First Pre-Calculus • Simplify expressions containing absolute value
Quarter • Graph: a) y = l f (x) l
Limits b) y = F l x l
Derivative • Solve absolute value equations
• Graph and solve F (x) s a
• Graph and solve lF (x) l s a
• Determine whether a function is odd, even or neither
• Determine which, if any, symmetries a relation has
• Find limits of a function algebraically, graphically, and numerically
• Determine whether or not a function is continuous
• Be able to graph functions
• Find the derivative of a function using the definition
• Be able to find derivative graphically, algebraically, and numerically
• Be able to use the calculator to evaluate derivatives numerically
• Be able to do velocity problems algebraically and graphically
• Apply the chain rule
• Find the equation of a line tangent to the curve
• Find the equation of a line that best approximates the curve
Second Application of • Find the global and local extreme of a function
Quarter Derivatives • Be able to do application of Rolle's and mean value theorem
• Be able to graph derivative given, function, and graph function given derivative
Integration • Be able to determine where a function is increasing and decreasing
• Be able to determine the concavity of a function and its points of inflection
• Do related rates and problems
• Be able to do initial condition problems
• Use the right approximation method and left approximation method
• Make a connection between differential and integral calculus
• Find antiderivative of appropriate functions
• Be able to do velocity problems
AP Calc AB 09-10.doc FPS 2009-2010
Page1
AP Calculus AB Curriculum Map
Freeport Public Schools
Time Topics Skills
Line (Use of graphing calculator is required on a regular basis)
Students will:
Third Integration
Quarter • Find the approximation to an integral by using trapezoidal rite
Application of • Find area using integrals
Integration • Find volume
• Find derivative of natural log
Functions • Integrate with ⊥
• Differentiate and integrate with e
• Do exponential growth and decay problems
• Find derivatives and integrals of "a"
• Be able to differentiate inverse trig functions and do antiderivative problems with inverse trig in answer
• Know when and how to use L'Hospital's rule in a limit problem
• Be able to find the derivative of the inverse of a function without finding the inverse
Fourth Review • Be able to do Part I questions with and without a calculator
Quarter • Be able to do Part II with and without calculator
Final Exam
AP Calc AB 09-10.doc FPS 2009-2010
Page2 | 677.169 | 1 |
Your student's problem-solving and reasoning skills will be strengthened, while his or her understanding of math as a tool of commerce, the language of science, and a means for solving everyday problems will be developed. The biblical basis and revelence of math is made evident from beginning to end. | 677.169 | 1 |
I'm a college student who is having some issues really understanding Calculus II, which is a problem as A) I am a Comp Sci major, and B) I need to take Calc III as well, and an advanced math elective as well. I've not heard good things about the school provided tutors, (IE, one is not too skilled at math, and the other is really smug and poor pedagogically) and while I could get a private tutor to help me, I was wondering if there are any good resources for online math tutors, like there are for online language tutoring over Skype. Does a directory of such tutors exist, has anyone had a good experience doing this (maybe even with names?), and how much can I expect to pay? [more inside]
posted by mccarty.tim
on Jan 14, 2013 -
11 answers
My math skills are no where near where I'd like them to be. Can you recommend a self-paced math learning site? Pretty much any branch of math can apply. [more inside]
posted by Ookseer
on Aug 13, 2012 -
7 answers
I'm teaching myself to code (Python, mainly), and it's going well, except I keep on running into one big problem: I haven't done any math since high school (6 years ago). I used to be top of my class, and now I can't do simple word problems anymore. This gets tough because they inevitably pop up in the books I'm using, and then I stop dead in my tracks. Could anyone recommend a couple of books or web resources to help me get back up to speed? I never took Calculus, so a good Calculus book would help, too. [more inside]
posted by flibbertigibbet
on Dec 10, 2011 -
22 answers
Calculusfilter. A man is led to the center of a valuable field which he does not own. He coats his feet in blue paint so that his path can be traced. At dawn he begins walking. At a randomly selected time he will be told to stop walking, whereupon he will walk in a perfectly straight line back to the starting point. Then he will be given all the land that has been circumscribed by his blue path. [more inside]
posted by foursentences
on Aug 30, 2011 -
89 answers
The area between f(x), the x-axis and the lines x=a and x=b is revolved around the x-axis. The volume of this solid of revolution is b^3-a*b^2
for any a,b. What is f(x)? [more inside]
posted by stuart_s
on Sep 29, 2010 -
27 answers
I'm taking a calc-based physics class as well as a calculus class. The last time I took a math class was 5 years ago and I would love some refresher resources - or even better, an intensive algebra-trig-precalc course. Are there any online or in the DC area? [more inside]
posted by alaijmw
on Sep 2, 2010 -
10 answers
I need help understanding the "principle domain" (a term only my professor seems to use) of a polar function. That is, how do I find the smallest value delta such that [0,delta] plots all of the unique points on the curve; any values greater than delta re-trace points. I suspect that if MeFi could identify the more common name for this, uh, procedure, I'd be set.
posted by phrontist
on Aug 4, 2010 -
10I'm looking for an example of an alternating series: the terms of which are (-1)^n b_n, where b_n -> 0 as n -> infinity, but the sequence {b_n} is not decreasing, and the sum from n=1 to infinity diverges. [more inside]
posted by evinrude
on Apr 15, 2009 -
25 answers
Planning on teaching myself Calculus I and II in order to take the AP Calculus BC exam this May. If you've taught or taken either class, at a high school, university, or independently, read on. [more inside]
posted by Precision
on Aug 16, 2008 -
28Where can I take (or simulate taking) a basic calculus course for free or cheap. I don't care about credits or anything, I just need to defeat calculus. This time, it's personal. [more inside]
posted by dumbledore69
on Oct 25, 2007 -
14 answers
I remember reading an anecdote about Feynman, written by Feynman either in Surely, You're Joking or What Do You Care What Other People Think. He was describing how in his undergraduate years people were really impressed by his ability to do integrals, all because he knew this integration technique that wasn't taught very often. What was that technique?
posted by phrontist
on Dec 4, 2006 -
10 answers
Could someone suggest book(s) that deal with tips/tricks/methods of performing mathematical calulations faster. I mean higher mathematics and not just elementary operations like addition/multiplication/finding the root etc.
What I am looking for are hints and shortcuts that would help me with stuff like calculus, linear albegra, vectors and such.
Thanks!
posted by sk381
on Sep 20, 2006 -
7 answers
"Math 51H provides a rigorous, proof-based introduction to linear algebra and differential calculus in several variables." Recommend a book to catch me up to the starting point for this course! [more inside]
posted by devilsbrigade
on Jul 8, 2006 -
20 answers
I'd like to learn Math. I'm particularly interested in learning trig and calculus. I'm don't need to learn these disciplines for any purpose. I'm just interested. I'm a reasonably bright guy, with a logical mind (I've worked as a programmer), and I'm a good self-learner. I'm not in a rush (don't mind working at this for a few years). What books/resources would you recommend? I should probably go all the way back to Algebra, which is pretty much where I left off in High School years ago.
posted by grumblebee
on Dec 27, 2003 -
12 answers | 677.169 | 1 |
Questions About This Book?
The Used copy of this book is not guaranteed to inclue any supplemental materials. Typically, only the book itself is included.
Summary
Building on the success of its first three editions, the Fourth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with additional chapters on solid geometry, analytic geometry, and an introduction to trigonometry. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery. New! Tables provide visual connections between figures and concepts and help students better assess their level of mastery and test readiness. New! Chapter Tests have been added to the end of every chapter. New! Proofs have been varied to include written and visual proofs, as well as comparisons, to support students with different learning styles. New! Exercise sets in the Student Study Guide, with cross-references to the text, offer additional practice and review. New! Technology-related margin features encourage the use of the Geometer's Sketchpad, graphing calculators, and further explorations. New! Coverage now includes Section 2.6, Symmetry and Transformations. New! Technology Package includes mathSpace tutorial CD and the HM ClassPrep CD with computerized test bank. Updated! The number of Exercises and Explorations has been increased. Highly visual approach begins with the presentation of an idea, followed by the examination and development of a theory, verification of the theory through deduction, and finally, application of the principles to the real world. Discovery features reinforce the text's inductive approach: activities integrated throughout enable students to discover geometry concepts on their own, and section tools provide with hands-on application of geometric concepts Applications reinforce the connection of geometry to the real world: high-interest Chapter Openers introduce the principal notion of the chapter and relate to the real world and A Perspective On... sections conclude each chapter, providing sketches that are interesting, sometimes historical, and always informative. Summaries of constructions, postulates, and theorems are provided, and an easy-to-navigate numbering system for postulates and theorems provides a user-friendly structure. In response to user feedback, paragraph proofs feature more prominently in this edition. Comprehensive appendices include Algebra Review and An Introduction to Logic. A glossary of terms, a summary of applications in the text, and selected answers are also provided in the back of the text. | 677.169 | 1 |
Maths
To support students enrolled in maths and statistics courses, The Learning Centre provides a range of activities associated with mathematics and learning skills.
Semester 2, 2013 workshops
Success in Maths for Statistics (SIMS)
Topics include formulas, arithmetic, calculator, basic statistics, graphing. See the workshop program (PDF*68kb). Complete the online readiness testing (UConnect username and password required) or complete the first CMA on your STA2300 course webpage, to self assess your knowledge and determine whether you need to attend this workshop. Completing the first CMA is part of your first assignment in STA2300.
You will need to bring a copy of the SIMS workbook (PDF* 1.34mb) with you to the workshop. If you are unable to attend a workshop, the workbook will still be useful for your data analysis studies. | 677.169 | 1 |
Analytic Trigonometry With Application - 9th edition
Summary: Featuring updated content, vivid applications, and integrated coverage of graphing utilities, the ninth edition of this hands-on trigonometry text guides readers step by step, from the right triangle to the unit-circle definitions of the trigonometric functions. Examples with matched problems illustrate almost every concept and encourage readers to be actively involved in the learning process. Key pedagogical elements, such as annotated examples, think boxes, cautio...show moren warnings, and reviews, help readers comprehend and retain the material | 677.169 | 1 |
We've heard you say that all students are not created equal when it comes to reasoning and math skills. Furthermore, we share your belief that the ability to reason in an organized and mathematically correct manner is essential to solving problems. That's why helping students improve their reasoning skills is also one of Cutnell & Johnson's primary goals. The following features will help students improve their reasoning skills:
Video Help, available through WileyPLUS, provides 3–5 minute office hour style videos tailored to the more challenging problems that bring together two or more physics concepts. These videos do not solve the problems, rather they point the student in the right direction by using a proven problem–solving technique: 1. Visualize the problem 2. Organize the data 3. Develop a reasoning strategy.
Math Skills appears as a sidebar throughout the text. It is designed to provide additional help with mathematics for students who need it, yet be unobtrusive for students who don't.
There's also a math skills module in WileyPLUS (a chapter 0) for students who want even more help.
Explicit reasoning steps in all examples explain what motivates the procedure for solving the problem before any algebraic or numerical work is done.
Reasoning Strategies for solving certain classes of problems are called out to encourage frequent review of the techniques used and help students focus on the related concepts
Analyzing Multiple–Concept Problems prompt students to combine one or more physics concepts before reaching a solution. First, they must identify the physics concepts involved in the problem, then associate each concept with an appropriate mathematical equation, and assemble the equations to produce a unified algebraic solution.
In order to reduce a complex problem into a sum of simpler parts, each Multiple-Concept example consists of four sections: Reasoning, Knowns and Unknowns, Modeling the Problem, and Solution.
Homework problems with associated Guided Online (GO) Tutorials have increased by 45% in this edition. Each of these problems in WileyPLUS includes a guided tutorial option (not graded) that instructors can make available for student access with or without penalty.
* GO tutorials facilitate strong problem–solving skills by providing a step by step guide on how to approach a problem. Multiple–choice questions in the GO tutorial include extensive feedback for both correct and incorrect answers. These multiple–choice questions guide students to the proper conceptual basis for the problem. The GO tutorial also includes calculational steps
Interactive LearningWare, available in WileyPLUS, consists of interactive examples, presented in a five-step format, designed to help improve each student's problem–solving skills.
Interactive Solutions, available in WileyPLUS, enable students to work out problems in an interactive manner while providing a model for the corresponding homework problem. | 677.169 | 1 |
Course 1- make sure you study the notes given today and the notes in your notebook. Know the formulas found on the KNOW THESE paper in your notebook. Practice doing some of the perimeter and area problems on the review sheet. You should also know about PEMDAS, exponents, and perfect squares. Don't forget to do your graphs.
Course 2- make sure you review all about central tendency. You should know all about stem and leaves, box and whiskers, and frequency tables. You should also know about exponents, PEMDAS, prime factorization, and gcf. | 677.169 | 1 |
purpose of this book is to present material on elementary statistical methods in a succinct manner, to extend the introductory ideas into analysis of variance and experimental design, and to explain without formal mathematical proof the assumptions on data necessary for the v ...
We use math every day, sometimes without even realizing it! Kid-friendly, real-life situations show readers how they can put math to work in their day-to-day activities. A variety of problem-solving activities and graphic organizers make these books ideal for young learners. . | 677.169 | 1 |
This is a challenging and rigorous course offered to those students who have demonstrated an advanced proficiency in mathematics in sixth grade. The material covered in the accelerated course is presented at a faster pace with the expectation that the students have retained their advanced skills and can perform with greater proficiency and on their own.The accelerated course focuses on using the order of operation principles, solving equations and inequalities, applying rational numbers and integers to real life problems, relating rates, proportions, and percents, developing spatial thinking skills and exploring linear functions.A course grade of 85% in the 6th grade advanced course is recommended. | 677.169 | 1 |
Useful both as a text for students and as a source of reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory which is most useful for its application in modern analysis. Topics studied include sets and classes, measures and outer measures, measurable functions, integration, general set functions, product spaces, transformations, probability, locally compact spaces, Haar measure and measure and topology in groups. The text is suitable for the beginning graduate student as well as the advanced undergraduate.
Reviews
P.R. Halmos Measure Theory "As with the first edition, this considerably improved volume will serve the interested student to find his way to active and creative work in the field of Hilbert space theory."--MATHEMATICAL REVIEWS
You can earn a 5% commission by selling Measure Theory: v. 18 (Graduate Texts in Mathematics | 677.169 | 1 |
math skills needed for a successful foodservice career—now in a new edition
Culinary Calculations, Second Edition provides the mathematical knowledge and skills that are essential for a successful career in today's competitive foodservice industry. This user-friendly guide starts with basic principles before introducing more specialized topics like recipe conversion and costing, AP/EP, menu pricing, and inventory costs. Written in a nontechnical, easy-to-understand style, the book features a running case study that applies math concepts to a real-world example: opening a restaurant.
This revised and updated Second Edition of Culinary Calculations covers relevant math skills for four key areas:
Basic math for the culinary arts and foodservice industry
Math for the professional kitchen
Math for the business side of the foodservice industry
Computer applications for the foodservice industry
Each chapter is rich with resources, including learning objectives, helpful callout boxes for particular concepts, example menus and price lists, and information tables. Review questions, homework problems, and the case study end each chapter. Also included is an answer key for the even-numbered problems throughout the book.
Culinary Calculations, Second Edition provides readers with a better understanding of the culinary math skills needed to expand their foodservice knowledge and sharpen their business savvy as they strive for success in their careers in the foodservice industry. | 677.169 | 1 |
College Algebra and Trigonometry: A Graphing Approach
Intended to provide a flexible approach to the college algebra and trigonometry curriculum that emphasizes real-world applications, this text ...Show synopsisIntended to provide a flexible approach to the college algebra and trigonometry curriculum that emphasizes real-world applications, this text integrates technology into the presentation without making it an end in itself, and is suitable for a variety of audiences. Mathematical concepts are presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving. Pedagogical elements including chapter opening applications, graphing explorations, technology tips, calculator investigations, and discovery projects are some of the tools students will use to master the material and begin applying the mathematics to solve real-world problems. CONTEMPORARY COLLEGE ALGEBRA AND TRIGONOMETRY includes a full review of basic algebra in Chapter 0 and full coverage of trigonometry to prepare students for the standard science/engineering calculus sequence. (The companion volume, CONTEMPORARY COLLEGE ALGEBRA includes all of the non-trigonometry topics, covered in sufficient detail to prepare a student for a business/social science calculus course.) Those who are familiar with the author's CONTEMPORARY PRECALCULUS should note that this book covers topics in a different order, and with a slower, gentle approach. Also, more drill exercises are included | 677.169 | 1 |
Applied mathematics, which investigates theoretical models of real world systems, expressed in the language of differential equations. Such equations are used to model, for example, fluid flow (eg the flow of air over an aircraft wing) and dynamical systems and chaos theory (used to model global and local atmospheric conditions)
Statistics, which involves finding order where there is, at first sight, only randomness. Statistical techniques are constantly finding new uses, such as in the detection of long-term changes in the environment, the analysis of DNA structure, or in quality assurance
You have the flexibility to tailor the combination of pure mathematics, applied mathematics and statistics content to suit your interests.
There is also some flexibility at each Stage to choose topics from other areas of the University, for example, accounting, music, a foreign language or another science.
Quality and ranking
The quality of the mathematics and statistics study experience at Newcastle is recognised with an overall student satisfaction score of 91% in the 2012 National Student Survey.
We assess your performance in each module through a combination of assignments (many of which take place online) and examinations. Teaching and assessment methods may vary from module to module; more information can be found in our individual module listings.
Visit our Teaching and Learning pages to read about the outstanding learning experience available to you at Newcastle University.
Flexible degree structure
Studying mathematics and statistics builds on the knowledge you have gained at school/college. Some topics will be familiar and others will be completely new.
All of our mathematics and statistics degrees follow a common core of modules at Stages 1 and 2. These common modules are designed to equip you with the key skills and knowledge that all mathematicians and statisticians need.
They include topics such as:
analytical geometry
modelling with differential equations
foundations of analysis
vector calculus
probability
linear algebra
They constitute a significant proportion of your time in the early Stages of your programme. This provides you with a solid foundation on which to build more specialist knowledge later in your degree, as well as making it relatively easy to transfer between degrees within the School.
Learning technologies
We have excellent computing facilities and make extensive use of IT to support teaching, preparation and revision, including:
computer-based exercises with instant review of model solutions
problem-solving video tutorials
recording system for video capture of lectures, which you can download and watch again to help with your revision
The School also has a dedicated mathematics and statistics library and reading room that complements the wealth of resources available through the main University Library Service.
School of Mathematics and Statistics
We run an induction programme for first-year students including social events to help you to get to know your fellow students and the members of staff who will be teaching you. We also have a 'buddy scheme', which begins before you even arrive at the University.
As well as the support of a personal tutor, you will be encouraged to join our extremely active student society, MathSoc. MathSoc organises a range of social events throughout the year to help you get to know people on your course and beyond.
Visit the School's website to take a virtual tour of the Herschel Building, which is on the central campus and a two-minute walk from the city centre.
At Newcastle, we offer mathematics and statistics degrees at two levels:
Bachelor of Science (BSc) – three years
Master of Mathematics (MMath)/Master of Mathematics and Statistics (MMathStat) – four years
Whilst broadly similar, our four-year degrees (also known as Integrated Masters' degrees) cover more advanced topics, a wider choice of modules and a specialist study, tailored to your own interests, that develops your skills in research and communication.
They also cover more technical skills for those who wish to enhance their employability or proceed to postgraduate study.
Transfer between the MMath/MMathStat and BSc degree programmes is possible up until the middle of Stage 3.
We recommend registering for the MMath/MMathStat degree initially if it is at all likely that you will want to take one of these degrees.
To qualify for Stages 3 and 4 of the MMath/MMathStat degree, you must normally have obtained at least an upper-second-class average mark in Stages 2 and 3. | 677.169 | 1 |
Is your student's Intermediate Algebra fast approaching? Are you like many homeschool parents feeling just a bit overwhelmed! At Alpha Omega Publications, we've got the help you need! During the high school years, it is vitally important that math instruction provide adequate preparation for college entrance exams. Now that your child has completed Algebra I and Geometry, it's time for the LIFEPAC Algebra II Set. In this homeschool program, students focus on mastery of a single skill, and then move on to learn new concepts, laying a foundation for ever-increasing levels of proficiency. In LIFEPAC Algebra II, students will study concepts such as axioms, relations and functions, absolute value, graphs, linear equations, operations with polynomials, radical expressions, laws of radicals, quadratic equations and formulas, quadratic relations and systems, exponential functions, matrices, progressions, permutations, and probability.
But we've added even more features to help make homeschooling parents' lives easier! In LIFEPAC Algebra II, student worktexts include detailed math instruction and review, as well as plenty of opportunity for assessment of student progress. In order to encourage individualized instruction, we have included a teacher's guide designed to help you guide your student's learning according to his specific interests and needs. The Alpha Omega curriculum teacher's guide includes detailed teaching notes and a complete answer key which includes solutions for algebra-challenged parents! Are you ready to give it a try? Order the LIFEPAC Algebra II Set for your high school student | 677.169 | 1 |
Book DescriptionBook Description
SMP Interact at Key Stage 3 has been written to support the new Framework for teaching mathematics: Years 7, 8 and 9. Teacher's Guide to Book C2 accompanies the second book of the C (Circle) series, which provides a route to the Key Stage 3 SATs at levels 5-7.
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more | 677.169 | 1 |
More from this developer
Description
Application made to make mathematical calculus, that are considered laborious and exhaustive when made by hand, and make easier the life of engineers and mathematicians. Solve 2nd grade equations, equations linear systems, make conversions between rectangular and polar formats... You can also work with matrices. Calculate determinant, make multiplications between matrices, calculate the inverse and adjoint.
Test review and rating
What's New
New features: - History salved of each calculation made, and you can rescue the typed values to redo the calculation; It's possible to setup how many lasts histories to save: 10, 20 or 30, of each operation. - The number of decimal places rounded on the calculations are settable, from 1 up to 15. - New visual on the operations list. - Change on the visual of the operation: Quadratic Equation. - New operation: Cartesian and Spherical coordinates | 677.169 | 1 |
Welcome to Santa Ana College Math Center!
The Math Center is a resource center that provides individual and group assistance in mathematics. The Math Center also facilitates Directed Learning Activities. Faculty instructors, instructional assistants, and Student tutors are available to assist students with challenging topics, answer questions, encourage understanding, and provide support for all math students. Students also have access to textbooks, graphing calculators, instructional videos, and computer programs.
Math Center's Goals
To help some students further develop basic skills in mathematics and keep them coming to school.
To assist other students to further sharpen their pre-existing math skills and advance through math courses.
To guide all students toward success in math and encourage them to excel through their scholastic endeavors and beyond.
What is SAC Math Jam?
Math Jam is a free 2 week intensive math review session designed to improve a student's preparation for up coming math classes. It is usually held 2 weeks prior to the start of each semester. The session consists of: interactive learning, group learning, tutoring, individual instruction.
How can students benefit from it?
•Build stronger mathematics knowledge and study skills
•Boost your math confidence.
•Have fun with math and make friends who share the same goals.
•Enhance your chances for success in college
Who can sign up?
All Santa Ana College students who are going into Math 160-Trigonometry, Math 170-PreCalculus, or Math 180 Calculus 1. | 677.169 | 1 |
Elementary Linear Algebra Applications Version
9780471669593
ISBN:
0471669598
Edition: 9 Pub Date: 2005 Publisher: John Wiley & Sons Inc
Summary: This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide ...variety of interesting, contemporary applications. Clear, accessible, step-by-step explanations make the material crystal clear. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues | 677.169 | 1 |
Costs
Course Cost:
$300.00
Materials Cost:
None
Total Cost:
$300
Special Notes
State Course Code
02061Integrated Math I provides a first-year integrated math curriculum that combines material traditionally covered in high school algebra, geometry, and statistics courses. Integrated Math I is uniquely organized around thematic learning tasks that integrate concepts from the various strands of math. Within the course, a balance is struck between task-based discovery and focused development of skills and conceptual understanding.
Carefully paced, guided instruction is accompanied by interactive practice that is engaging and accessible. Interactive tasks allow students to approach and explore topics through real-world situations, helping them to gain an intuitive understanding while learning at the appropriate depth and rigor of a standards-based curriculum. Formative assessments help students to understand areas of weakness and improve performance, while summative assessments chart progress and skill development. Throughout the course, students develop general strategies to hone their problem-solving skills.
The content is based on the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics, as well as the Georgia Performance Standards and Instructional Frameworks in Mathematics. Detailed correlations to state-specific standards are available on request. | 677.169 | 1 |
Speedstudy Algebra 1
Speedstudy Algebra 1 provides a solid educational foundation that will raise grades and test scores and improve math skills in the classroom and beyond. Using step-by-step animations, real-time quizzes and a fun 3-D interface, Quickstudy Algebra 1
* Improve grades and test scores
* Multimedia learning system makes even the toughest math concepts come alive
* Great for new learners or students studying for college entrance exams | 677.169 | 1 |
Pre-Calculus Homework Help
Pre-calculus is an interesting area of math for students because of its multi-purpose nature. It reviews previously learned topics like trigonometry, introduces new topics like matrices and determinants, and prepares students for a formal course in calculus for the following year.
Typical content for a regular pre-calculus course includes:
functions and their graphs
polynomial and rational functions
exponential and logarithmic functions
trigonometry
systems of equations and inequalities
matrices and determinants
sequences, series, and probablility
While all these topics are important, it is fair to say that the topic of exponential and logarithmic functions is the most widespread in various fields of study, from business math to theoretical physics. As an interesting example, consider the following equation where we would like to solve for x:
ex + 2e-x = 3
A quick review of three basic logarithm rules:
product rule: ln (ab) = ln a + ln b
quotient rule: ln (a/b) = ln a - ln b
power rule: ln an = n ln a
shows that none will be helpful here. One technique for solving this equation is to multiply both sides by ex. The result is:
e2x + 2 = 3ex
After subtracting 3ex from both sides, we have:
e2x - 3ex + 2 = 0
After careful consideration of this equation, you may recognize it as a quadratic, with ex taking the place of x. We can therefore factor this just as we would any quadratic equation:
(ex-2)(ex-1) = 0
Setting each factor equal to zero, we have:
ex-2 = 0 and ex-1 = 0
Adding 2 and adding 1 to the left and right equations, respectively gives:
ex = 2 and ex = 1
Now, finally, in each case we can take the natural log of both sides:
ln ex = ln 2 and ln ex = ln 1
Remembering that ln ex = x, we have our two solutions:
x = ln 2 and x = 0
This example has served to review some of the basic properties of logarithms and to illustrate an early creative twist that was necessary for solving the given equation.
To fulfill our mission of educating students, our online tutoring centers are standing by 24/7, ready to assist students who need extra practice in pre-calculus. | 677.169 | 1 |
Powderly, TX Algebra am knowledgeable at the TI-83 and TI-84 calculators since I coached UIL calculator applications. Algebra 2 revisits Algebra 1 and some Geometry. However, Algebra 2 goes into more depth and adding more concepts. | 677.169 | 1 |
GeoGebra is a dynamic mathematics software for education in secondary schools that joins geometry, algebra and calculus.
On the one hand, GeoGebra is a dynamic geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards.
On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum.
The GeoGebraWiki is a free pool of educational materials for GeoGebra. Everyone can contribute and upload materials there:
International GeoGebraWiki - pool of educational materials for GeoGebra and the German GeoGebraWiki
The Dynamic Worksheets
GeoGebra can also be used to create dynamic worksheets:
Pythagoras
visualisation of Pythagoras' theorem
Ladder against the Wall
application of Pythagoras' theorem
Circle and its Equation
connection between a circle's center, radius and equation
Slope and Derivative of a Function (3 sheets)
relation between slope, derivative and local extrema of a function
Derivative of a Polynomial
interactive exercise to practice finding the derivative of a cubic polynomial
Upper- and Lower Sums of a Function
visualisation of the backgrounds of Riemann's Integral | 677.169 | 1 |
... Author(s): Shalayna Lair
Statistics Online Compute Resources This site offers software tools, instructional materials and online tutorials about college-level probability and statistics. The SOCR tool has interactive graphs and information about dozens of distribution models, as well as a large collection of statistical techniques for online data analysis, visualization, ... Author(s): Ivo Dinov
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angles standard position intro to positive West Virginia Math and Science Initiative - Trigonometry - angles standard position intro to positive - American Military University > ACADEMICS AND TRAINING > West Virginia Math and Science Initiative > Trigonometry > angles standard position intro to positive Author(s): No creator set
Introduction to Coordinate Geometry A web page that introduces the concepts behind coordinate geometry. Can be used as a reference for students to learn about the topic when away from class. Has links to other related pages that contain animated demonstrations. This resource is a component of the Math Open Reference Interactive Geometry textbook project at Author(s): John Page
Introduction to Storyboarding This lecture takes you through the steps to create a storyboard for film and animation projects. It is given by Illustration and Animation Lecturer Francis Lowe. Author(s): No creator set
Introduction to Ethical Studies These readings provide convenient sources for almost anyone seeking to learn about ethics and ethical theory. Our present collection is composed almost entirely of public domain sources, edited and emended, and subject to the legal notice following the title page which references Appendix A. Author(s): No creator set
Introduction to OpenOffice.org Impress An introduction to using OpenOffice.org Impress for presentations - aimed at getting learners comfortable with OOo Impress basics and giving them the confidence to go further on their own. Author(s): No creator set
Faith Complex: An Introduction Faith Complex is a show about the collision of religion, politics and art. Faith Complex is a joint production of Georgetown University's Program for Jewish Civilization and the Berkley Center for Religion, Peace and World Affairs, and it airs weekly at WashingtonPost.com Author(s): No creator set | 677.169 | 1 |
Ummer2013-05-19T07:29:04Z Mathematics with Mathematica for Economics, Business and Finance Ummer book can help overcome the widely observed math-phobia and math-aversion among undergraduate students in these subjects. The book can also help them understand why they have to learn different mathematical techniques, how they can be app...496 pages13.6 MB69.29 | 677.169 | 1 |
Applied Calculus (looseleaf) - 4th edition
Summary: APPLIED CALCULUS, 4/E exhibits the same strengths from earlier editions including the "Rule of Four", an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.
The fourth edition gives readers the skills to apply calculus on the job. It highlights the appl...show moreications' connection with real-world concerns. The problems take advantage of computers and graphing calculators to help them think mathematically. The applied exercises challenge them to apply the math they have learned in new ways. This develops their capacity for modeling in a way that the usual exercises patterned after similar solved examples cannot do. The material is also presented in a way to help business professionals decide when to use technology, which empowers them to learn what calculators/computers can and cannot do | 677.169 | 1 |
I believe having a good foundation in pure math is very, very helpful for approaching applied math (in my experience, and as my teachers have also taught me). I believe the more math you know, the better off you will be.
To address your question on how much pure math to learn, I suggest at the very minimum the following: Real Analysis , Basic Functional Analysis, Graduate Real Analysis (Lebesgue Integration, Measure Theory, Lp Spaces), some familiarity with point set topology, and some familiarity with basic algebra.
To reiterate, learn your real analysis first. If you have absolutely zero background in proving things, start with a nice introductory book such as Elementary Analysis by Ross, which is an excellent introduction to analysis. Then, work your way up to a typical undergraduate course in real analysis (especially focus on the concepts of pointwise and uniform convergence of functions), which I personally strongly recommend N. L. Carothers extremely affordable and phenomenal textbook titled Real Analysis. Others will recommend Walter Rudin's Principles of Mathematical Analysis, and it is also quite good, but I prefer Carothers. These subjects will show you how calculus really works, and how the concept of convergence of functions works, which is very important for approximation theory, PDEs, etc. The reason these concepts are important is because in applied math (at least for me), we typically want to guess a function by using functions from some finite dimensional subspace (as in finite elements or other forms of approximation theory), so we want to have a solid, rigorous and meaningful way of saying "This approximate guess we constructed from our numerical algorithm will be very close to the true function we want to approximate".
Once you know these subjects, try out Kreyszig's Functional Analysis book, so you learn about the appropriate spaces to do analysis. All three fields you highlighted (Inverse problems, PDEs, Approximation Theory) rely on real and functional analysis, so learn it! If you're feeling up to it, approach graduate real analysis to learn measure theory and the Lebesgue integral (which will give you a solid footing in the concept of Lp spaces, which are spaces of functions often used in PDEs and numerical analysis). I recommend Folland's analysis book.
I personally really enjoy topology, so I'd say give Munkres Topology book a whirl and see if you enjoy it. I recommend this because its a wonderful subject and because it is important if you want to pursue any differential geometry (which has many, many applications! Physics uses this constantly).
You should be at least familiar with some basic algebra (groups, rings, fields), but I personally don't use too much algebra (at least, not explicitly). However, I would never say "don't learn it", because you'd be shocked at where these things pop up. Also, if you happen to take an interest in cryptography or computational algebraic geometry, this will be fundamental. I'll let someone else recommend a good introductory algebra textbook.
Elsewhere in this post, myFriendsCallmeRaz recommended going to the library and checking out Keener's book Principles of Applied Mathematics. I used this book for two semesters, and personally detest the writing, and yet I still completely agree with his suggestion. I don't like how its written, but it contains an incredible amount of information. It will teach you basic functional analysis and operator theory, calculus of variations, and more importantly, why we care about these fields. These are all pure topics, but you can use them to understand how to solve PDEs, how to construct a numerical algorithm to solve PDEs( the Galerkin method follows from results in functional analysis), learn how to mathematically derive the way a wire sags between two poles (calculus of variations, catenary), and other things.
Once you feel comfortable with all of this (this will take a long time!), you will have your basics down, and you will understand the fundamental language used in subjects like approximation theory and PDEs. I'm not saying you'll be able to pick up a paper in approximation theory and say "Ah, how clear", but you will have the basic tools down. Knowing your basics is crucial!
In that, do you not think that going into Applied Math to begin with is good enough?
I'm not exactly sure how to interpret this. I enrolled in a Ph.D. program and my program is just "Mathematics".I know some schools have separate "applied math" programs, and I honestly can't comment on them because I'm not familiar with them. When considering applying for a Ph.D. program, you should be very careful and study the school and how their program works. I can't comment on them, because there are so many and I really only know how my school works. At my school, however, I took the same breadth courses as any typical pure math student and was in no way separated as an "applied" student until I chose an adviser in an applied field (approximation theory, which the more I learn about, feels more and more pure to me). In my experience, my pure math classes have been helpful to me, not a hindrance. The only downside to the way I approached things is that I did not take many computational sort of classes which emphasize programming and scientific computation, so I have had to pick that up on my own. Hopefully other students in an Applied Math Ph.D. program can discuss how their programs work.
Feel free to ask any more questions (especially if you want some clarification on analysis, approx theory, etc.). Good luck! | 677.169 | 1 |
Be aware of the need for mathematical theory to support numerical problem solving techniques.
Understand the relationship between the theoretical solution of a problem and a computational solution.
Extend his/her mathematical abilities in linear algebra and analysis.
Construct programs and use current mathematical programming tools such as LINPACK and the International Mathematical and Statistical Library (IMSL) to solve problems involving systems of equations, interpolation and least squares approximation of functions.
COURSE OUTLINE:
Floating Point Arithmetic and Rounding Errors
Taylor's Theorem
Non-linear Equations
Solution of Systems of Linear Equations Using Direct and Iterative Methods, Error Analysis and Norms | 677.169 | 1 |
quiz4
Course: MATH 1132, Fall 2009 School: UConn Rating:
Document Preview 7 Solutions s
Name: Math 1132 Section 4 Spring 2009 Quiz 5: Series Directions: There are two sides to this quiz. Clearly show your work and indicate your answers. 1. (4 pts) Circle T if the following statement is true and F if the statement is false. No justifica
Math 1132 Spring 2009 11.7 Homework Solutions1. Test the series for convergence or divergence.(1)nn=19n n+9Solution: The series is alternating, so lets try using the alternating series test. Condition (ii) is usually easier to verify:nli
Quiz 7 seriesn=1
Study Guide for the Final Exam The nal exam is comprehensive. It covers all the sections that we covered in class. This is: The review of Chapter 5. All of Chapter 6. Sections 7.1, 7.2, 7.3 (I guarantee at least one problem about work), and 7.4.
Josephson Effects and a -State in Superfluid HeliumPaul B. Welander May 6, 2002Abstract In this paper, I shall discuss the recent discovery of a metastable -state in a 3 He Josephson junction. This state is characterized by low frequency current os
CATALOG DESCRIPTION Graduate Certificate Program Graduate Certificate in NeuroscienceGeneral Information Neuroscience constitutes a truly interdisciplinary area of scientific study and research that incorporates physiology, molecular and cellular bi
CS 598CSC: Approximation Algorithms Instructor: Chandra ChekuriLecture date: April 15, 2009 Scribe: Qiang MaIn computer science, when dealing with dicult problems involving graphs and their associated metrics, one technique we usually resort to i
Exam 2 1.Math 115Fall 2007(15 pts) For each part, if the statement is always true, circle the printed capital T. If the statement is sometimes false, circle the printed capital F. For each T/F question, write a careful and clear justication or
Name Math 227 Exam 3: 1 May 2006Directions. Read each question on this exam before you start working so you can get the avor of the questions. If you arent sure what the question is asking for, its possible I can clarify for you. Please show all | 677.169 | 1 |
algebra
Tag details
Algebra is one of the basic building blocks to learning mathematics at a higher level.
According to Answers.com, the primary definition of algebra is "A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set." Within algebra, there are several categories within the discipline, including elementary algebra, abstract algebra, linear algebra, universal algebra, algebraic number theory, algebraic geometry, and algebraic combinatorics.
Latest blogosphere posts tagged "algebra"
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by edshelf: Reviews & recommendations of tools for education Trapper Hallam is a math teacher at Eisenhower High School that integrates technology seamlessly into his classroom. Among the websites and mobile apps that he recommends for Algebra... The post The Latest Math Apps: 15 Algebra 1 Tools From edshelf ...
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Öffnet 16. Mai in Berlin in der FSK-Kino unter dem poetischen Titel "Algebra in Love." Whit Stillman's Damsels in Distress (known as Algebra in Love in Germany), is opening in Berlin on May 16th at the FSK-KinoAlgebra 2 may be falling out of political favor in another state, this time Michigan. A Michigan House committee this month approved changes to state graduation requirements, including allowing students to skip Algebra 2 if they instead take a career and technical education course, the Associated Press reports . ...
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Motivation is important when you want to Improve your math skills You don't have to be born with math skills; solving problems is a matter of studying and motivation.That may not seem like such a surprise, but it's become easy to say 'I just can't do math.' While some element of math achievement may be [...]
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Dave brings Elihu Feustel on the show today to dig into the numbers behind his mathematical approach to sports betting. Elihu is a professional sports gambler, lecturer and author of the book Conquering Risk: Attacking Vegas and Wall Street.Elihu has a vast background in statistical analysis and specialises inOnly 5 percent of students will use calculus in college or the workplace, concludes a new report on college and career readiness by the National Center on Education and the Economy . Most community college students could succeed in college courses if they've mastered "middle school mathematics, especially ...
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Overview: Solving Linear Systems In order to solve systems of two sentences, the solution has to be true for both sentences. For example, the solution of a problem such as 2x-3y=13 and 3x +y = 3 has to work fox x and y all throughout the problem. Linear systems can be solved by graphing, by substitution, and byOverview: What Are Relations and Functions? A relation in algebra is a set of ordered pairs. The first element of the ordered pair is the domain, and the second element in the ordered pair is the range. If every first element is paired with only one second element, or every domain has a range, it is a function. ...
Combinatorics and more
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Margulis' paper Ramanujan graphs were constructed independently by Margulis and by Lubotzky, Philips and Sarnak (who also coined the name). The picture above shows Margulis' paper where the graphs are defined and their girth is studied. (I will come back to the question about girth at the end of the post.) ...
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Out in Left Field proudly presents the twelth in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names have been changed to protect privacy. Dedicated readers of my letters may recall my reaction to the Common Core's "Standards for—
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Logical connectives (Photo credit: Cuito Cuanavale) In their infinity of appearance, numbers can be clothed in the generality and variability of letters. Then their difference in value is hushed over, covered up. Except in those languages where letters and numerals do have the same value – as it was in Ancient ...
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When you go to college, math becomes more complicated that you will find a hard time to understand it. If you search for help with solving college algebra problems, you can choose online tutoring as the most flexible option. Not only you can get the online tutoring anywhere you are, but also you can get [...]
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Overview: What Is a Conic Section? Conic sections are the curves formed when a right circular cone intersects with a plane. The angle that the plane makes when it "cuts through" the cone determines the shape of the section. The four main types of conic sections are the circle, the parabola, the ...
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This Technorati Tag page contains the latest posts from around the Blogosphere about algebra.
If you're writing about algebra | 677.169 | 1 |
This activity would be done at the end of the school year in a pre-algebra class. It is a way to introduce algebra and its history, putting some personality into the abstractness of the subject by researching the individuals behind algebraic concepts. It was initially found on the following site five years ago when I first did it with my classes: It has since disappeared, however, so the specific modifications I made at the time are fuzzy at best, but I have made recent adjustments to every portion.
Introduction:
Algebra, what does it mean? Where did it come from? Who thought up this stuff? Have you ever wondered what the word algebra means or when and where algebra was developed or who developed algebraic concepts? In this project your group will go on a journey through time and the history of mathematics to discover the answers to these questions.
Task:
Each group will go on a quest to find the mathematicians' histories that have named as being the fathers or founders of algebra. On this journey your group will collect information about the mathematician responsible for developing the algebraic concept assigned to your group, create a timeline to show when the concept was developed in relation to other significant events in history, and find examples of the algebraic concept. Each group will prepare a Powerpoint to present the information to the class.
Group I The Father of Algebra (Algebraic thought and equations)
Group II Founder of Cartesian Plane and Graphing Equations
Group III Developer of Polynomials
Group IV Set Notation and Venn Diagrams Designer
Each group will need a Researcher, Recorder, Mathematician, and a Reporter.
Researcher - Using the resources below, work with the Recorder to find and record needed information for your topic.
Recorder - Record information on your topic and citation for where the information was found. Work with the Researcher and the Reporter to prepare a report of the findings of your group.
Mathematician - Work with the Researcher and the Recorder to find examples of mathematical problems from your assigned topic. Choose two examples that you can share, with which you can demonstrate the topic for the class.
Reporter - Work with the other members of your group to create a presentation, using PowerPoint, which you will present to the class. | 677.169 | 1 |
A Computational Introduction to Number Theory and Algebra
This book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
Appropriate for both math and computer engineering students, this text is a blend of carefully explained theory and practical applications, imparting the fundamentals of both information theory and ...
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, ...
This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a ... | 677.169 | 1 |
How to Solve It: A New Aspect of Mathematical MethodHow to Solve It: A New Aspect of Mathematical Method Book Description
George Polya was a Hungarian mathematician. He wrote this, perhaps the most famous book of mathematics ever written, second only to Euclid's "Elements." "Solving problems," The method of solving problems he provides and explains in his books was developed as a way to teach mathematics to students.
About the Author :
George Polya has contributed to How to Solve It: A New Aspect of Mathematical Method as an author.
Biography of George Polya Born in Budapest, December 13, 1887, George Polya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy. After a year in Gottingen and a short stay in Paris, he received an appointment at the ETH in Zurich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He al
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The book How to Solve It: A New Aspect of Mathematical Method by George Polya, Sam Sloan
(author) is published or distributed by Ishi Press [4871878309, 9784871878302].
This particular edition was published on or around 2009-6-1 date.
How to Solve It: A New Aspect of Mathematical Method has Paperback binding and this format has 280 number of pages of content for use.
This book by George Polya, Sam Sloan | 677.169 | 1 |
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Algebra Through Visual Patterns: A Beginning Course in Algebra
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Price: $50.00
Item #: ATVP
Gr Level:
6-12
Product Description:
This two volume set of teachers guides provides a semester's worth of student activities designed to help teachers address algebra instruction. Students learn about and connect algebra and geometry through the use of manipulatives, sketches, and diagrams. The course also links the resulting visual developments to symbolic rules and procedures.
The ideas and lessons presented are appropriate for all students learning first-year algebra whether their instruction is taking place in middle school, high school, or community college.
The Algebra Manipulative Kit is optional and sold separately. Although blackline masters of required manipulatives are included in the teachers guide, the manufactured items in the manipulative kit are more colorful and durable. | 677.169 | 1 |
Mathematics, General Colleges
A general program that focuses on the analysis of quantities, magnitudes, forms, and their relationships, using symbolic logic and language. Includes instruction in algebra, calculus, functional analysis, geometry, number theory, logic, topology and other mathematical specializations | 677.169 | 1 |
Graphing
$9.95
This program generates graphs that students read and interpret data using specific vocabulary; least and most, fewest and greatest. Additionally, this program also provides the data and the student must place the corresponding information on the graph. | 677.169 | 1 |
Microsoft Mathematics 4.0 4.0 includes a full-featured graphing calculator that's designed to work just like a handheld calculator. Additional math tools help you evaluate triangles, convert from one system of units to another, and solve systems of equationsHave you listened to The Morning Jam aka "The Shareen and Joe Show"? If not, you should. And I'm very sure those who have listened, you would have all heard the jingle regarding Joe Augustin's Little Cupboard. I just happened to have the chance to actually see the cupboard and take a few photos of it. I couldn't believe he actually created a studio from a corner cupboard. This is where our favourite Joe Augustin does his voice overs and other recordings. Apparently, Shareen actually sits behind Joe whenever "The Shareen and Joe Show" gets recorded. | 677.169 | 1 |
Objective 4.02
Objective 4.03
Objective 4.04
Design experiments and list all possible outcomes and probabilities for an event.
Goal 5
Algebra - The learner will demonstrate an understanding of mathematical relationships.
Objective 5.01
Identify, describe, and generalize relationships in which:
Quantities change proportionally.
Change in one quantity relates to change in a second quantity.
Objective 5.02
Translate among symbolic, numeric, verbal, and pictorial representations of number relationships.
Objective 5.03
Verify mathematical relationships using:
Models, words, and numbers.
Order of operations and the identity, commutative, associative, and distributive properties | 677.169 | 1 |
Middle School Advantage 2008 delivers the most award-winning content aligned with classroom curriculum. Get the best results with over 9,000 lessons and 2,400 exercises in the core subjects. Take advantage of a premier educational tool that offers state standards-driven content to increase scores in key subject areas.
A Complete Student Resource Center now on DVD with 10 core subjects along with after school extras including PC games and more!
Skills Learned:
Pre-algebra
Algebra I
Geometry
Reading
Vocabulary
Grammar
Earth Science
U.S. History
Foreign Language
Typing
Features:
10 Core Subjects Expanding on Key Academic Areas
9,000+ Lessons Deliver Easy-to-Understand Concepts and Tutorials
2,400+ Exercises Adapt to Different Learning Levels and Styles
Supports State Standards
Student Planner
After School Extras for today's students include music, PC games, mobile games, ringtones
Mathematics
Over 70 Lessons and 200 Exercises
Build a solid math foundation by mastering the fundamentals.
Pre-Algebra
Formulas
Decimals
Percentages
Factorization
Measurements
Scientific Notation
Variables
Word Problems
Calculating Fractions
Ratios and Proportions
Order of Operations
Algebra I
Functions
Radicals
Exponents
Linear Inequalities
Absolute Values
Graphs
Lines and Slopes
Geometry
Pythagorean Theorem
Reasoning
Angles
Triangles
Volumes
Surface Area
English
Over 100 Lessons and 2,000 Exercises
A variety of entertaining interactive activities and lessons strengthen Language Arts aptitude.
Reading
Prefixes and Suffixes
Root Words
Comprehension
Main Ideas
Topic Sentences
Summarizing
Making Predictions
Syllables
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Homophones
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Nouns and Verbs
Punctuation
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Verb Tense
Subject/Verb Agreement
Regular and Irregular Plurals
Science
Over 200 Illustrations and Animations,7,500 Keywords, 800 Cross-References
Explore the origin, structure and development of planet Earth through this fascinating multimedia program. Investigates current issues such as the ozone hole, greenhouse effect, and acid rain.
Earth Science
Weather
Properties of Air
Motion
The Solar System
Planets
Space
Galaxies
History
Over 106 Lessons and 280 Video Clips
Students retrace historical events form the early settlement of North America through the Internet revolution of the late 20th and early 21st century.
U.S. History
Colonization and Settlement
Three Worlds Meet
Revolution and the New Nation
Expansion and Reform
The Emergence of Modern America
World War II
The Great Depression
Postwar United States
The Civil War and Reconstruction
The Development of the Industrial United States
The Contemporary United States
Foreign Language Over 1,000 Key Words and Phrases
Learn basic vocabulary and sentence structure in Spanish, French, German and Italian. Each one comes complete with the Native Speak pronunciation flashcard system | 677.169 | 1 |
pre-algebra course centers on building the foundations of the student?s algebra. They will be introduced to variables, expressions, order of operations and basic problem solving skills. The course also introduces students to absolute value, the coordinate plane and different algebraic properties | 677.169 | 1 |
Representing Polynomials
This lesson unit is intended to help educators assess how well students are able to translate between graphs and algebraic representations of polynomials | 677.169 | 1 |
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$166.40Normal 0 false false false MicrosoftInternetExplorer4 Intended for a 2-semester sequence of ElementaryandIntermediate Algebrawhere students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course. Operations on Real Numbers and Algebraic Expressions; Equations and Inequalities in One Variable; Introduction to Graphing and Equations of Lines; Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions and Equations; Graphs, Relations, and Functions; Radicals and Rational Exponents; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conics; Sequences, Series, and The Binomial Theorem; Review of Fractions, Decimals, and Percents; Division of Polynomials; Synthetic Division; The Library of Functions; Geometry; More on Systems of Equations For all readers interested in elementary and intermediate algebra. | 677.169 | 1 |
The Sequoia Math Department teaches a comprehensive series of courses aligned to state standards designed to increase students' understanding and competency in increasingly complex mathematics. Our goals are to improve the success rate of all of our students and support all students in completing a high level of mathematics. We encourage students to go beyond the minimum two year requirement and strive to get the majority of the students to complete required a-g courses. Our highest level of coursework include IB Standard Level and Higher Level mathematics with further courses in Multivariable Calculus, Differential Equations, and Linear Algebra. We also offer additional Support classes for students below grade level in grades 9 and 10 and have an Algebra Readiness course for those students far below grade level upon entering high school.
The teachers in the Mathematics Department work collaboratively in curricular teams to provide consistency and support. All teams meet on a regular basis to discuss pacing, strategies, and assessments. Algebra I and Support classes benefit from a dedicated coach to provide additional leadership on best practices, instructional strategies, multiple assessments and support for testing and data evaluation.
The department adopted the College Preparatory Math (CPM) curricula for Geometry, Algebra II, and Pre-Calculus. This program comes from the University of California at Davis and is a nationally recognized program named as one of five exemplary math programs nationwide by the US Department of Education. CPM is a time-tested program and has been adopted by thousands of schools throughout the U.S. It includes the same curriculum as the traditional math textbooks, but it is presented in a unique fashion. Each unit includes an overriding problem anchored in the real world. Teachers coach, lead students to discovery, pose questions, lecture, monitor learning, clarify, and summarize concepts. The integrated curriculum spirals concepts throughout the course. Mastery is not expected the first time that a student is exposed to a concept; rather, mastery is expected over time as the students come in contact with concepts over and over again. The approach focuses on core concepts throughout the year.
Algebra I curricula is coordinated throughout the district and utilizes the state-adopted Prentice Hall textbook as well as a variety of supplemental materials. Students in Algebra I are required to take a common benchmark assessment each quarter. Algebra II students use the newly district-adopted Glencoe Algebra II textbook. IB courses utilize approved instructional materials in addition to other texts.
There are sixteen fully-credentialed math teachers in our department. We all make ourselves available to tutor individually by posting office hours. Most teachers are available during brunch and lunch and frequently before or after school. In addition, we offer a math support program through our 7th period Learning Center where students can get help on all levels of math. Every Tuesday we offer evening tutorials; one section for our Pre-Calculus and Calculus students and another section for our other courses. Students may drop in during the three hours to get assistance on concepts and assignments from a department math teacher.
Mathematics Courses
Our curriculum currently includes:
Algebra Readiness (elective credit)
Algebra Support (elective credit)
Algebra I
Geometry
Accelerated Geometry/Algebra II Trigonometry
Algebra II, Algebra II/trigonometry
Pre-Calculus
IB Math Studies
IB Math SL (AP AB Calculus)
IB Math HL Year 2 (BC Calculus + IB calculus topics)
Multivariable Calculus
Ordinary Differential Equations
Linear Algebra
If you have any questions about our curriculum or department, please contact the department chair, Laura Larkin, at [email protected]
Algebra Readiness
This is a remedial course for freshmen students who are not ready to take Algebra I. Algebra Readiness includes the study of pre-algebraic skills and concepts described in the Mathematics Framework for California Public Schools. The nine topics are whole numbers, operations on whole numbers, rational number, operations on rational numbers, symbolic notation, equations and functions, the coordinate plane, graphing proportional relationships, and algebra. Students must enroll concurrently in Algebra Readiness support. The two courses function as a single class, meeting a total of 100 minutes daily. Elective credit earned for this course will not count toward the Math graduation requirement.
Algebra Support
This is a course to support freshmen and sophomore students who are concurrently enrolled in Algebra I. The course focuses on the prerequisites and skills needed for Algebra I and preparation for CAHSEE. Alternative methodologies such as hands on manipulatives are used in this class. Elective credit earned for this course will not count toward the Math graduation requirement.
A rigorous college-prep course required by all 4-year colleges. Geometrical concepts are discovered by and taught to students through guided lessons. Topics covered include inductive and deductive reasoning, angles, polygons, congruent triangles, constructions, circles, right triangles, similarity, solids, logic, and introductory trigonometry.
Prerequisite: Completion of Algebra I or department recommendation. Open to 9th-graders who have earned a B or better in a formal full-year algebra course in the 8th grade.</p>
Accelerated Geometry/Algebra II Trigonometry
This course is designed to accelerate advanced students to enable them to take calculus and higher level math (after calculus) in their junior and/or senior years. The material is covered at an honors level, and is accelerated so that two courses are taught in one year. The course is excellent preparation for the analysis and synthesis required in advanced math courses. The course covers geometry from a deductive perspective. Topics include proofs, lines, triangles, polygons, vectors, circles, and 3D geometry. The algebra 2 portion of the course covers functions, graphing, polynomials, transcendental functions, rational expressions and equations, radical expressions and equations, trigonometry, complex numbers, and sequences and series. In addition, some topics in probability and statistics will be included as time allows. Students successfully completing this accelerated course may directly enroll in precalculus the following year.
Prerequisites: Algebra 1 with an B or better, teacher recommendation highly encouraged, and a strong desire to learn mathematics.
Algebra II
A math elective, Algebra 2 is a college-prep class. Algebra 1 concepts are reviewed and are taken to a more sophisticated level. The new topics include the applications of linear, quadratic, exponential, and logarithmic equations, systems of equations, determinants, Cramer's Rule, exponential and logarithmic functions, and introductions to conic sections, probability, and statistics.
Prerequisite: Completion of Algebra 1 and Geometry with C- or better
Algebra II/Trigonometry
A math elective, Algebra II/Trigonometry is a college-prep class. Algebra I concepts are reviewed and taken to a more sophisticated level. New topics include the applications of linear, quadratic, exponential and logarithmic equations, determinants, systems of equations, exponential and logarithmic functions, conic sections, sequences, statistics, and probability. The course also includes trigonometry including sine, cosine, and tangent functions and the Laws of Sine and Cosine. Special emphasis is placed on mathematical modeling, graphical representations, and investigations.
Prerequisite: Completion of Algebra I and Geometry with a C or better.
IB Math Studies
This rigorous, one-year math offering is designed to provide a realistic mathematics course for students with varied backgrounds and abilities Students most likely to select this course are those whose main interests lie outside the field of mathematics. The course develops the skills needed to cope with the mathematical demands of a technological society with an emphasis on the application of math to real-life situations. Some of the topics covered include logic, statistics, introductory calculus, as well as a review of geometry and topics from Algebra II. Students enrolled in this course will take the IB Math Studies exam.
A challenging elective course, whose purpose is to prepare students to take AP Calculus and/or IB Math SL/HL the following year. The first semester covers a wide range of topics, including trigonometry, inverse functions, including circular trig, triangle trig, vector, logarithms, and real world modeling with sinusoidal functions. The emphasis is on integrating graphing into the study of all concepts. The second semester is function theory, rational functions, matrices, probability and statistics, Algebra for college Mathematics, polar functions, and series.
This course covers the Calculus curriculum as set forth by the College Board Advanced Placement program and the International Baccaluareate Programme. The course includes topics such as limits, definition of the derivative, applications of the derivative, the Mean Value Theorum, and integral calculus concepts. In addition, the course reviews vectors, matrices, trigonometry, and other IB topics. Students who successfully complete this course will be prepared to take the APAB Calculus exam and IB Standard Level Math exam. This course is also the first year of the two year higher level IB/AP math
Prerequisite: Successful completion of Pre-Calculus with a C- or better. (B highly recommended)
IB Higher Level (HL) Year 2B Higher Level Year 2, AP Calculus (BC)
This course follows the IB Higher Level Year 1/AP Calculus (AB) course, and is designed for gifted math students. The course covers all of the material from BC calculus that was not covered in AP Calculus (AB), and uses the textbook from UC Berkeley's core calculus for math majors sequence. Additionally, a wide range of other advanced topics are covered including calculus based probability theory, complex analysis, functional analysis, separable and first order nonhomogeneous differential equations, advanced induction proofs, multivariable vector geometry and introductory vector calculus. This course not only provides excellent preparation for the BC calculus AP exam, but it also gives students a big advantage in their college mathematics courses. Students who successfully complete the course will be prepared to take the AP/BC exam and the IB Higher Level exam. Students will also receive transferable college credit from Canada college.
Prerequisite: Completion of IB Math HL Year 1/Advanced Placement Calculus (AB or BC) with a C or better (B is highly recommended)
Multivariable Calculus
This course follows IB Higher Level Year 2/AP Calculus (BC), and covers the traditional university level multivariable calculus curriculum. The course covers parametric equations and polar, spherical, and cylindrical coordinates (calculus based), vectors and the geometry of space, vector functions, the calculus of functions of several variables, multiple integrals, vector calculus, including Green's Theorem and Stoke's Theorem, and second order differential equations and their applications. Additionally, the material from IB Higher Level Year 2 is reviewed to make sure that students are prepared for the IB exam. Students will receive transferable collge credit for this class from Canada college.
Prerequisite: Successful completion of IB HL Y2
Ordinary Differential Equations
This is a standard, top university level introductory course in ordinary differential equations. The textbook we have adopted is the book used for the same course at Stanford University. Topics include, but are not limited to: separable ordinary differential equations (ODEs), first order homogeneous and nonhomogenous linear ODEs, second order homogeneous and nonhomogeneous linear ODE's, higher order linear ODE's, systems of linear ODE's, series solutions, a wide variety of applications to ODE's, numerical methods, computing and ODE's, and nonlinear ODE's based on student interest. Students completing this course will also receive transferable college credit from Canada College.
Linear Algebra
This is a standard, top university level introductory course in linear algebra. The textbook we have adopted is also used by Stanford University and several UC campuses. Course curriculum includes, but is not limited to: matrix computations/matrix algebra, methods of solving systems of linear equations in linear algebra, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and least squares, symmetric matrices and quadratic forms, a wide variety of applications to linear algebra, and computing in linear algebra and based on student interest. Students completing this course will also receive transferable college credit from Canada College. | 677.169 | 1 |
Book
Introduction to Book
The Language of Mathematics
The purpose of any language, like English or Zulu, is to make it possible for people to communicate. All languages have an alphabet, which is a group of letters that are used to make up words. There are also rules of grammar which explain how words are supposed to be used to build up sentences. This is needed because when a sentence is written, the person reading the sentence understands exactly what the writer is trying to explain. Punctuation marks (like a full stop or a comma) are used to further clarify what is written.
Mathematics is a language, specifically it is the language of Science. Like any language, mathematics has letters (known as numbers) that are used to make up words (known as expressions), and sentences (known as equations). The punctuation marks of mathematics are the different signs and symbols that are used, for example, the plus sign (+), the minus sign (-), the multiplication sign (××), the equals sign (=) and so on. There are also rules that explain how the numbers should be used together with the signs to make up equations that express some meaning | 677.169 | 1 |
Description
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
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2000 Solved Problems in Discrete Mathematics
9780070380318
ISBN:
0070380317
Pub Date: 1991 Publisher: McGraw-Hill
Summary: Master discrete mathematics with Schaum'sNthe high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! I...f you don't have a lot of time but want to excel in class, use this book to: Brush up before tests;Study quickly and more effectively; Learn the best strategies for solving tough problems in step-by-step detail. Review what you've learned in class by solving thousands of relevant problems that test your skill. Compatible with any classroom text, SchaumOs Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to rememberNfast! And SchaumOs are so complete, theyOre perfect for preparing for graduate or professional exams. Inside you will find: 2000 solved problems with complete solutionsNthe largest selection of solved problems yet published in discrete mathematics; A superb index to help you quickly locate the types of problems you want to solve; Problems like those you'll find on your exams; Techniques for choosing the correct approach to problems. If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have!Chapters include: Set Theory; Relations; Functions; Vectors and Matrices; Graph Theory; Planar Graphs and Trees; Directed Graphs and Binary Trees; Combinatorial Analysis; Algebraic Systems; Languages, Grammars, Automata; Ordered Sets and Lattices; Propositional Calculus; Boolean Algebra; Logic Gates | 677.169 | 1 |
Summary: Updates the original, comprehensive introduction to the areas of mathematical physics encountered in advanced courses in the physical sciences. Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded | 677.169 | 1 |
Incorporating Technology into Today's Mathematical Curriculum
Dr. Belinda Wendt
June 11, 1999
Abstract
To adequately prepare students for advanced scientific and engineering courses and applications, PSEs (Problem-Solving Environments) such as MAPLE, MATLAB, and advanced scientific calculators have become essential to a scientific curriculum. Within these environments, students can better visualize mathematical problems and approaches. They can tackle more complicated problems that would be very tedious without such a automated tool, opening the door for more creativity and a more thorough understanding of mathematics. Furthermore, the implementation of software code enhances the theoretical understanding of mathematical approaches. The logical process of software development forces the student to completely understand the procedures being implemented. This can result in increased confidence, which is typically a stumbling block for teaching mathematics. Moreover, the experience the students derive from the PSEs is essential since industrial companies, government agencies, and academic institutions now commonly use these and other similar tools.
An overview of MAPLE and MATLAB will be presented. A method for integrating PSEs within a calculus curriculum will be discussed. Samples will be provided that elicit the benefits listed above. | 677.169 | 1 |
What''s Calculus all about?
Does Calculus have any relevance to our daily lives? Or is it just another conglomeration of mathematical symbols hardly making sense to most? This is a presentation to remove the 'fear' of Calculus among students and introduce the subject to a anyone who is a total stranger to the subject but not a stranger to Mathematics. The presentation starts with the nature and scope of Calculus and the type of problems solved using Calculus. Mention is also made of the mathematicians who 'invented' the subject. Some interesting curves are also shown in the end. | 677.169 | 1 |
Book Description: Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well-motivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and well-motivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it.
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it | 677.169 | 1 |
Book Description: Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions. | 677.169 | 1 |
Product Details
Visual Group Theory by Nathan Carter
Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music, and many other contexts. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theorybring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. Although the book stands on its own, the free software Group Explorer makes an excellent companion. It enables the reader to interact visually with groups, including asking questions, creating subgroups, defining homomorphisms, and saving visualizations for use in other media. It is open source software available for Windows, Macintosh, and Unix systems from | 677.169 | 1 |
Approximating Perfection
A Mathematician's Journey into the World of Mechanics a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. "Approximating Perfection" considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications.
Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of calculus from a fully applied point of view; subsequent chapters explore selected topics from solid mechanics, hydrodynamics, and the natural sciences.
Emphasis is placed on the logic that underlies modeling in mechanics and the many surprising parallels that exist between seemingly diverse areas. The mathematical demands on the reader are kept to a minimum, so the book will appeal to a wide technical audience. | 677.169 | 1 |
Purchasing Options
Features
Addresses all aspects of mathematical modeling with mathematical tools used in subsequent analysis
Incorporates MATLAB, Mathematica, and MatCont
Covers spatial and stochastic models
Presents real-life examples of discrete and continuous scenarios
Includes examples and exercises that can be used as problems in a project
Summary
This how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB®, Mathematica®, and MatCont are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project.
Table of Contents
About Mathematical Modeling What Is Mathematical Modeling? History of Mathematical Modeling Latest Development in Mathematical Modeling Various Functional Forms in Mathematical Modeling Merits and Demerits in Mathematical Modeling | 677.169 | 1 |
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Algebra = Success in high school and beyond
Revolution K12's math programs are based on research-based best practices in assessment and intervention to help students at different levels of preparation. Our Algebra curriculum uses innovative and effective tools that build proficiency in math concepts aligned to state and Common Core standards. All programs scaffold to target foundational skills on an individual level and support teachers' efforts to effectively close the achievement gap.
Mentor Session technology provides a customized, engaging, and relevant online experience by providing differentiated instruction, breaking each question into manageable concepts to meet the needs of students at all levels. When a student selects an incorrect answer, Mentor Sessions guide the student through the question, breaking the problem into its foundational parts. This helps the student learn to analyze the concept.
Real-time, standards-based, diagnostic reports—available to both administrators and teachers—quickly guide instruction, and teacher reports can easily be printed to share student successes, weaknesses, and next steps with students and their parents. Learning barriers are reduced through the availability of English and Spanish text and audio tracks. | 677.169 | 1 |
Physics with Calculus as a Second Language: Mastering Problem-Solving
Get a better grade in Physics Solving physics problems can be challenging at times. But with hard work and the right study tools, you can learn the ...Show synopsisGet a better grade in Physics Solving physics problems can be challenging at times. But with hard work and the right study tools, you can learn the language of physics and get the grade you want. With Tom Barrett's University Physics as a Second Language(TM): Mastering Problem Solving, you'll be able to better understand fundamental physics concepts, solve a variety of problems, and focus on what you need to know to succeed. Here's how you can get a better grade in physics: Understand the basic concepts University Physics as a Second Language(TM) focuses on selected topics in calculus-based physics to give you a solid foundation. Tom Barrett explains these topics in clear, easy-to-understand language. Break problems down into simple steps University Physics as a Second Language(TM) teaches you to approach problems more efficiently and effectively. You'll learn how to recognize common patterns in physics problems, break problems down into manageable steps, and apply appropriate techniques. The book takes you step-by-step through the solutions to numerous examples. Improve your problem-solving skills University Physics as a Second Language(TM) will help you develop the skills you need to solve a variety of problem types. You'll learn timesaving problem-solving strategies that will help you focus your efforts, as well as how to avoid potential pitfalls | 677.169 | 1 |
Algebra: Everyday Explorations
If you've ever wondered, "What is algebra good for?" Alice Kaseberg will help you answer this age-old question with her respected text. INTRODUCTORY ...Show synopsisIf you've ever wondered, "What is algebra good for?" Alice Kaseberg will help you answer this age-old question with her respected text. INTRODUCTORY ALBEGRA, FOURTH EDITION, uses guided discovery, explorations, and problem solving to help you learn new concepts and strengthen the retention of new skills. Known for an informal, interactive style that makes algebra more accessible while maintaining mathematical accuracy, INTRODUCTORY ALGEBRA: EVERYDAY EXPLORATIONS, FOURTH EDITION, includes a host of learning tools that work together to help you succeed. A robust website and Enhanced WebAssign support you with practice problems, end-of-chapter problems that incorporate figures and examples, and quizzes that provide immediate feedback on your progress80618918782-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions. ISBN: 9780618918782.
Description:Acceptable. 4th. Pre-loved books for the budget-conscious...Acceptable. 4 | 677.169 | 1 |
Mr
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Forward
Preface
Acknowledgments
The Calculator
Using the Calculator
Review of Basic Math Fundamentals
Numbers, Symbols of Operations, and the Mill
Addition, Subtraction, Multiplication, and Division
Fractions, Decimals, Ratios, and Percents
Math Essentials and Cost Controls in Food Preparation
Weights and Measures
Using the Metric System of Measure
Portion Control
Converting Recipes, Yields, and Baking Formulas
Food, Recipe, and Labor Costing
Math Essentials in Food Service Record Keeping
Determining Cost Percentages and Pricing the Menu
Inventory Procedures and Controlling Costs
Purchasing and Receiving
Daily Production Reports and Determining Liquor Costs
Essentials of Managerial Math
Front of the House and Managerial Mathematical Operations
Personal Taxes, Payroll, and Financial Statements
Appendix A
Glossary
Index
List price:
$124.95
Edition:
6th 2012
Publisher:
Delmar Cengage Learning
Binding:
Trade Cloth
Pages:
384
Size:
8.50" wide x 10.75" long x 0.75 Math Principles for Food Service Occupations - 9781435488823 at TextbooksRus.com. | 677.169 | 1 |
***IMPORTANT DEADLINES***
Math 7:Current Book:
Math 8:Current Book:
Algebra:Current Chapter:
**REMINDER: The day of a test is always the last day to turn in quiz corrections for the chapter/book and also the deadline for assignments for that particular week! (The cutoff date for a quarter in terms of grading also works the same way)
April Assignments - Ms. Bayne
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I have a friend here who is in high school, who is crazy about math and who wants to major in mathematics in college. She has already learned some of the college subjects but she wonders whether she has learned the right ones.
Would anybody who knows sometihng about college math curriculum kindly help her? She needs a detailed math curriculum (courses you must take if you are a math major in college) in time order. Many thanks to those who'd like to help. Thank youNot sure exactly what there is someone would need to know about the curriculum. I'm a Chem. Engr. but I was pretty familiar with a math major's schedule because I considered minoring in it...I never finished since I couldn't fit the the last two math electives in my course schedule since they had to be 4 credit courses rather than the 3 credits I always had room for.
Basically you have to take Calculus 1-4 as the main requirements the first two years, then the rest is up in the air because (also depending on the school) you basically pick and choose the math electives based on what you want to specialize in. Usually the required couses for Juniors and Seniors are some type of Geometry, and Modern/Linear Algebra courses. Except for Calc I-III, I don't think any order is really required...except upper level courses that are I and II also. Calc III and IV sometimes go by different names (ie, calc 4 = differential equations), and technically they don't require each other. I managed to take III and IV in the same semester.
it also depends on what schools you're talking about. i know virginia tech has two different math majors: calculatory and discrete (algebraic? i'm not sure which one's on the title), though that doesn't make too much of a difference in starting out...
Waterloo is also the home of MAPLE, which is 100 times better than Mathematica.
At my school, a math major takes the following required courses (plus some math electives to fulfill academic calender requirements):
Code:
year 1: calculus I (differentiation)
calculus II (integration)
a full-year course in programming (C++) <- it is helpful to know some of this before arriving at school, btw
year 2: calculus III (series, etc)
calculus IV (vector calc)
linear algebra I & II
year 3: differential equations I & II
a course or two on numerical analysis
year 4:
electives OR whatever your school is offering this year (ie. complex variables, applied math, geometry/topography, differential geometry)
You friend should be able to schedule a chat with one of his math profs to discuss his/her scheduling during his/her first year at school.
In your first two years, students take a sequence covering everything from one variable calculus through multivariable, differential equations, and linear algebra (20A-20F). The same course is taken by physicists and other science majors, and students can place out of it if they've taken Calculus before and do well on a placement exam.
Towards the end of their second year, students take 'Mathematical Reasoning' (109), a course giving an introduction to the basics of writing proofs and making arguments rigorous.
Their third and fourth year, students take upper division math classes (About 2 per term). The students have a fairly flexible selection (any courses above 100), but their courseload must include
1 year of an "Algebra" course (100ABC or 102/103). Not much relation to High School Algebra I and II, the course consists of studying what happens when we have operations which share some, but not all of the properties of addition or multiplication. For example, what if we have a function which is associative (a+(b+c)=(a+b)+c), has an identity(0+a=a), and is invertible (a+(-a)=0), but may not be commutative (a+b may not equal b+a)?
1 year of an "Analysis" course. Depending on the course chosen, this can be anything from just a MUCH more rigorous look at calculus (142 AB) to a study on how concepts like a distance function and continuity can be adapted to more general systems than the real numbers (140ABC).
Around the third and fourth year students do start to spread out a bit more depending on what their future plans are (people going on to graduate school tend to take the more abstract courses when they have a choice, people going into industry often do the reverse).
If your friend thinks she may have had some of the stuff before (especially above calculus) she probably would want to take to the Professor of whichever course she thinks she's had before skipping it. I've had a couple instances where I knew 80% of the content of a course before taking it, but if I tried skipping the course the other 20% would cause huge problems in the next math class I tried to take.
Bloody hell. If I'm understanding these links correctly, the stuff I'm studying as part of my CS degree here is second year material for math majors in the US. Have I mentioned how I hate the Technion lately?
Antrax _________________ After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!
If it makes you feel any better, I had to take a few CS courses along the way to my math degree too (%$#% logic class). I think we were the exception rather than the rule though.
What kind of logic class?
Historically, many a computer science department was spun off from the math department (often not amicably), sometimes taking with it courses that were previously taught by the math department. Courses in computability theory, for instance, are based on mathematical work that predates all but the first few (or perhaps just all) computers, and were taught by the math department, but are now often taught by computer science. Similarly mathematical logic, incompleteness, formal languages, complexity theory, discrete math.
Yeah, the duality exists here regarding those courses, as well as a few others (for example, the dreaded combinatorics, where in the CS version of the course there's more focus on graph theory and especially trees). My problem is with stuff like advanced calc 2 (I took it this semester) which is basically multiple-variable functions, vectors, surface integrals and other crap like that, which has absolutely no bearing on anything I will ever do, and yet is compulsory.
Antrax _________________ After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!
Combinatorics and graph theory - how could I forget those? I actually liked them quite a bit. Theorems about graphs, algorithms that work on graphs, proofs that they work, and their complexity - fun stuff. Traditional math courses would deal more with the just the graphs and less with algorithms that opearte on them.
antrax: don't blame it on technion. i was done with all the courses specified in lepton's post, minus the linear II and diff eq. II, by the end of my first year. required. in fact, i'd finished other courses, too.
most degrees will require many credits that you will never use in the future, and most tech-related degrees require lots of advanced math (which, of course, means you have to take the lesser maths as well)
You cannot post new topics in this forum You can reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum | 677.169 | 1 |
Book Description: With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.The Essentials For Dummies SeriesDummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject. | 677.169 | 1 |
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An introduction to several areas in classical and modern geometry: analytic geometry, conic sections, Platonic solids and polyhedra, tessellations of the plane, projective, hyperbolic, and differential geometry. Students will see how symmetry groups serve as a unifying theme in geometry. This course will introduce students to the skill of writing formal mathematical proofs. | 677.169 | 1 |
Unit specification
Aims
The programme unit aims to introduce the basic ideas of metric spaces.
Brief description
A metric space is a set together with a good definition of the distance between each pair of points in the set. Metric spaces occur naturally in many parts of mathematics, including geometry, fractal geometry, topology, functional analysis and number theory. This lecture course will present the basic ideas of the theory, and illustrate them with a wealth of examples and applications.
This course unit is strongly recommended to all students who intend to study pure mathematics and is relevant to all course units involving advanced calculus or topology.
Intended learning outcomes
On completion of this unit successful students will be able to:
deal with various examples of metric spaces;
have some familiarity with continuous maps;
work with compact sets in Euclidean space;
work with completeness;
apply the ideas of metric spaces to other areas of mathematics.
Future topics requiring this course unit
A wide range of course units in analysis, dynamical systems, geometry, number theory and topology. | 677.169 | 1 |
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Modules
MTH4104 Introduction to Algebra
Description
This module is an introduction to the basic notions of algebra, such as sets, numbers, matrices, polynomials and permutations. It not only introduces the topics, but shows how they form examples of abstract mathematical structures such as groups, rings and fields, and how algebra can be developed on an axiomatic foundation. Thus, the notions of definition, theorem and proof, example and counterexample are described. The module is an introduction to later modules in algebra. | 677.169 | 1 |
Office Hours
Office hours are for going over problems that you are having
with homework, tests, or lectures you have attended. They are not
for making up missed lectures. Coming to class is your
responsibility and lecture material will be crucial to course
development and your success.
Course Description
Math 248 is a unique course, in which 1) you will learn to program in
MATLAB and 2) you will write
efficient and well-structured programs to perform a variety of
numerical tasks: find the roots of a nonlinear
equation, find the solution of a linear system of equations,
numerically evaluate a definite integral, and
determine and evaluate an interpolating polynomial. The relative
emphases on these two objectives will
be approximately 1/3 to 2/3. Most people, even those proficient
in the daily use of computers, are
unaware that computers can sometimes provide inaccurate or erroneous
results, even when they are
functioning correctly. Consequently, we will spend a good deal of
effort identifying sources of error and
performing error analyses. When all is said and done, you will not only
be able to program numerical
algorithms, you will be able to argue that your answers are (almost)
correct! Prerequisite: MATH 236, or
corequisite MATH 236 and consent of instructor. This course is not
open to students who have previously earned credit in MATH/CS 448.
Objectives
Learn stuctured programming in MATLAB
Program useful algorithms for performing numerical tasks as mentioned
above
Solve real world problems using the aforementioned techniques
Develop critical thinking and problem-solving skills
Grading
Homework (weekly)
35%
Programming Assignments (2)
30%
Exams (2)
20%
Final Exam
15%
Note: All assignments factor into your grade. This means: no
grades will be dropped.
Your weighted average (as a percentage) determines your grade for the
class on the standard 10pt scale (i.e. 100-90 = A to A-, 89-80 = B+ to
B-, 79-70 = C+ to C-, 69-60 = D, below 60 = F). The grades for this class
are generally not curved.
Homework
It is impossible to learn to program without getting your hands dirty.
Homework assigned will be a combination of computer programming and pencil
problems. Homework will be collected electronically. All assignments
are to be emailed to [email protected]. You must
send it from your JMU account for it to be received.
To receive proper credit, you must name your files according to the naming
convention given on the assignment. Assignments are due
by 11:59pm on the due date. For example, if your assignment is
due 1/20, then
it must be submitted by 11:59pm 1/20. Unless announced,
Late homework will be accepted up to
one date late with 20% penalty. No homework will be accepted more than
one day past the due date.
The format for submitting HW will be specified on the assignment.
You will be graded on the submission instructions, clarity, programming
style, functionality, and efficiency.
NOTE:[email protected] is an account solely setup for the
purposes of sending completed HW assignments. Do not attempt to contact me
with this email or send text. You may contact me through my email address
listed at the top of this document.
Projects
There will be two programming projects. These are of a larger-scale
than the weekly HW assignments. These assignments be in general
by quite challenging and will take most students a LARGE
block of time to complete properly. To minimize late nights in the lab,
it is paramount to get started on these assignments right away.
The last few days prior to the due date should be devoted primarily
to the writeup. If your program is not completed at least a few days before the due date, your writeup will suffer and it will show.
Specific instructions and submission
criteria will come later.
Exams
There will be two exams given during the semester and a final exam.
A portion of exam 1 and the final exam including writing code. The coding
portions are open-notes and are conducted on separate days. The written
portions are close-notes.
The Final Exam is mandatory, and unless you have documentation of
extenuating circumstances, you cannot pass the class if you do not
take the final.
Attendance
Attendance is one of the most important aspects of any mathematics
course. There is a strong correlation between attendance and success.
If you have extended illness or other extenuating circumstances that
prevent you from attending daily, you should contact me as soon as possible.
Bonus Points
Bonus points will be awarded sporadically throughout the semester.
These include attending
department colloquia (Mondays 3:45-4:45pm),
turning in dept problem of the week, or attending the
MAA Section Meeting
at JMU in April (more on this later).
Academic Integrity
Honesty with oneself and with others is of utmost importance in life.
We will strictly abide by the
JMU Honor Code. Any breach of the honor code results in failure
in this course. I encourage working in groups but not copying in groups.
Functionally or logically identical programs are considered violations
of the honor code to be prosecuted rigorously. If you have any questions
about what does or does not fit under the umbrella of academic integrity,
please contact me.
Words of Wisdom
Advice from Spring 2007 248 students:
Be prepared to dedicate a lot of time to this course. Really understand the material backwards and forwards for the tests because it is not enough to just know the formulas and plug and chug to get answers. Don't be afraid to ask questions and get help; office hours are your friends.
Do not put things off to the last minute, this is NOT a class you can procrastinate in.
The first few weeks, you will think that you will fail the class. It does take a lot of work and you must stay on top of your assignments from the beginning. Study really hard for the two exams and put forth a lot of effort on the labs and projects and you'll be fine.
Ask questions in class till you COMPLETELY understand the concept. This will really help when it comes to exams.
Spend plenty of time in the lab and do not wait until the night before to do assignments. Start on the programming assignments as soon as they are assigned. Do not be afraid go talk to the professor.
This class is what you make of it. | 677.169 | 1 |
Introduction to Algebra
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Develop a rich understanding of the rudiments of algebra in a relaxed and supportive learning environment. This course will help you understand some of the most important algebraic concepts, including orders of operation, units of measurement, scientific notation, algebraic equations, inequalities with one variable, and applications of rational numbers.
An emphasis on practical applications for your newfound skills will help you learn to reason in a real-world context. As a result, you will acquire a wide variety of basic skills that will help you find solutions to almost any problem.
This unique and thought-provoking course integrates algebra with many other areas of study, including history, biology, geography, business, government, and more. By the time you finish this course, you will understand how algebra is relevant to almost every aspect of your daily life.For complete course details, please visit the ed2go Online Career Training web site. | 677.169 | 1 |
…
This series by K A Hesse, published by Longman, was written at the time of decimalisation. The series consists of five books. Each book contains a large number of routine exercises. There is some brief explanation where required. The books are aimed at Key Stage Two students but could be appropriate for routine revision and practice…
This unit from the Continuing Mathematics Project is designed to enable students to cope confidently with expressions of the type A/B= C/D, where A, B, C and D, may be integers or algebraic products like mv2 or functions like log x, or sin y.
So equipped, students will be able to solve simple equations, change the subject of a…
This unit from the Continuing Mathematics Project goes into detail on how logarithms can be used to determine the laws which connect two variables on which experimental data has been collected. The unit follows naturally from the unit entitled The Theory of Logarithms.
The objectives of the unit are that students:
(i) understand…
Transformation of Formulae from the Continuing Mathematics Project builds on the work covered in the unit entitled Working with Ratios.
The objectives of this unit are to enable students to acquire the skills necessary to transform formulae which involve algebraical fractions, brackets, and roots, as well as formulae in which…
The unit from the Continuing Mathematics Project focuses on the x2 test as it is one of the most widely used statistical techniques. It is employed to compare theory with practice in biology, geography and the social sciences.
This unit is concerned with the practicalities of using the x2 test; stating a suitable hypothesis;…
This unit from the Continuing Mathematics Project is concerned with the calculation of the sides and angles of triangles and how this is used by the surveyor, the navigator, and the cartographer. The development of the television, the light and the road have all relied on trigonometry.
The objectives of the unit are that students…
This is the second part of the unit on The Theory of Logarithms from the Continuing Mathematics Project. It assumes that the user has completed the first part of the unit.
The objectives of the unit are to enable students to:
(i) acquire the concept of a logarithm as an extension of the concepts of a 'power' and of…
These two units from the Continuing Mathematics Project assumes that the word 'logarithm' will be familiar to students using it, and that they will have used tables of logarithms to reduce the labour of working out expressions by arithmetic methods.
The units assume that students are interested in knowing why logarithms…
This resource from the Continuing Mathematics Project has three units covering probability.
Introducing Probability is the first unit and its objectives are that students will learn that a probability can be from intuitive considerations or actual experimental results; the meaning of 'outcomes', 'sample space',…
This unit from the Continuing Mathematics Project assumes that students have met and used directed numbers, but that their use has become rusty. The unit briefly justifies the rules by which the four operations (+, -, x and ÷) can be accurately carried out. In this sense the unit could be said to form an introduction to the…
For students to benefit from this Mathematics in Geography 4 unit from the Continuing Mathematics Project they should be familiar with simple ratios and square roots, and with algebraic symbolism and quadratic equations. A fair amount of arithmetic is involved in the unit.
The objectives of the unit are;
(i) to introduce students…
This unit from the Continuing Mathematics Project is about linear programming - a procedure which is used widely in industry to solve management problems. The work here is an introduction to the subject.
There are no really new mathematical techniques in the unit. It is rather an amalgamation of things students have probably learnt…
This unit from the Continuing Mathematics Project has been planned to help students learn how to handle inequalities, and how to represent them graphically. Students should be familiar with manipulating positive and negative numbers, representing equations of the form y + 3x = 6 as a graph and finding the solution of equations like…
This unit from the Continuing Mathematics Project has been planned to help students remember and understand what indices indicate and the rules they obey. As with all the units in this collection the text is designed to test as it teaches and is in sections.
The content of the booklet starts with a diagnostic test then covers:…
This resource from the Continuing Mathematics project is made up of three units covering hypothesis testing.
The first unit covers the Wilcoxon Rank Sum Test and aims to teach the use of a non-parametric test for assessing the significance of the difference between two independent samples. In this context, the objectives for…
This unit from the Continuing Mathematics Project on flowcharts and Algorithms employs, three basic conventions:
(i) the use of a flowchart and the appropriate symbols
(ii) the use of computer statements, such as 'c = c + I1
(iii) the use of the inequality signs >, <, ≤ and ≥
Three very short programmes at the…
Descriptive Statistics is the name the continuing Mathematic Project has given to a sequence of four units which deal with distributions, histograms, bar charts, frequency tables and measures of central tendency and dispersion.
The first unit, Presenting Statistics, aims to teach some basic statistical techniques that are useful…
This unit from the Continuing Mathematics Project is the first of two units on Critical Path Analysis (CPA). The broad objective of this unit is for students to become familiar with the diagrammatic conventions and with some of the terminology used in CPA.
The first half of the unit is devoted to exposition and illustration of…
This unit from the Continuing Mathematics Project is about the relationship between two quantities (correlation). If the two quantities are height of father and height of son, then we often want to know the extent to which 'tall fathers have tall sons'. Two quantities may be correlated quite strongly while another two quantities…
The purpose of Primary Mathematics Today, first published in 1970 by Longman, was to give training teachers in Colleges of Education, as well as experienced teachers, an in-depth view of primary mathematics as at the time only a minority of primary teachers had special mathematical training.
The book is not in the first instance…
The Nuffield Advanced Mathematics reader provided articles as background or extensions to topics covered elsewhere in the course. The aim was to encourage students to make further study of the development and applications of the ideas about which they were learning. This was one of the ways by which the course team illustrated how… | 677.169 | 1 |
Course starts out easy and then suddenly gets difficult. The math isn't too tough but there are a LOT of formulas to memorize. We didn't need the book at all for the class as we used StatsPortal (a service you need to purchase) but that has an ebook on it. | 677.169 | 1 |
Mathematics is the bridge between the arts and the sciences and is used across the whole curriculum. We aim, therefore, to give all pupils a good understanding and appreciation of the four areas of Number, Algebra, Geometry and Measure and Statistics. We hope to spark the pupils' imagination, as well as develop their knowledge, spatial awareness and use of logical thought.
Mathematics has a spiral curriculum and so the textbooks we use help us to revise and extend prior subject knowledge. This is complemented by a wealth of other resources, enabling us to extend and encourage as appropriate. In the First Year pupils are taught in their Form groups for Mathematics, enabling us to get to know each child's mathematical ability fully before they are placed in sets in the Second Year and the Third Year. There is movement between sets, if and when this is felt appropriate, and each set is taught the same material. Each teaching group is usually made up of between fifteen and twenty pupils.
In the Fourth and Fifth Year (Year 10 and Year 11), pupils are placed in four sets and follow the 2 tier linear specification for IGCSE with the Edexcel examination board. All sets start by following the Higher Tier specifications and the decision of which tier each student is entered at for public exams is made after the mock examinations in the January of the Fifth Form. Our International Centre students also follow the Edexcel IGCSE course in a year. There is an option for the most able pupils to study OCR Additional Mathematics in Year 11 as an extra-curricular activity.
Mathematics is a popular subject choice for Sixth Formers at Ackworth. In the Lower Sixth we have three groups following Mathematics AS using the OCR MEI Mathematics course and there is an average of about ten students in each group. The Further Mathematics group of between ten and fifteen students follows the OCR MEI Mathematics modules that lead to an AS in Further Mathematics. The Upper Sixth has two sets of between twelve and fifteen students following A2 Mathematics, continuing with the MEI modules. There is also a Further Mathematics group of about twelve students taking MEI modules to complete the Further Mathematics A2 qualification.
Some of our gifted students study extra modules to gain further additional Advanced Level qualifications. Some students enter a Sixth Term Entrance Paper (STEP) or an Advanced Extension Award (AEA) in Mathematics when this is felt appropriate or is necessary for their further studies.
Extra-curricular activities within the Mathematics Department include the UK Maths Challenge, which is entered by students throughout the School. There is a puzzle and board games club, open to all students, where different aspects of Maths are investigated. Workshops are available for anyone needing extra help from First Year up to and including the Sixth Form. There is also a club for students who enjoy code-breaking and ciphers. We also enjoy participating in the UKMT team challenge and the Leeds University pop quiz. | 677.169 | 1 |
Elementary Statistics: A Step by Step Approach
"Elementary Statistics: A Step by Step Approach" is for general beginning statistics courses with a basic algebra prerequisite. The book is non ...Show synopsis"Elementary Statistics: A Step by Step Approach" Minitab, and the TI-83 Plus and TI 84-Plus graphing calculators, computing technologies commonly used in such courses Elementary Statistics: A Step by Step Approach
Easy to follow book. Very well prepared for an individual not knowledgeable in using Excel for statistics. I love the step by step Procedure Tables that show the process and the numerous | 677.169 | 1 |
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Starting at $31.09Worksheets for Classroom or Lab Practice for Elementary and Intermediate Algebra
Summary
KEY BENEFIT:Elementary and Intermediate Algebra, Third Edition, by Tom Carson, addresses two fundamental issuesindividual learning styles and student comprehension of key mathematical conceptsto meet the needs of todayrs"s students and instructors.Carsonrs"s Study System, presented in the "To the Student" section at the front of the text, adapts to the way each student learns to ensure their success in this and future courses. The consistent emphasis on thebig picture of algebra, with pedagogy and support that helps students put each new concept into proper context, encourages conceptual understanding. KEY TOPICS: Foundations of Algebra; Solving Linear Equations and Inequalities; Problem Solving; Graphing Linear Equations and Inequalities; Systems of Linear Equations and Inequalities; Polynomials; Factoring; Rational Expressions and Equations; Roots and Radicals; Quadratic Equations MARKET: For all readers interested in algebra.
Author Biography
Tom Carson's first teaching experience was teaching guitar while an undergraduate student studying electrical engineering. That experience helped him to realize that his true gift and passion are for teaching. He earned his MAT. in mathematics at the University of South Carolina. In addition to teaching at Midlands Technical College, Columbia State Community College, and Franklin Classical School, Tom has served on the faculty council and has been a board member of the South Carolina Association of Developmental Educators (SCADE). Ever the teacher, Tom teaches outside the classroom by presenting at conferences such as NADE, AMATYC, and ICTCM on topics such as Combating Innumeracy, Writing in Mathematics, and Implementing a Study System.
Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Jordan has served as the chair of the math department at Seminole Community College and has taught at Rollins College. He has been a member and leader of numerous professional organizations, including the Florida Two-Year College Mathematical Association (president), Florida Council of Teachers of Mathematics (district director), and others. In addition to his work on the Carson series, Jordan is also the lead author of _Integrated Algebra and Arithmetic, 2/e, also published by Pearson. In his spare time, he enjoys fishing, traveling, and hiking.
Table of Contents
1. Foundations of Algebra
1.1 Number Sets and the Structure of Algebra
1.2 Fractions
1.3 Adding and Subtracting Real Numbers; Properties of Real Numbers
1.4 Multiplying and Dividing Real Numbers; Properties of Real Numbers
1.5 Exponents, Roots, and Order of Operations
1.6 Translating Word Phrases to Expressions
1.7 Evaluating and Rewriting Expressions
2. Solving Linear Equations and Inequalities
2.1 Equations, Formulas, and the Problem-Solving Process
2.2 The Addition Principle of Equality
2.3 The Multiplication Principle of Equality
2.4 Applying the Principles to Formulas
2.5 Translating Word Sentences to Equations
2.6 Solving Linear Inequalities
3. Problem Solving
3.1 Ratios and Proportions
3.2 Percents
3.3 Problems with Two or More Unknowns
3.4 Rates
3.5 Investment and Mixture
4. Graphing Linear Equations and Inequalities
4.1 The Rectangular Coordinate System
4.2 Graphing Linear Equations
4.3 Graphing Using Intercepts
4.4 Slope-Intercept Form
4.5 Point-Slope Form
4.6 Graphing Linear Inequalities
4.7 Introduction to Functions and Function Notation
5. Polynomials
5.1 Exponents and Scientific Notation
5.2 Introduction to Polynomials
5.3 Adding and Subtracting Polynomials
5.4 Exponent Rules and Multiplying Monomials
5.5 Multiplying Polynomials; Special Products
5.6 Exponent Rules and Dividing Polynomials
6. Factoring
6.1 Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x2 + bx + c
6.3 Factoring Trinomials of the Form ax2 + bx + c, where a ≠ 1
6.4 Factoring Special Products
6.5 Strategies for Factoring
6.6 Solving Quadratic Equations by Factoring
6.7 Graphs of Quadratic Equations and Functions
7. Rational Expressions and Equations
7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with the Same Denominator
7.4 Adding and Subtracting Rational Expressions with Different Denominators | 677.169 | 1 |
Sunday, October 01, 2006
Up next, students will learn to evaluate composite functions. First, they will do a worksheet with function notation practice problems. I set the problems up in groups of 4 as follows: f(2), f(-4), f(a), f(2x - 5). I think that sneaking up this way on the idea of plugging in an expression for x will help students better understand how to evaluate f(g(x)) as an expression. I remember having a lot of difficulty when I first learned this concept, and this method helps make it clearer for me anyway...
Then, we'll use this dual lens model. I hope it will help them visualize what "the output of f is the input of g" means. After the model, we'll go through the concept of composing functions, and do some example problems together.
In an upcoming class, I will give students a chance to do function composition when given graphs or tables instead of equations.
5 comments:
Anonymous
said...
Not only do kids have trouble with function composition, the young adults in introductory abstract algebra classes seem to have the worst time with it. Luckily you are working on maps from R to R, so the lens approach will probably serve you well.
One thing that's worth doing is asking them to figure out whether or not map composition is associative, and then commutative.
Thanks for your response. For commutativity, they can switch the order of the lenses and see if the final projection is the same or not. This should help them understand why they get different results when switching the order of the functions.
But I'm not clear on what you mean by associativity. In the mapping model, you have to start at the initial input and follow the order of the lenses. If you try to start somewhere else, there will be no data to use.
Could you give an example of what you mean, because it sounds interesting and I don't think I'm getting it..
I use the lens just for the first day as a way to introduce the concept. We also look at composition in other ways. I'm not sure yet if it is helpful or not, but I think different students will remember different methaphors for the same concept. On the first quiz, I ask them to use the lens model, but I don't assess them on it by the time we get to the unit test or final exam. At that point, I just care if they have mastered the skill of composition | 677.169 | 1 |
Explorations in College Algebra, 5th Edition
Explorations in College Algebra, 5/e and its accompanying ancillaries are designed to make algebra interesting and relevant to the student. The text adopts a problem-solving approach that motivates students to grasp abstract ideas by solving real-world problems. The problems lie on a continuum from basic algebraic drills to open-ended, non-routine questions. The focus is shifted from learning a set of discrete mathematical rules to exploring how algebra is used in the social, physical, and life sciences. The goal of Explorations in College Algebra, 5/e is to prepare students for future advanced mathematics or other quantitatively based courses, while encouraging them to appreciate and use the power of algebra in answering questions about the world around us.
Explorations in College Algebra was developed by the College Algebra Consortium based at the University of Massachusetts, Boston and funded by a grant from the National Science Foundation. The materials were developed in the spirit of the reform movement and reflect the guidelines issued by the various professional mathematics societies (including AMATYC, MAA, and NCTM).
for Explorations in College Algebra, 5th Edition. Learn more at WileyPLUS.com
Explore & Extend: are a new feature in this edition. These "mini exploration" problems provide students with ideas for going deeper into topics or previewing new concepts. They can be found in every section.
Accumulation of tools: The authors added a transformation to each chapter that covers functions. The intention of these changes is to progressively accumulate (about one per chapter) the tools for transforming functions. This is a way to discuss properties of functions using function notation and to use the transformations as new functions are introduced.
Chapter 8 reconfigured: Ch. 8 has been split into two chapters: New Ch 8 covers quadratics and polynomials, while Ch. 9 is titled "Creating New Functions from Old."
Data: Data are updated throughout.
Extended Explorations: The two Extended Explorations have been integrated into the text as sections in relevant chapters.
Algebra developed from real-world applications: These materials are based on problems using actual data drawn from a wide variety of sources including: the U.S. Census, medical texts, the Educational Testing Services, the U.S. Olympic Committee, and the Center for Disease Control.
Flexibility of use: The materials are designed for flexibility of use and offer multiple options for adapting them to a wide range of skill levels and departmental needs. The text is currently used in both small and large classes, two and four-year institutions, and taught with technology (graphing calculators and/or computers) or without. Many optional special features are described in following points.
Many opportunities for students to practice: Each section includes Algebra Aerobics, which are intended to help the student practice the skills they just learned. At the end of each chapter the Check Your Understanding and Review Summary sections can help students review the major ideas of the chapter.
Actively involved students: The text advocates the active engagement of students in class discussions and teamwork. The Something To Think About questions, open-ended exercises, and the Explorations are tools for stimulating student thought. The Explorations are an opportunity for students to work collaboratively or on their own to synthesize information from class lectures, the text, and the readings, and most importantly from their own discoveries.
Emphasis on verbal and written communication: This text encourages students to verbalize their ideas in small group and class discussions. Suggestions for writing "60-second summaries" are included in the first chapter, and many of the assignments require students to describe their observations in writing. Throughout the text there references to wide a variety of essays, articles, and reports included either in the Anthology of Readings (in the appendix of the text) or on the book companion website at: Many of the Explorations conclude with group presentations to the class.
Technology integrated throughout: While the materials promote the use of technology and include many explorations and exercises using graphing calculators and computers, there are no specific technology requirements. Some schools use graphing calculators only, others use just computers, and some use a combination of both. This flexible approach allows Explorations in College Algebra, 4/e to meet the needs of many varying courses.
Student Solutions: Step-by-step solutions to selected problems are provided at the end of the book. | 677.169 | 1 |
The teaching and learning of mathematics are increasingly dependent on technology. Computer programs have become an integral part of mathematics education at all levels but most especially at the tertiary and pretertiary levels. Graphing packages are widely used at the secondary level, as are those that investigate the foundations of calculus, such as A Graphic Approach to the Calculus (Tall, Blokland, and Kok 1985). At the tertiary level, computer algebra systems such as Mathematica and Maple have become essential tools for university mathematics, and statistics packages such as Minitab and SPSS are a sine qua non for data analysis and display. The Internet and e-mail are widely used for finding information and for communicating with fellow students and teachers. Mathematics education is very different technologically from what it was even 10 years ago. | 677.169 | 1 |
Project Description
The
main thrust of the grant program is to improve student mathematics
scores on standardized tests. The grant project will enrich the
academic program of students by enhancing the mathematics curriculum
with the exploration of mathematical modeling, data analysis,
statistics, forming conjectures, establishing justifications,
and other problem-solving topics by integrating hand-held technology,
specifically, graphing calculators with computer connectivity.
Students will discover mathematics with the TI-73 graphing calculator
as they work through a series of investigations that are designed
to spark their curiosity and make them want to discover the mystery
of why, and to motivate them to want to probe into some important
mathematical concepts. All of the math concepts that will be
addressed are indicated across the strands in the Core Curriculum
Content Standards. The interesting problems and investigations
that students will explore will enable them to gain a deeper
understanding of mathematical concepts that will help them better
approach the more routine problems that are on the standardized
tests. | 677.169 | 1 |
RESOURCES
Absorb Mathematics Absorb Mathematics is an interactive course written by Kadie Armstrong, a mathematician and an expert in developing interactive online content. It offers a huge amount of interactivity - ranging from simple animations that show hidden concepts, to powerful models that allow flexible experimentation. Absorb Mathematics is divided into units – roughly corresponding to a lesson – so you can follow the structure of the course all the way through or use the units individually when covering a particular topic or concept. Each unit provides an engaging narrative supported by interactive animations, our unique simulations and exercises to ensure concepts have been understood. Try the free sample units in your class.
Throughout the years as an engineer, I have needed to research topics on engineering, physics, chemistry, mechanics, mathematics, etc. The Internet has made the job infinitely simpler, with the caveat that you have to be careful of your sources. Anyone can post anything on the Internet without peer review, and errors are rampant. The topics listed below are primarily ones that I have researched and generated custom pages for the content. I welcome visitor review and comments on my material to help ensure accuracy. Click here for an incredible resource from the the U.S. | 677.169 | 1 |
Math-Quadratic Equation-PSS-4
This is a numerical based class that will cover the fundamental concepts of Quadratic Equation. In this class we will cover different question of the quadratic equation. This class has been designed for Engineering Aspirant. This class covers curriculum of 11th-grade Mathematics, CBSE, ISC and various state board examinations. This session will gradually take you to various pattern of question with different level of difficulty. The session has been specially designed to cover problems of different pattern of IITJEE-Math, AIEEE-Math, BITSAT-Math, VIT-Math and other entrance examinations. The session will cover various concepts with their application in different problems.
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Learner's Planet is a rich source of online content, video lectures, mock tests, educational games and much more in kindergarten to Grade-12 segment. A subscription for Learner's Planet would bring tons of learning material at your mouse click. Print thousands of worksheets, try online quizzes and see instant results. Brush up your concepts with the help of recorded lectures by experienced teachers. Learn anytime anywhere at your own pace ! | 677.169 | 1 |
MAT
206
- Math for Elementary Education II
This is the second course of a two-semester sequence which explores the mathematics content in grades K-6 from an advanced standpoint. Topics include: descriptive statistics; probability; algebra; geometry and measurement. This course is open to elementary education and early childhood students only. | 677.169 | 1 |
The Learn Math Fast System is a math program designed to be read by older students from the beginning to the end in about one year. A younger student will quickly advance and have a solid foundation in math at a young age, but it will take longer than one year. All lessons, worksheets, tests, and answers are included in each book with the option of printing duplicate worksheets yourself. Watch the demo video in the drop down menu and read the explanation of what is in each volume. Then read through the testimonials and reviews on the "Testimonials" page. If you still have questions about the books, send us and email or call us during business hours (Pacific time). | 677.169 | 1 |
Course Lecture Titles
36
Lectures
30
minutes/lecture
1.
An Introduction to Precalculus—Functions
Precalculus is important preparation for calculus, but it's also a useful set of skills in its own right, drawing on algebra, trigonometry, and other topics. As an introduction, review the essential concept of the function, try your hand at simple problems, and hear Professor Edwards's recommendations for approaching the course.
19.
Trigonometric Equations
In calculus, the difficult part is often not the steps of a problem that use calculus but the equation that's left when you're finished, which takes precalculus to solve. Hone your skills for this challenge by identifying all the values of the variable that satisfy a given trigonometric equation.
2.
Polynomial Functions and Zeros
The most common type of algebraic function is a polynomial function. As examples, investigate linear and quadratic functions, probing different techniques for finding roots, or "zeros." A valuable tool in this search is the intermediate value theorem, which identifies real-number roots for polynomial functions.
20.
Sum and Difference Formulas
Study the important formulas for the sum and difference of sines, cosines, and tangents. Then use these tools to get a preview of calculus by finding the slope of a tangent line on the cosine graph. In the process, you discover the derivative of the cosine function.
3.
Complex Numbers
Step into the strange and fascinating world of complex numbers, also known as imaginary numbers, where i is defined as the square root of -1. Learn how to calculate and find roots of polynomials using complex numbers, and how certain complex expressions produce beautiful fractal patterns when graphed.
21.
Law of Sines
Return to the subject of triangles to investigate the law of sines, which allows the sides and angles of any triangle to be determined, given the value of two angles and one side, or two sides and one opposite angle. Also learn a sine-based formula for the area of a triangle.
4.
Rational Functions
Investigate rational functions, which are quotients of polynomials. First, find the domain of the function. Then, learn how to recognize the vertical and horizontal asymptotes, both by graphing and comparing the values of the numerator and denominator. Finally, look at some applications of rational functions.
22.
Law of Cosines
Given three sides of a triangle, can you find the three angles? Use a generalized form of the Pythagorean theorem called the law of cosines to succeed. This formula also allows the determination of all sides and angles of a triangle when you know any two sides and their included angle.
5.
Inverse Functions
Discover how functions can be combined in various ways, including addition, multiplication, and composition. A special case of composition is the inverse function, which has important applications. One way to recognize inverse functions is on a graph, where the function and its inverse form mirror images across the line y = x.
23.
Introduction to Vectors
Vectors symbolize quantities that have both magnitude and direction, such as force, velocity, and acceleration. They are depicted by a directed line segment on a graph. Experiment with finding equivalent vectors, adding vectors, and multiplying vectors by scalars.
6.
Solving Inequalities
You have already used inequalities to express the set of values in the domain of a function. Now study the notation for inequalities, how to represent inequalities on graphs, and techniques for solving inequalities, including those involving absolute value, which occur frequently in calculus.
24.
Trigonometric Form of a Complex Number
Apply your trigonometric skills to the abstract realm of complex numbers, seeing how to represent complex numbers in a trigonometric form that allows easy multiplication and division. Also investigate De Moivre's theorem, a shortcut for raising complex numbers to any power.
7.
Exponential Functions
Explore exponential functions—functions that have a base greater than 1 and a variable as the exponent. Survey the properties of exponents, the graphs of exponential functions, and the unique properties of the natural base e. Then sample a typical problem in compound interest.
25.
Systems of Linear Equations and Matrices
Embark on the first of four lectures on systems of linear equations and matrices. Begin by using the method of substitution to solve a simple system of two equations and two unknowns. Then practice the technique of Gaussian elimination, and get a taste of matrix representation of a linear system.
8.
Logarithmic Functions
A logarithmic function is the inverse of the exponential function, with all the characteristics of inverse functions covered in Lecture 5. Examine common logarithms (those with base 10) and natural logarithms (those with base e), and study such applications as the "rule of 70" in banking.
26.
Operations with Matrices
Deepen your understanding of matrices by learning how to do simple operations: addition, scalar multiplication, and matrix multiplication. After looking at several examples, apply matrix arithmetic to a commonly encountered problem by finding the parabola that passes through three given points.
9.
Properties of Logarithms
Learn the secret of converting logarithms to any base. Then review the three major properties of logarithms, which allow simplification or expansion of logarithmic expressions—methods widely used in calculus. Close by focusing on applications, including the pH system in chemistry and the Richter scale in geology.
27.
Inverses and Determinants of Matrices
Get ready for applications involving matrices by exploring two additional concepts: the inverse of a matrix and the determinant. The algorithm for calculating the inverse of a matrix relies on Gaussian elimination, while the determinant is a scalar value associated with every square matrix.
10.
Exponential and Logarithmic Equations
Practice solving a range of equations involving logarithms and exponents, seeing how logarithms are used to bring exponents "down to earth" for easier calculation. Then try your hand at a problem that models the heights of males and females, analyzing how the models are put together.
28.
Applications of Linear Systems and Matrices
Use linear systems and matrices to analyze such questions as these: How can the stopping distance of a car be estimated based on three data points? How does computer graphics perform transformations and rotations? How can traffic flow along a network of roads be modeled?
11.
Exponential and Logarithmic Models
Finish the algebra portion of the course by delving deeper into exponential and logarithmic equations, using them to model real-life phenomena, including population growth, radioactive decay, SAT math scores, the spread of a virus, and the cooling rate of a cup of coffee.
29.
Circles and Parabolas
In the first of two lectures on conic sections, examine the properties of circles and parabolas. Learn the formal definition and standard equation for each, and solve a real-life problem involving the reflector found in a typical car headlight.
12.
Introduction to Trigonometry and Angles
Trigonometry is a key topic in applied math and calculus with uses in a wide range of applications. Begin your investigation with the two techniques for measuring angles: degrees and radians. Typically used in calculus, the radian system makes calculations with angles easier.
30.
Ellipses and Hyperbolas
Continue your survey of conic sections by looking at ellipses and hyperbolas, studying their standard equations and probing a few of their many applications. For example, calculate the dimensions of the U.S. Capitol's "whispering gallery," an ellipse-shaped room with fascinating acoustical properties.
13.
Trigonometric Functions—Right Triangle Definition
The Pythagorean theorem, which deals with the relationship of the sides of a right triangle, is the starting point for the six trigonometric functions. Discover the close connection of sine, cosine, tangent, cosecant, secant, and cotangent, and focus on some simple formulas that are well worth memorizing.
31.
Parametric Equations
How do you model a situation involving three variables, such as a motion problem that introduces time as a third variable in addition to position and velocity? Discover that parametric equations are an efficient technique for solving such problems. In one application, you calculate whether a baseball hit at a certain angle and speed will be a home run.
14.
Trigonometric Functions—Arbitrary Angle Definition
Trigonometric functions need not be confined to acute angles in right triangles; they apply to virtually any angle. Using the coordinate plane, learn to calculate trigonometric values for arbitrary angles. Also see how a table of common angles and their trigonometric values has wide application.
32.
Polar Coordinates
Take a different mathematical approach to graphing: polar coordinates. With this system, a point's location is specified by its distance from the origin and the angle it makes with the positive x axis. Polar coordinates are surprisingly useful for many applications, including writing the formula for a valentine heart!
15.
Graphs of Sine and Cosine Functions
The graphs of sine and cosine functions form a distinctive wave-like pattern. Experiment with functions that have additional terms, and see how these change the period, amplitude, and phase of the waves. Such behavior occurs throughout nature and led to the discovery of rapidly rotating stars called pulsars in 1967.
33.
Sequences and Series
Get a taste of calculus by probing infinite sequences and series—topics that lead to the concept of limits, the summation notation using the Greek letter sigma, and the solution to such problems as Zeno's famous paradox. Also investigate Fibonacci numbers and an infinite series that produces the number e.
16.
Graphs of Other Trigonometric Functions
Continue your study of the graphs of trigonometric functions by looking at the curves made by tangent, cosecant, secant, and cotangent expressions. Then bring several precalculus skills together by using a decaying exponential term in a sine function to model damped harmonic motion.
34.
Counting Principles
Counting problems occur frequently in real life, from the possible batting lineups on a baseball team to the different ways of organizing a committee. Use concepts you've learned in the course to distinguish between permutations and combinations and provide precise counts for each.
17.
Inverse Trigonometric Functions
For a given trigonometric function, only a small part of its graph qualifies as an inverse function as defined in Lecture 5. However, these inverse trigonometric functions are very important in calculus. Test your skill at identifying and working with them, and try a problem involving a rocket launch.
35.
Elementary Probability
What are your chances of winning the lottery? Of rolling a seven with two dice? Of guessing your ATM PIN number when you've forgotten it? Delve into the rudiments of probability, learning basic vocabulary and formulas so that you know the odds.
18.
Trigonometric Identities
An equation that is true for every possible value of a variable is called an identity. Review several trigonometric identities, seeing how they can be proved by choosing one side of the equation and then simplifying it until a true statement remains. Such identities are crucial for solving complicated trigonometric equations.
36.
GPS Devices and Looking Forward to Calculus
In a final application, locate a position on the surface of the earth with a two-dimensional version of GPS technology. Then close by finding the tangent line to a parabola, thereby solving a problem in differential calculus and witnessing how precalculus paves the way for the next big mathematical adventure.
Course Lecture Titles
36
Lectures
30
minutes/lecture
1.
A Preview of Calculus
Calculus is the mathematics of change, a field with many important applications in science, engineering, medicine, business, and other disciplines. Begin by surveying the goals of the course. Then get your feet wet by investigating the classic tangent line problem, which illustrates the concept of limits.
19.
The Area Problem and the Definite Integral
One of the classic problems of integral calculus is finding areas bounded by curves. This was solved for simple curves by the ancient Greeks. See how a more powerful method was later developed that produces a number called the definite integral, and learn the relevant notation.
2.
Review—Graphs, Models, and Functions
In the first of two review lectures on precalculus, examine graphs of equations and properties such as symmetry and intercepts. Also explore the use of equations to model real life and begin your study of functions, which Professor Edwards calls the most important concept in mathematics.
20.
The Fundamental Theorem of Calculus, Part 1
The two essential ideas of this course—derivatives and integrals—are connected by the fundamental theorem of calculus, one of the most important theorems in mathematics. Get an intuitive grasp of this deep relationship by working several problems and surveying a proof.
3.
Review—Functions and Trigonometry
Continue your review of precalculus by looking at different types of functions and how they can be identified by their distinctive shapes when graphed. Then review trigonometric functions, using both the right triangle definition as well as the unit circle definition, which measures angles in radians rather than degrees.
21.
The Fundamental Theorem of Calculus, Part 2
Try examples using the second fundamental theorem of calculus, which allows you to let the upper limit of integration be a variable. In the process, explore more relationships between differentiation and integration, and discover how they are almost inverses of each other.
4.
Finding Limits
Jump into real calculus by going deeper into the concept of limits introduced in Lecture 1. Learn the informal, working definition of limits and how to determine a limit in three different ways: numerically, graphically, and analytically. Also discover how to recognize when a given function does not have a limit.
22.
Integration by Substitution
Investigate a straightforward technique for finding antiderivatives, called integration by substitution. Based on the chain rule, it enables you to convert a difficult problem into one that's easier to solve by using the variable u to represent a more complicated expression.
5.
An Introduction to Continuity
Broadly speaking, a function is continuous if there is no interruption in the curve when its graph is drawn. Explore the three conditions that must be met for continuity—along with applications of associated ideas, such as the greatest integer function and the intermediate value theorem.
23.
Numerical Integration
When calculating a definite integral, the first step of finding the antiderivative can be difficult or even impossible. Learn the trapezoid rule, one of several techniques that yield a close approximation to the definite integral. Then do a problem involving a plot of land bounded by a river.
6.
Infinite Limits and Limits at Infinity
Infinite limits describe the behavior of functions that increase or decrease without bound, in which the asymptote is the specific value that the function approaches without ever reaching it. Learn how to analyze these functions, and try some examples from relativity theory and biology.
24.
Natural Logarithmic Function—Differentiation
Review the properties of logarithms in base 10. Then see how the so-called natural base for logarithms, e, has important uses in calculus and is one of the most significant numbers in mathematics. Learn how such natural logarithms help to simplify derivative calculations.
7.
The Derivative and the Tangent Line Problem
Building on what you have learned about limits and continuity, investigate derivatives, which are the foundation of differential calculus. Develop the formula for defining a derivative, and survey the history of the concept and its different forms of notation.
25.
Natural Logarithmic Function—Integration
Continue your investigation of logarithms by looking at some of the consequences of the integral formula developed in the previous lecture. Next, change gears and review inverse functions at the precalculus level, preparing the way for a deeper exploration of the subject in coming lectures.
8.
Basic Differentiation Rules
Practice several techniques that make finding derivatives relatively easy: the power rule, the constant multiple rule, sum and difference rules, plus a shortcut to use when sine and cosine functions are involved. Then see how derivatives are the key to determining the rate of change in problems involving objects in motion.
26.
Exponential Function
The inverse of the natural logarithmic function is the exponential function, perhaps the most important function in all of calculus. Discover that this function has an amazing property: It is its own derivative! Also see the connection between the exponential function and the bell-shaped curve in probability.
9.
Product and Quotient Rules
Learn the formulas for finding derivatives of products and quotients of functions. Then use the quotient rule to derive formulas for the trigonometric functions not covered in the previous lecture. Also investigate higher-order derivatives, differential equations, and horizontal tangents.
27.
Bases other than e
Extend the use of the logarithmic and exponential functions to bases other than e, exploiting this approach to solve a problem in radioactive decay. Also learn to find the derivatives of such functions, and see how e emerges in other mathematical contexts, including the formula for continuous compound interest.
10.
The Chain Rule
Discover one of the most useful of the differentiation rules, the chain rule, which allows you to find the derivative of a composite of two functions. Explore different examples of this technique, including a problem from physics that involves the motion of a pendulum.
28.
Inverse Trigonometric Functions
Turn to the last set of functions you will need in your study of calculus, inverse trigonometric functions. Practice using some of the formulas for differentiating these functions. Then do an entertaining problem involving how fast the rotating light on a police car sweeps across a wall and whether you can evade it.
11.
Implicit Differentiation and Related Rates
Conquer the final strategy for finding derivatives: implicit differentiation, used when it's difficult to solve a function for y. Apply this rule to problems in related rates—for example, the rate at which a camera must move to track the space shuttle at a specified time after launch.
29.
Area of a Region between 2 Curves
Revisit the area problem and discover how to find the area of a region bounded by two curves. First imagine that the region is divided into representative rectangles. Then add up an infinite number of these rectangles, which corresponds to a definite integral.
12.
Extrema on an Interval
Having covered the rules for finding derivatives, embark on the first of five lectures dealing with applications of these techniques. Derivatives can be used to find the absolute maximum and minimum values of functions, known as extrema, a vital tool for analyzing many real-life situations.
30.
Volume—The Disk Method
Learn how to calculate the volume of a solid of revolution—an object that is symmetrical around its axis of rotation. As in the area problem in the previous lecture, you imagine adding up an infinite number of slices—in this case, of disks rather than rectangles—which yields a definite integral.
13.
Increasing and Decreasing Functions
Use the first derivative to determine where graphs are increasing or decreasing. Next, investigate Rolle's theorem and the mean value theorem, one of whose consequences is that during a car trip, your actual speed must correspond to your average speed during at least one point of your journey.
31.
Volume—The Shell Method
Apply the shell method for measuring volumes, comparing it with the disk method on the same shape. Then find the volume of a doughnut-shaped object called a torus, along with the volume for a figure called Gabriel's Horn, which is infinitely long but has finite volume.
14.
Concavity and Points of Inflection
What does the second derivative reveal about a graph? It describes how the curve bends—whether it is concave upward or downward. You determine concavity much as you found the intervals where a graph was increasing or decreasing, except this time you use the second derivative.
32.
Applications—Arc Length and Surface Area
Investigate two applications of calculus that are at the heart of engineering: measuring arc length and surface area. One of your problems is to determine the length of a cable hung between two towers, a shape known as a catenary. Then examine a peculiar paradox of Gabriel's Horn.
15.
Curve Sketching and Linear Approximations
By using calculus, you can be certain that you have discovered all the properties of the graph of a function. After learning how this is done, focus on the tangent line to a graph, which is a convenient approximation for values of the function that lie close to the point of tangency.
33.
Basic Integration Rules
Review integration formulas studied so far, and see how to apply them in various examples. Then explore cases in which a calculator gives different answers from the ones obtained by hand calculation, learning why this occurs. Finally, Professor Edwards gives advice on how to succeed in introductory calculus.
16.
Applications—Optimization Problems, Part 1
Attack real-life problems in optimization, which requires finding the relative extrema of different functions by differentiation. Calculate the optimum size for a box, and the largest area that can be enclosed by a circle and a square made from a given length of wire.
34.
Other Techniques of Integration
Closing your study of integration techniques, explore a powerful method for finding antiderivatives: integration by parts, which is based on the product rule for derivatives. Use this technique to calculate area and volume. Then focus on integrals involving products of trigonometric functions.
17.
Applications—Optimization Problems, Part 2
Conclude your investigation of differential calculus with additional problems in optimization. For success with such word problems, Professor Edwards stresses the importance of first framing the problem with precalculus, reducing the equation to one independent variable, and then using calculus to find and verify the answer.
35.
Differential Equations and Slope Fields
Explore slope fields as a method for getting a picture of possible solutions to a differential equation without having to solve it, examining several problems of the type that appear on the Advanced Placement exam. Also look at a solution technique for differential equations called separation of variables.
18.
Antiderivatives and Basic Integration Rules
Up until now, you've calculated a derivative based on a given function. Discover how to reverse the procedure and determine the function based on the derivative. This approach is known as obtaining the antiderivative, or integration. Also learn the notation for integration.
36.
Applications of Differential Equations
Use your calculus skills in three applications of differential equations: first, calculate the radioactive decay of a quantity of plutonium; second, determine the initial population of a colony of fruit flies; and third, solve one of Professor Edwards's favorite problems by using Newton's law of cooling to predict the cooling time for a cup of coffee. | 677.169 | 1 |
DescriptionThe text is available with a robust MyMathLab® course–an online homework, tutorial, and study solution designed for today's students. In addition to interactive multimedia features like Java™ applets and animations, thousands of MathXL® exercises that reflect the richness of those in the text are available for students.
Part 2 consists of chapters 9—15 of the main text.
Table of Contents
9. Infinite Sequences and Series
9.1 Sequences
9.2 Infinite Series
9.3 The Integral Test
9.4 Comparison Tests
9.5 The Ratio and Root Tests
9.6 Alternating Series, Absolute and Conditional Convergence
9.7 Power Series
9.8 Taylor and Maclaurin Series
9.9 Convergence of Taylor Series
9.10 The Binomial Series and Applications of Taylor Series
10. Parametric Equations and Polar Coordinates
10.1 Parametrizations of Plane Curves
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Graphing in Polar Coordinates
10.5 Areas and Lengths in Polar Coordinates
10.6 Conics in Polar Coordinates
11. Vectors and the Geometry of Space
11.1 Three-Dimensional Coordinate Systems
11.2 Vectors
11.3 The Dot Product
11.4 The Cross Product
11.5 Lines and Planes in Space
11.6 Cylinders and Quadric Surfaces
12. Vector-Valued Functions and Motion in Space
12.1 Curves in Space and Their Tangents
12.2 Integrals of Vector Functions; Projectile Motion
12.3 Arc Length in Space
12.4 Curvature and Normal Vectors of a Curve
12.5 Tangential and Normal Components of Acceleration
12.6 Velocity and Acceleration in Polar Coordinates
13. Partial Derivatives
13.1 Functions of Several Variables
13.2 Limits and Continuity in Higher Dimensions
13.3 Partial Derivatives
13.4 The Chain Rule
13.5 Directional Derivatives and Gradient Vectors
13.6 Tangent Planes and Differentials
13.7 Extreme Values and Saddle Points
13.8 Lagrange Multipliers
14. Multiple Integrals
14.1 Double and Iterated Integrals over Rectangles
14.2 Double Integrals over General Regions
14.3 Area by Double Integration
14.4 Double Integrals in Polar Form
14.5 Triple Integrals in Rectangular Coordinates
14.6 Moments and Centers of Mass
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
14.8 Substitutions in Multiple Integrals
15. Integration in Vector Fields
15.1 Line Integrals
15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
15.3 Path Independence, Conservative Fields, and Potential Functions
15.4 Green's Theorem in the Plane
15.5 Surfaces and Area
15.6 Surface Integrals
15.7 Stokes' Theorem
15.8 The Divergence Theorem and a Unified Theory
16. First-Order Differential Equations (Online)
16.1 Solutions, Slope Fields, and Euler's Method
16.2 First-Order Linear Equations
16.3 Applications
16.4 Graphical Solutions of Autonomous Equations
16.5 Systems of Equations and Phase Planes
17. Second-Order Differential Equations (Online)
17.1 Second-Order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.3 Applications
17.4 Euler Equations
17.5 Power Series Solutions
This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course. | 677.169 | 1 |
Winter Quarter 2003
The Many Hats of CHE 1205
In CHE 1205 Computation Lab, you will solve chemical engineering
problems using mathematical tools and software applications in
Excel, MatLab, and Maple. The following paragraphs describe the
overall goals of this course, the relevance of this course to your
role as a chemical engineer, and the specific concept goals of this
course.
Overall Goals of CHE 1205
The overall goal of this course is to
to fortify the chemical engineering concepts you are learning in CHE 1201
to give you the mathematical tools for solving several types of problems encountered as engineers
to apply Excel, MatLab, and Maple to simplify problem solving or to minimize repetitive calculations
to develop problem solving strategies and good documentation skills
Relevance of CHE 1205 to Your Role as a Chemical Engineer
CHE 1205 will introduce you to the types of problems you will
face as a chemical engineer. Say that you are a process engineer
for the production of an important pharmaceutical. You have been
given the responsibility of overseeing the production of this
product. Below are some of problems associated with this process
and the Lecture # where you will learn the concepts involved in
addressing these problems.
Lecture #1 and #2: Graphing and Least Squares Method You
notice that the volumetric flow rate of the gas in the pipeline
changes with the pressure. At a given pressure, the volumetric
flow rate of the gas is measured. At a given temperature, what is
the mathematical relationship between the pressure and the
volumetric flow rate of the gas? Can you predict the volumetric
flow rate of the gas under a new operating pressure?
Lecture #3: Numerical Integration You want to operate a
batch reactor at the temperature which optimizes the production of
the desired compound while minimizing the undesired reactions.
Working with the chemists in process development, the optimum
operating temperature has been determined experimentally in the
laboratory. Determine the total amount of heat that has to be
supplied to the reactor to change the temperature of the vessel from
room temperature to the initial optimum operating temperature.
Lecture #4 and #5: Numerical Solution to Ordinary Differential
Equations You start a process by filling an empty tank with two
different reactants. Reactant A in Stream #1 is pumped into the
tank at a constant rate while Reactant B in Stream #2 is being
pumped into the tank at a rate which is increasing linearly. The
concentration of the reactants and products in the tank are changing
as the tank is being filled. Determine the concentration of
Reactants A and B and the products with time.
Lecture #6 and #7: Material Balances on Multiple Unit
Processes with Reactions The chemists in the chemistry and drug
discovery group have determined the optimum temperature and pressure
for the reaction steps required to produce the drug. You are
involved in designing the process by which the reactants are mixed,
reacted, and separated from the products. You have been given the
desired production rate. However, the reactions do not go to
completion and moreover side reactions also decrease the amount of
desired product generated. What percent of the reactants are
converted to the product at the optimum conditions? What is the
flow rate of product lost in the product purification step? What
are the flow rates of the unreacted compounds? Can they be
separated from the by-products and recycled back with the fresh feed
to the reactor?
Concept Goals:
By the end of this course, you will understand the following chemical engineering concepts and be able to:
write the material balances for a reactive system using the
extent of reactions and determine the fractional conversion at a
given temperature and pressure given the equilibrium constant
(K)
You will also learn to apply the following mathematical tools and be able to:
recognize what a line, power, exponential function looks
like on a rectangular, semi log, or log plot
determine a mathematical equation which describes how y
changes with x using the least squares method
evaluate the integral of a function numerically using the
trapezoidal rule
solve an ordinary differential equation numerically using
the Runge-Kutta method
solve for the root of a nonlinear equation using Newton's rule
solve a set of linear algebraic equations for the unknowns
using matrices
solve a set of nonlinear equations for the unknowns
In the process you will be able to utilize the following functions in Excel, MatLab, and Maple:
Apply the least squares method to determine the coefficients
for the proposed equation and to determine the best fit equation
by comparing the sum of the square of the errors and the r
2value using following built-in functions:Ê SLOPE, INTERCEPT,
Trendline in Excel
Calculate the integral of a function numerically using the
trapezoidal rule in Excel and quad in MatLab
Solve ordinary differential equations in Excel and MatLab
using the Runge-Kutta method
Find the roots of a nonlinear equation using the GoalSeek /
Solver function in Excel
Solve a set of nonlinear equations using Solve in
Maple
No matter what career you pursue, the ability to critically think
and communicate effectively are just as important as your technical
abilities. In CHE1205, you will also learn to communicate and
document your solutions effectively and compile your projects into a
well-organized notebook. This notebook will serve as your personal
reference guide to the application of various mathematical tools and
programs in (Excel, MatLab, Maple) for your later courses.
Welcome to CHE1205 and I'm looking forward to a great quarter together! | 677.169 | 1 |
Linear Algebra encompasses the various methodologies for using multiple equations to solve for multiple unknowns. Below | 677.169 | 1 |
About America's Math Teacher
Rick Fisher is a math instructor for the Oak Grove School District in San Jose, California. Since graduating from San Jose State University in 1971 with a B.A. in mathematics, Rick has devoted his time to teaching fifth and sixth grade math students. Each year approximately one-half of his students bypass the seventh grade math program and move directly to a high-powered eighth grade algebra program.
Course 1 Basic Math Skills
This course is for 4th and 5th graders. Topics include whole numbers, fractions, decimals, percents, integers, geometry, and much more.
Course 2 Advanced Math Skills
This course is for middle grades students. Students will master the critical skills necessary for success in pre-algebra. Topics include whole numbers, fractions, decimals, percents, integers, geometry, and much more.
Course 3 Pre-Algebra
This course is a must for students prior to taking Algebra I. Integers, exponents, order of operations, ratios & proportions number theory, linear equations, probability & statistics are just a few of the topics that students will learn and master.
Course 4 Algebra I
This course will guide students to master the "gateway" subject, algebra. Algebra opens the doors to more advanced classes in math, science, and technology. Students will learn and master all of the essential algebra skills. The lessons are carefully explained in clear, simple terms, so that all students will understand, learn, and master each and every topic.
Rick has developed a highly functional, successful mathematics teaching system that produces amazing results. Results that he shares on this website in both elementary and middle grades versions.
This is a tested teaching strategy that will produce dramatic results for students. This easy to follow, step-by step program provides all the video tutorials and exercises you will need to super-charge any math program. There is plenty of free video's and exercise material available for you to see how valuable this system will be to your students.
Rick designed this system for elementary, middle grades and even high school students who were not prepared for algebra, to help bring them to algebra-readiness in less than one school year. Through this program, many of Rick's students have improved several grade levels in their math abilities in just one school year. Rick has also used the program successfully with students who are struggling with math and have limited English skills. This award winning program compliments all basic math textbooks, so it is a perfect partner program for schools. | 677.169 | 1 |
Course 18C Mathematics with Computer Science
Mathematics and computer science are closely related fields. Problems in computer science are often formalized and solved with mathematical methods. It is likely that many important problems currently facing computer scientists will be solved by researchers skilled in algebra, analysis, combinatorics, logic and/or probability theory, as well as computer science.
The purpose of this program is to allow students to study a combination of these mathematical areas and potential application areas in computer science. Required subjects include linear algebra (18.06, 18.700 or 18.701) because it is so broadly used; discrete mathematics (18.062J or 18.310) to give experience with proofs and the necessary tools for analyzing algorithms; and software construction (6.005 or 6.033 or 6.170) where mathematical issues may arise. The required subjects covering complexity (18.404J or 18.400J) and algorithms (18.410J) provide an introduction to the most theoretical aspects of computer science.
Some flexibility is allowed in this program. In particular, students may substitute the more advanced subject 18.701
Algebra I for 18.06, and if they already have strong theorem-proving skills, may substitute 18.314 for 18.062 or
18.310. Students who have taken 6.001 before the course 6 curriculum change
may use it instead of 6.01, and similarly students who have taken 6.170
may use it instead of 6.005 or 6.033. Students who have taken 18.410J before the curriculum change should not take 6.006, but must replace it with another Course 6 subject of at least 12 units.
One Subject from Each of the Following Pairs
18.400J (Automata, Computability, and Complexity) or 18.404J (Theory of Computation)
6.005 (Principles of Software Development) or 6.033 (Computer System Engineering)
Restricted Electives
Four additional 12-unit subjects from Course 18 and one additional subject of at least 12 units from Course 6. The Course 6 subject may be 6.02, 6.041, 6.17x, a Foundation or Header subject, or, with permission of the Mathematics Department, an advanced Course 6 subject. The overall program must consist of subjects of essentially different content and must include at least five Course 18 subjects with first decimal digit one or higher. | 677.169 | 1 |
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