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Algebra World – An Introduction
Algebra World software will turn struggling students into successful math learners and average students into accelerated math learners!
Algebra World teaches and reinforces introductory algebra concepts and meets NCTM standards. Mathematics topics have series of lessons and real world examples that accompany them. Equations and their relationship to word problems are emphasized throughout the program.
The major topics covered in Algebra World are: Expressions, Variables, Algebra Notation, Pattern Recognition, Integers, One Variable Equations, Two Step Equations, Ratio, Proportion and Percent, and Geometry. Each topic has a series of detailed lessons designed to teach key mathematical concepts. The lessons are followed by challenges in three skill levels that assess understanding of the subject and mathematical reasoning ability.
MathRealm's research showed that students are not as responsive to long narrations in software as they are to interactive visuals and audio effects that draw them into the program as active learners, rather than passive listeners.
Hands-on virtual manipulatives with limited text reading and immediate visual feedback will capture your students' attention and help them understand concepts, as well as develop logical reasoning. | 677.169 | 1 |
Thinking and Quantitative Reasoning
Designed for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need ...Show synopsisDesigned for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need to learn in order to be better quantitative thinkers and decision-makers. The author team's approach emphasizes collaborative learning and critical thinking while presenting problem solving in purposeful and meaningful contexts. While this text is more concise than the author team's Mathematical Excursions ((c) 2007), it contains many of the same features and learning techniques, such as the proven Aufmann Interactive Method. An extensive technology package provides instructors and students with a comprehensive set of support toolHide synopsis80618777389-5777372Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780618777372Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780618777389-2 | 677.169 | 1 |
Buy now
E-Books are also available on all known E-Book shops.
Short description Featuring a unique CD that contains a virtual computer/calculator software program, The Definitive Guide to How Computers Do Math begins by explaining fundamental math concepts, such as the use of powers and different place-value number systems (specifically binary, decimal, and hexadecimal). The book then introduces the concepts of computers and calculators and discusses fundamental concepts such as the stack and the use of subroutines. Readers then use what they have learned to create a set of basic math subroutines for addition, subtraction, multiplication, and division. Finally, these routines are gathered together into a framework program that the authors use to implement a simple four-function calculator. | 677.169 | 1 |
AEPA Mathematics 10
Be prepared for your AEPA Mathematics certification exam with the help of this comprehensive study guide from XAMonline. Aligned specifically to current state standards, this study covers the sub-areas of Number Sense; Data Analysis and Probability; Patterns, Algebra, and Functions; Geometry and Measurement; Trigonometry and the Conceptual Foundations of Calculus; and Mathematical Structure and Logic. Study and master the 28 competencies/skills found on the AEPA Mathematics certification exam, and improve your score with the 125 sample-test questions. | 677.169 | 1 |
General Mathematics
Problems with and Without ... Problems!
This book is addressed to College honor students, researchers, and professors.
It contains 136 original problems published by the author in various scientific journals around the world.
The problems could be used to preparing for courses, exams, and Olympiads in mathematics.
Many of these have a generalized form.
For each problem we provide a detailed solution.
I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco.
I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the Moroccan student team for the International Olympiad of Mathematics in Paris, France, 1983. | 677.169 | 1 |
"More than 2 million books sold in the DeMYSTiFieD series! A straightforward, step-by-step approach for fast and fun mastery of everyday math from the trusted DeMYSTiFieD brand"-- Provided by publisher.
A theoretical physicist and author of the controversial best-seller The Trouble with Physics describes his new approach for thinking about the reality of time and explains his theory about the laws of physics not being timeless but rather capable of evolving.
"This book provides a comprehensive review of algebra 2 for advanced high school and junior college students. It includes practice exercises to reinforce concepts and terms reviewed in the book"-- Provided by publisher.
"Ponderables: 100 breakthroughs that changed history. Who did what when"--Cover.
"Includes: Fold-out timeline with over 1000 milestone facts"--Cover.
Introduction -- Prehistory to the Middle Ages -- The Renaissance and the Age of Enlightenment -- New numbers, new theories -- Modern mathematics -- 101 mathematics: a guide -- Imponderables -- The great mathematicians.
Counting, measuring, and calculating are as old as civilization itself, as are many of the theorems and laws of math. This book tells the fascinating stories behind mathematical discoveries. The 12-page foldout timeline sets the saga of mathematics against the backdrop of world history.
Signs of men -- An abstraction from the gabble -- Common beliefs -- Darker by definition -- The axioms -- The greater Euclid -- Visible and invisible proof -- The devil's offer -- The Euclidean Joint Stock Company -- Euclid the great. | 677.169 | 1 |
This comprehensive study guide will help Grd. 12 learners to understand and master all the basic concepts and procedures required for the matric Mathematics examinations. It contains many exercises (with complete solutions) which enable learners to apply these concepts and skills in various contexts. The book follows a simple approach, dealing with one Learning Outcome at a time, explaining and providing examples and exercises about all the compulsory topics, such as Logarithms; Patterns, Sequences and Series; Financial Mathematics; Functions and their Inverses; Linear Programming; Remainder and Factor Theorem; Differential Calculus: Theory and tangent to curves, Graphs, Rate of change, Maximum and Minimum values; Trigonometry: Identities and Equations (compound and double angles) and Solving 2-D and 3-D Triangles; Coordinate Geometry (Analytical Geometry) and Transformation Geometry. | 677.169 | 1 |
IIT Foundation MATHEMATICS Class 9300 Our Price:165 You Save: 135
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IIT Foundation MATHEMATICS Class 9 Book Description
About the Book :
A child with a strong foundation takes much less time to understand a subject as compared to other students. MATHEMATICS FOUNDATION CLASS 9 aims at providing the right foundation to the students as they enter class 11. This book will prove to be a stepping stone to success in higher classes and competitive exams like Olympiads, IIT-JEE etc. The book covers a very broad syllabus so as to build a strong base. The USP of the book is its style and format. The book is supplemented with "Do You Know," "Knowledge Enhancer," "Checkpoints," and "Idea Box." Another unique feature is the Exercise Part which is divided into 2 levels. The broad variety of questions covered are Short, Very Short, Long, Fill in the Blanks, True/ False, Matching, HOTS, Chart/ Picture/ Activity Based, MCQ's - one option correct, multiple options correct, Passage based, Assertion-Reason, Multiple Matching etc. Solutions to selected questions has been provided at the end of each chapter.
Popular Searches
The book IIT Foundation MATHEMATICS Class 9 by Disha Experts
(author) is published or distributed by Disha Publication [9381250685, 9789381250686].
This particular edition was published on or around 2011-1-1 date.
IIT Foundation MATHEMATICS Class 9 has Paperback binding and this format has 428 number of pages of content for use.
This book by Disha Experts | 677.169 | 1 |
Next: Related Rates
Previous: Linearization and Newton's Method
Chapter 3: Applications of Derivatives
Chapter Outline
Loading Content
Chapter Summary
Description
Students gain practice with using the derivatives in related rates problems. Additional topics include The First Derivative Test, The Second Derivative Test, limits at infinity, optimization, and approximation errors. | 677.169 | 1 |
Math 8
Doug Ingamells, Periods 1, 2 & 6
All classes are composed of 7th and 8th graders. They are usually on
the same page and assignment, except that they have different "block"
days so assignment and due dates can differ. There are two other
sections of Math 8, both taught by Kerry Bayne.
PPS has decided that the first four (of twelve total) chapters in the
algebra text will be part of the Math 8 curriculum. This means that
Algebra 1-2 now starts at Chapter 5, and students must complete the
first four chapters before enrolling in Algebra 1-2. The district
calendar has us completing the Algebra first, then proceeding with
pre-algebra topics at the end of the year. All students in Math 8 should
be in Algebra 1-2 the following year.
PPS uses standard A-F grades. In this class grades are weighted so
that tests count 60% and homework/classwork counts 40%. We use the
standard 90%(A), 80%(B), 70%(C), 60%(D) breakpoints.
A copy of the general information letter for this class can be found here: | 677.169 | 1 |
Mathematics
To achieve the goal, the department develops and improves its curriculum integrating strengths of American, Japanese and other countries' curricula. In particular, American textbooks contain various types of basic practice problems, which help students build a solid foundation of each mathematical concept, while Japanese textbooks and problem solving books contain many problems requiring multiple steps for their solution, which help students develop ability to apply their knowledge to solve complex problems. Both American and Japanese textbooks are used. Indian textbooks are also used to take advantage of their clear and easy-to-understand presentation of proofs of theorems and formulas.
The curriculum is constructed taking the cognitive development of each student into account. In general, more abstract concepts are introduced at higher grade levels. At each grade level, students are placed in one of two to three levels that best fits their cognitive and mathematical development. The goal for each level is set so that students will feel that they can reach the goal if, but only if, they put effort into studying mathematics. Each grade level has the following goal:
9th Grade
In the 9th grade, all students are required to take the course "Algebra and Geometry." The goal of this course is to develop student competence to deal with mathematical expressions, the basic language of mathematics. In particular, the course is designed to develop students' fluency in algebraic manipulations with polynomials and irrational numbers and to develop the ability to construct geometric proofs. Students are placed in either an intermediate or an honors level class, based on the results of a placement test. The course includes the following topics: Equations, Inequalities, Exponents and Polynomials, Polynomials and Factoring, Systems of Equations, Radical Expressions and Equations, Relations and Functions, Quadratic Equations, Introduction to Probability and Statistics; Congruent Triangle, Applying Congruent Triangles, Quadrilaterals, Similarity, Circles, Polygons and Areas, Surface Area and Volume.
10th Grade
In the 10th grade, all students are required to take the course "Algebra and Trigonometry." The goal of this course is to continue developing student competence to deal with mathematical expressions. The course develops fluency in algebraic manipulations, especially with rational and radical expressions, and in solving quadratic equations. Students are placed in either an elementary, intermediate or honors level class based on the results of a placement test. The course includes the following topics: Equations and Inequalities, Systems of Equations and Problem Solving, Polynomials and Polynomial Equations, Equations of Second Degree, Rational Expressions and Equations, Polynomial Functions, Powers, Roots, and Complex Numbers, Quadratic Equations, Relations, Functions and Graphs, Quadratic Functions and Transformations, Exponential and Logarithmic Functions, Trigonometric Functions, Trigonometric Identities and Equations, Counting and Probability.
11th Grade
In the 11th grade, all students are required to take the course "Pre-calculus." The goal of this course is to develop student competence in logical and abstract thinking. Building on the competence developed in previous courses, 11th grade students fully utilize their ability to understand mathematically-expressed abstract concepts and to express their own ideas mathematically. This training logical and abstract thinking will be extremely valuable throughout their lives. Students are placed either in an elementary, intermediate, or honors level class, based on their Algebra and Trigonometry course grades. The course includes the following topics: Trigonometric Functions, Introduction to Three dimensional Geometry, Vector Algebra, Permutations and Combinations, Binomial Theorem, Probability, Straight Lines, Conic Sections, Matrices, Determinants, Sequence and Series, Mathematical Induction, Three Dimensional Geometry.
The mathematics core curriculum is structured on mathematical content areas. To develop students' problem solving ability of utilizing knowledge of various mathematical content areas, 11th graders can elect "Advanced Problem Solving" course. Although the course mainly focuses on mathematical problems, it may include real world social, economical, and environmental problems as well. For students to qualify for the course, they must (1) be in an honor level Algebra and Trigonometry class at the end of the 10th grade and (2) participate in the American Mathematics Competition (AMC-10) during the 10th grade. The course includes the topics as follows: Combinatorics, Complex Numbers, Inversion in Plane, Mathematical Induction, Proofs by Contradiction, Sequence/Series, Basic Probability, Law of Sine/Cosine, Basic Mod Computation, Basic Functions and Graphs, Basic Geometry, Checking the Validity of the Answer, Working Backward, Work with Algebra and Geometry on a Same Problem, Analogy (Find Similar Problem), and Use of Symmetry.
12th Grade
In the 12th grade, all students are required to study calculus, and students who wish to major in science, mathematics, medicine, pharmacy, or engineering at college are required to study linear algebra as well. Students who wish to major in economics and commerce in college are strongly encouraged to take linear algebra. Other students may take linear algebra as an elective course. The goal of these courses is to introduce 12th graders directly to their study of mathematics at Keio University and other colleges in Japan and the United States.
"Calculus for Non-Science Majors" course includes the following topics and students will be placed either in an elementary or intermediate level class by grades of Pre-Calculus: Limits of Functions, Derivatives (The Chain Rule, Implicit Differentiation, Parametric Representation, Differentiation of Exponential and Logarithmic Functions, Higher Derivatives), Applications of Differentiation (Maxima and Minima, Inflexion Points, Graph Sketching), Indefinite Integrals (Method of Substitution, Integration by Parts, Partial Fractions), Definite Integrals and Applications (Areas and Volumes).
"Advanced Calculus & Linear Algebra for Science Majors" course is a requirement for students applying to faculty of science and technology, faculty of medicine and faculty of Pharmacy. The calculus part in this course deals with single variable calculus and includes the following topics: Limit of Functions, Continuity, Differentiation, Sketching a Graph, Integration including Integration by Parts and Integration by Substitution, Surface area, Volume, Polar Coordinates, Differential Equations and Infinite Sequences and Series. Linear algebra part in this course includes the following topics: Basic Notions of Vector Spaces, Systems of Linear Equations, Determinants, Eigenvalues and Eigenvectors, Inner Product Spaces up to Orthogonal Projection and Gram-Schmidt Orthogonalization. The calculus part will be taught in the first three quarters of the school year and the linear algebra part will be taught in the forth quarter. This is a very demanding fast paced course and all the students enrolled in the course are expected to devote a lot of time and effort to study outside of class by reading textbooks and solving problems in the textbooks | 677.169 | 1 |
I have a number of problems based on online rational expression calculator I have tried a lot to solve them myself but in vain. Our teacher has asked us to figure them out ourselves and then explain them to the whole class. I reckon that I will be chosen to do so. Please help me!
Due to health reasons you may have not been able to attend a few classes at school, but what if I can you can simulate your classroom, in the place where you live? In fact, right on the laptop that you are working on? All of us have missed some lectures at some point or the other during our life, but thanks to Algebra Buster I've never been left behind. Just like an instructor would explain in the class, Algebra Buster solves our queries and gives us a detailed description of how it was solved. I used it basically to get some help on online rational expression calculator and quadratic equations. But it works well for just about everything you can think of.
I'm also using Algebra Buster to help me with my algebra homework problems. It really does help you quickly comprehend certain topics like subtracting fractions and long division which would take days to understand just by reading tutorials. It's highly recommended software if you're looking for something that can help you to solve math problems and show all pertinent step by step solution. Two thumbs up for this software.
You all must be pulling my leg! How could this not be popular knowledge or promoted here? How and where should I get additional info for trying Algebra Buster? Forgive anyone for being a bit doubtful, but do either of you know whether or not I can receive a test copy to use this software? | 677.169 | 1 |
This course will emphasize the study of linear functions. Student will use functions to represent, model, analyze, and interpret relationships in problem situations. Topics include graphing, solving equations and inequalities, and systems of linear equations. Quadratic and nonlinear functions will be introduced. This course counts for high school credit and will become a permanent part of the student�s high school transcript. Grade 8 Algebra I will be factored into the student�s overall high school grade average/GPA. Students will be administered the 2012 STAAR EOC for Algebra I in May. Students EOC score will NOT count as 15% of their final Algebra I grade. In order to graduate from high school, students must achieve a cumulative score in each of the four core content areas. For each of the four core content areas, the student�s cumulative score ≥ n times student�s passing scale score, where n = number of assessments taken. For more information regarding the STAAR EOC go to the TEA website at
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Assignment Heading
(7.4 KB)
When ever you turn in an assignment on notebook paper or a print out, you must include the following heading on your paper. | 677.169 | 1 |
TI-Nspire™ CAS with Touchpad
CAS Comparison Chart
CAS stands for Computer Algebra System. Using a CAS system on a calculator means that the calculator will be able to perform symbolic manipulation of variables without a value being assigned to those variables. The comparison chart below gives some examples of how answers might look different on TI-Nspire CAS as opposed to TI-Nspire and also some of the additional functionality of TI-Nspire CAS. Here are some of examples of the types.
Mathematical constants and variables are recognized and simplified symbolically
Simplify trigonometric identities
Will give exact values for special angles on the unit circle
Algebraic calculations
TI-Nspire handheld
TI-Nspire CAS handheld
Find approximate values for solution of an equation
Exact and approximate values for solutions of an equation
Polymonials are factored and expanded
Complex solutions and zeros can be found
Calculus calculations
TI-Nspire handheld
TI-Nspire CAS handheld
Find numerical approximations of the derivative at a point
Find numerical approximations of the integral value for a given interval
Calculate limits of an expression (including right-hand and left-hand limits)
Find derivatives of function as well as find a derivative at a point
Find values for definite and indefinite integrals
Uses correct notion for derivatives and integrals as students would see in a textbook or write on paper
CAS can help students develop algebraic patterns. In these examples, CAS is used as a learning tool and can help students discover the algebra themselves. This allows for a solid conceptual understanding and can provide a basis for learning of by-hand symbolic manipulation. | 677.169 | 1 |
Math 110: College Algebra
Course Objectives: This course is designed to cause the student to learn traditional college algebra concepts and problem solving skills. It should serve to prepare students for Math 180, Math 230, Math 265, or Math 270.
Prerequisite: Acceptable placement score or C grade in Math 001 or equivalent (typically high school algebra). See me right away if you have a question about your math background as it relates to this reqt. Text: College Algebra: Concepts and Models, second edition, by Larson, Hostetler, and Hodgkins. Heath. 1996. References: There are a number of college algebra texts in my office and in the library.
Note: Grades are based on points allocated above. No extra credit. Typically, 90%+ is A, 80%+ is B, 70%+ is C, and 60%+ is D.
Note: Quizzes are "open book, open notes"; exams are "closed book, closed notes".
Note: All tests taken in regular classroom at scheduled times. No exams taken in learning center unless diagnosed learning disability exists (verified by Mr. Wojeichowski in writing).
Note: Final exam must be taken at regularly scheduled time (Tuesday, December 14, 7:40 - 9:40) unless approved in writing by the Dean.
Attendance: Required. See Viterbo College catalog, page 36. All guidelines followed.
A valid verifiable excuse must be presented in order to make up missed exams or quizzes. "I overslept", "My ride is leaving early for vacation/ the weekend/ etc.", "I had a busy week and didn't have time to study" are examples of NON-valid excuses. Make-up exams for valid excused absences must be done in a timely manner, usually within one week of return.
Calculating Equipment: Hand-held calculators are permitted for quizzes and exams.
Cheating: First offense - half credit on pertinent work; second offense - zero credit on pertinent work; third offense - failure in the course.Note: accommodation for special test-taking needs will be made only after these needs are confirmed in writing by Mr. Wojciechowski. | 677.169 | 1 |
This course increases maths confidence and capability and is ideal for students who are C/D borderline and need to ensure a C or boost their grade to a B.
Students join a tutor in a group to match their year group and ability, and with our interactive lessons we are able to ensure every student is engaged and progressing.
Each course syllabus will vary according to exam board although most courses will cover linear inequalities, pythagoras, trigonometry, loci, change of a subject formula, shapes and all important exam practice. For specific information on what the lessons will include, please contact us on 0845 038 0017
What
1 x 1 hour lesson per week (10 weeks in total)
When
Starts 8th, 9th, 10th and 11th April
Time
Year 10: From 6:30-7:30pm on Wed or 5:00-6:00pm on Thu
Year 11: From 6:30-7:30pm on Mon or 5:00-6:00pm on Tue
Cost
£150 (inc VAT)
Times and dates are shown in the 'available course dates' panel on the right. | 677.169 | 1 |
MathSkills reinforces math in three key areas: pre-algebra, geometry, and algebra. These titles supplement any math textbook. Reproducible pages can be used in the classroom as lesson previews or reviews. The activities are also perfect for homework or end-of-unit quizzes. | 677.169 | 1 |
This program illustrates functions for solving systems of linear and quadratic equations. Using matrices, students solve equations in a time-efficient manner. A chef shows how mathematics keeps things cooking at his restaurant. | 677.169 | 1 |
Mathematical Communication
Wording and punctuation
This webpage lists resources for helping students to learn the wording and punctuation conventions of mathematics. Resources include online and print math dictionaries, handouts that include notes on word choice, etc. | 677.169 | 1 |
Discovering Advanced Algebra
Overview
Develop your students' understanding of abstract math concepts with Discovering Advanced Algebra, a research-based, CCSS-aligned Algebra 2 program that features real-world applications that resonate with all learners. Click here for a Discovering Mathematics series overview. To sign up for a free 30-day online trial, click here. | 677.169 | 1 |
Find a Hazard, CA MathPractice makes perfect, it's better to use examples that will be easier for students to comprehend. Furthermore, learning is a process. Students build up concepts gradually and examples may be used several times before they can fully understandAlgebra course on the Coast Guard base in San Pedro. | 677.169 | 1 |
Designed for undergraduate students, A Mathematics Companion for Science and Engineering Students provides a valuable reference for a wise variety of topics in pre-calculus mathematics. The presentation is brief and to-the-point, but also precise, accurate and complete.
Learn how to read mathematical discourse, write mathematics appropriately, and think in a way that is conducive to solving mathematical problems. Topics covered include: Logic, sets numbers, sequence, functions, powers and roots, exponentials and logarithms, possibility, matrices, Euclidean geometry, analytic geometry, and the application of mathematics to experimental data. The epilogue introduces advanced topics from calculus and beyond. A large appendix offers 360 problems with fully detailed solutions so students can assess their basic mathematical knowledge and practice their skills.
Here are just some of the questions answered in this book: How can
a) Logarithm be converted from one base to another?
b) Simultaneous linear equations be solved by hand painlessly?
c) Some infinities be bigger then other? | 677.169 | 1 |
Aims and Objectives This course is an introduction to pure mathematics. If you
follow the course, you will have a grasp of contemporary mathematical notation, and
will become familiar with various methods of proof.
Need Help? You have the following options
(in order of preference): 1 think, 2 read the lecture notes, 3 read the book, 4 talk to
fellow students, 5 ask the person in charge of your tutorial group,
6 go to a workshop drop-in session, 7
go to a
MASH
drop-in session, 8 Ask nRich (see below), 9 ask your personal tutor (unless you have one of
the odd ones who wants to discuss your life)
and if all else fails, 10 make an
appointment with me by e-mail.
The best bulletin board that supports undergraduate mathematicians is
nRich. You register at that site, and then click on
the Ask nRich link. There are bulletin boards at various levels. The one appropriate
to undergraduates is Higher
Dimension.
You may find some early undergraduate topics being discussed in Onwards and Upwards. The latter is
really for people aged 16-18, but smart school students often discuss university mathematics.
Discussions worth reading Over at Cambridge, Tim Gowers is introducing a new feature this year,
his Weblog.
While it will be tailored to his first year lectures at his university, I expect we will all learn a thing
or two from Tim. There are Terry Tao's
maths quizzes, which seem to
be very attractive aids to learning pure maths in general (not just
for this course). Both Terry
and Tim
have Fields Medals (these are like Nobel
prizes, but for clever people).
Timetable Here is the
course timetable.
For this course, Lectures (and Problem Classes) are at
Tuesday 9:15 University Hall,
Thursday 16:15 University Hall
and Friday 12:15 (Problem Class) University Hall.
The Mathematics Department has set up drop-in Workshops to advise students
on this course (and others). These are
14:15 -- 16:05 Monday 1W4.40,
10:15 -- 12:05 Tuesday 1W4.40
and 17:15 -- 19:05 1W4.40.
You can drop in to any of them for as long, or as short, as you wish.
The workshops will not run in Week 1 but
our Algebra 1A tutorials will run in week 1.
There are also drop-in help sessions organized by MASH.
These are on Tuesday 14:15 -- 16:05 in 1W2.5,
Wednesday 13:15 -- 15:05 in 1W3.15
and Thursday 13:15 -- 15:05 in 4W1.7. Please let me know if any of this information is broken.
Feedback The best way to get feedback on your progress is via your tutor. Hand-in work by the specified
time and date in the relevant 4W level 1 slot. Your tutor will comment on your work, which should be returned
to you about a week later. It is a crime to go to a tutorial without having tried the problems
on the current sheet. It is also a crime to go to a tutorial without knowing the meaning of every word
used on the problem sheet (since if you do not understand the words, you will not understand the questions).
It is most definitely not a crime to be stuck, confused or bamboozled, and your tutor should be able to help you there.
Do not ask your tutor to show you how to do the problems. Rather your tutor should help you understand the problems
with sufficient insight that you can do some of the problems yourself. Problems come in varying levels of difficulty,
and it would be an extraordinary student who could regularly do them all.
What do you do if you think I have made an error in lectures, on a question sheet or on a solution sheet? Well, first check if someone else agrees with you. Then if so, send me an e-mail with the relevant information.
Lecturer's Lecture Notes These are in my head, and therefore cannot be borrowed. If you miss a lecture or lectures, then borrow a set of notes from a reliable scribe, and copy them up by hand or photocopying machine.
Problem Sheet Solutions Written solutions will be put up at this site
after the work has been handed in.
Lecture 1Boole's rules
are here. Problem Sheet 1. In this lecture we made three definitions and introduced
some notation. We defined the notion of a set, and wrote
x ∈ A to mean that x is an element of the set A.
We defined the notion of a subset, and wrote A ⊆ B.
We decided to write A = B when both A ⊆ B and B ⊆ A.
It follows that there is a unique set with no elements,
so we can apply the definite article to the empty set ø.
The set of natural numbers is ℕ,
the set of integers is ℤ,
the set of rational numbers is ℚ,
the set of real numbers is ℝ and the set of complex numbers is ℂ.
We introduced interval notation (a,b), [a,b], (a, b] and [a,b].
Thus, for example, (1,2) = { x | x ∈ ℝ, 1 < x, x < 2}.
Finally I asked if there was a collection of open intervals with the property
that the intersection of each pair is not the empty set, but the intersection
of the whole collection is the empty set. Incidentally, I spent
last Sunday marking the 2012 UK
Mathematical Olympiad for Girls.
Lecture 2 We introduced more notation, including that
for intersection and union. We discussed Boole's rules
at some length, including De Morgan's laws. We began to discuss maps.
A dark warning was issued against allowing
the set
of all sets to be a set, for Bertrand Russell is waiting for the
unwary, and will hit you with a
paradox if
you do that. Note the quality of the
moustache.
Lecture 3 We introduced the identity map on a set, and constant
maps. We defined composition of maps, and showed that
composition of maps, where defined, is an associative process.
We defined injective, surjective and bijective maps.
We proved that each of these last three types of map
is closed under map composition (Proposition 10).
Here is Problem Sheet 2,
due in on Monday October 17.
Here are
Solutions to sheet 1. Note the use of the "maps to" symbol, a right arrow
with a short vertical tail. This is used to describe how a map acts.
Thus f: x |-> x^2 means the same as f(x) = x^2. Sorry about the home made symbols, I am still looking for the way to display the "maps to" symbol in html.
This is not the same symbol as the right arrow which sits between the
domain and codomain of a map.
Lecture 4
We characterized injections, surjections and bijections between
non-empty sets in terms of the existence of left, respectively right, respectively (unique) two sided inverses. We introduced the notion of the power
set of a set. We showed that if A is a finite set, then |P(A)| = 2n.
We began the proof that for any set B, there is no bijection between B and
P(B).
Lecture 5.
We finished the proof mentioned above. We proved that there is a bijection between
the natural numbers and the integers. We proved that if S is an infinite subset of
the natural numbers, then there is a bijection between S and the natural numbers.
We proved that there is a bijection between the set of ordered pairs of natural numbers
and the natural numbers. We stated (but will not prove) that if A and B are sets, then either
there is an injection from A to B, or there is an injection from B to A (or possibly both).
We also stated, but will not prove in lectures, the Schroeder-Bernstein Theorem, that
if A and B are sets, and there are injections both from A to B, and from B to A, then
there is a bijection between A and B.
Problem Sheet 3 and
Sheet 2 Solutions.
Lecture 6 We defined countability: a set S is countable
if (and only if) there is an injection f : S → ℕ
We proved that the set ℚ of rational numbers is (infinite) countable.
We used Cantor's diagonal argument to show that
the real interval [0,1/2] is not countable, and so
ℝ is not countable. Note that there was a typo (chalko?) in
the diagonal argument. At one point I wrote yi
when I should have written yii.
Lecture 7 Here are
notes v2 on partitions and equivalence relations.
here are the changes to version 1 in case you have it. First line, R is a subset of S X S, not R is a subset of S.
In "Properties of Relations", the erroneous spelling reflextive was eliminated. In Examples of Partitions (iii), change "for" to "form".
In Examples of Equivalence Relations (ii), insert the missing comma after the word "sets". In the discussion after teh Examples of Transversals,
correct the mangled spelling of "equivalence". In teh final part on scary notation, change [3] to [2].
At the Problems Class on Friday October 19 2012, a student called Miles
proposed a better solution to Sheet 2, problem 8(d), than the one
which I had suggested in the solutions sheet.
Lecture 8 We started number theory. We defined prime numbers, and proved that there are infinitely many of
them. We defined coprimality, and we showed that if m and n are integers and not both 0, then
the smallest positive integer g expressible as rm + sn (with integers r and s) is the greatest common divisor of
m and n, and moreover that every common divisor of m and n will divide g.
We stated the Fundamental Theorem of Arithmetic, that every positive integer greater than 1
is the product of prime numbers in a (more or less) unique way. We got as far as proving the existence of
such a factorization, and will address uniqueness in the lecture on Thursday.
This note addresses
the chalko in Euclid's proof, and the matter of good housekeeping (induction) as promised in the
lecture.
Here are Sheet 3 Solutions.
Lecture 9 We completed the proof of Gauss's Fundamental Theorem of Arithmetic.
We discussed how to
count the number of divisors of a natural number by
looking at its factorization into prime numbers. We compared the prime factorization of positive
integers m and n with their prime factorizations.
We discussed Euclid's algorithm, why it terminates, and why it gives the gcd of two positive integers as the output.
Here is a question which has a nice answer: "what is the sum of the divisors of 1000?". You can do it in your head
(provided that you are relaxed about multiplying a three-digit number by a two-digit number, and who isn't?).
Lecture 10 We endowed the integers mod n with well-defined
addition and multiplication. We defined the notion of a group, and gave
several examples. Here are some
notes
which will assist you with Sheet 5, Questions 1 and 2 in particular,
and life in general.
Thu Nov 8 Lecture 13 We introduced Euler's φ-function, and proved that it was multiplicative
with respect to coprime arguments (by exploiting the Chinese Remainder
Theorem). We also proved that of f, g are polynomials in K[X]
where K is a field, and g is not the zero polynomial,
then there are q, r in K[X] such
that f = qg + r and deg r < deg g. There were a couple of
glitches. (i) In the proof that deg(f + g) ≤
max {deg f, deg g}, I wrote
(al + bl)Xk+l but the exponent should
be l rather than k + l.
(ii) Also in the calculation of φ(pk), the set being subtracted
should have been { tp | 0 ≤ t < pk-1} (and
not { tp | 0 ≤ t < p}).
Tue Nov 20 Lecture 16 More on linear maps and matrices. Small glitch
in one proof. Fix to follow. How to invert a 2 by 2 real matrix (or indeed, any 2 by 2 matrix
with entries in a field). There was a glitch in the lecture, in (iii)
where we were establishing that if the determinant of a real 2 by 2 matrix
is 0, then it has no inverse. Here is a
fix.
Here is Problem Sheet 9Sheet 8 solutions.
Thu Nov 22 Lecture 17 The area/volume interpretation of determinants for 2 by 2 and 3 by 3
matrices with real entries.
Thu Dec 6 Lecture 20
Each element of S_n is either an even permutation or an odd permutation,
and no permutation is in both categories. Therefore S_n is the union of two cosets of A_n, and
A_n has size n!/2.
Sheet 10 solutions.
Vacation Problem Sheet 11.
Tue Dec 11 Lecture 21 The use of the sign of a permutation to define a determinant of a square matrix
as an alternating sum of monomials.
The email address
[email protected]
is the
official University of Bath format, though once upon a time the shiny new
format was [email protected] --
the one that people actually use
is, of course, entirely different: [email protected] -- as far
as I know, all these incantations work. | 677.169 | 1 |
Mathematics
Page Content
MATH 100. Basic College Mathematics (3; F, S)
Three hours per week. This
course may not be used to satisfy the University's Core mathematics
requirement. Students may not enroll in this course if they have
satisfactorily completed a higher numbered MATH course. An overview of basic
algebraic and geometric skills. This course is designed for students who lack
the needed foundation in college level mathematics. A graphing calculator is
required.
MATH 104. College Algebra (3; F, S) Three hours per week.
Prerequisite: MATH 100. This course may
not be used to satisfy the University's Core mathematics requirement.
Qualitative and quantitative aspects of linear, exponential, rational, and
polynomial functions are explored using a problem solving approach. Basic
modeling techniques, communication, and the use of technology is emphasized. A
graphing calculator is required.
MATH 110. The Mathematics of Motion & Change (3; F, S) Three hours per week. Prerequisite: MATH 104. A study of the mathematics of
growth, motion and change. A review of algebraic, exponential, and trigonometric
functions. This course is designed as a terminal course or to prepare students
for the sequence of calculus courses. A graphing calculator is required.
MATH 112. Modern Applications of Mathematics (3; F, S)
Three hours per week. Prerequisite: MATH 104. Calculus concepts as
applied to real-world problems. Topics include applications of polynomial and
exponential functions and the mathematics of finance. A graphing calculator is
required.
MATH 140. Calculus I (4; F, S) Four hours per week.
Prerequisite: A "C" or better in MATH 110. Rates of change, polynomial and
exponential functions, models of growth. Differential calculus and its
applications. Simple differential equations and initial value problems. A
graphing calculator is required.
MATH 141. Calculus II (4; F, S) Four hours per week.
Prerequisite: A "C" or better in MATH 140. The definite integral, the
Fundamental Theorem of Calculus, integral calculus and its applications. An
introduction to series including Taylor series and its convergence. A graphing
calculator is required.
MATH 150. Introduction to Discrete Structures (3; S) Three hours per week. Prerequisite: A "C" or better in one of MATH 110, MATH
112 or MATH 140. An introduction to the mathematics of computing. Problem
solving techniques are stressed along with an algorithmic approach. Topics
include representation of numbers, sets and set operations, functions and
relations, arrays and matrices, Boolean algebra, propositional logic, big O and
directed and undirected graphs.
MATH 199. Special Topics (var. 1-4; AR) May be repeated
for credit when topic changes. Selected topics of student interest and
mathematical significance will be treated.
MATH 206. Statistical Methods in Science (4; S) Four
hours per week. Prerequisite: A "C" or better in MATH 140. Credit cannot be awarded for both MATH 205
and MATH 206. Concepts of probability, distributions of random variables,
estimation, hypothesis testing, regression, ANOVA, design of experiments,
testing of assumptions, scientific sampling and use of statistical software.
Many examples will use real data from scientific research. A graphing calculator
is required.
MATH 220WI. Mathematics & Reasoning (3; S) Three
hours per week. Prerequisite: ENGL 103 and a "C" or better in MATH 141.
Fundamentals of mathematical logic, introduction to set theory, methods of proof
and mathematical writing.
MATH 306. Regression & Analysis of Variance Techniques
(3) Three hours per week. Prerequisites: A "C" or better in MATH
141, and a "C" or better in either MATH 205 or MATH 305. Theory of least
squares, simple linear and multiple regression, regression diagnostics, analysis
of variance, applications of techniques to real data and use of statistical
packages.
MATH 307. College Geometry (3) Three hours per week.
Prerequisite: A "C" or better in MATH 141. A critical study of deductive
reasoning used in Euclid's geometry including the parallel postulate and its
relation to non-Euclidean geometries.
MATH / PHIL 330. Symbolic Logic (3) Three hours per week.
A study of modern formal logic, including both sentential logic and predicate
logic. This course will improve students' abilities to reason effectively.
Includes a review of topics such as proof, validity, and the structure of
deductive reasoning.
MATH 351. Applied Mathematics (3; F) Three hours per
week. Prerequisite: A "C" or better in both MATH 300 and MATH 331. Advanced
calculus and differential equations methods for analyzing problems in the
physical and applied sciences. Calculus topics include potentials, Green's
Theorem, Stokes' Theorem, and the Divergence Theorem. Differential equations
topics include series solutions, special functions, and orthogonal
functions.
MATH 354. Introduction to Partial Differential Equations and Modeling
(3; S) Three hours per week. Prerequisite: A "C" or better in both
MATH 300 and MATH 331. Modeling problems in the physical and applied sciences
with partial differential equations, including the heat, potential, and wave
equations. Solution methods for initial value and boundary value problems
including separation of variables, Fourier analysis, and the method of
characteristics.
MATH 400SI. History of Mathematics (3) Three hours per
week. Prerequisite: A "C" or better in MATH 220WI and junior or senior status.
This course may not be used to satisfy
the University's Core mathematics requirement. A study of the history of
mathematics. Students will complete and present a research paper. Students will
gain experience in professional speaking.
MATH 411. Introduction to Real Analysis (3) Three hours
per week. Prerequisite: A "C" or better in both MATH 220WI and MATH 300.
Foundations of real analysis including sequences and series, limits, continuity,
and differentiability. Emphasis on the rigorous formulation and writing of
proofs.
MATH 412. Introduction to Complex Variables (3) Three
hours per week. Prerequisite: A "C" or better in both MATH 220WI and MATH 300.
Algebra of complex numbers, analytic functions, elementary functions, line and
contour integrals, series, residues, poles and applications.
MATH 423. Algebraic Structures (3) Three hours per week.
Prerequisite: A "C" or better in MATH 220WI. An overview of groups, rings,
fields and integral domains. Applications of abstract algebra.
MATH 440. Special Topics (var. 1-3; AR) Prerequisite: A
"C" or better in MATH 220WI or consent of the instructor. May be repeated for
credit when topic changes. Selected topics of student interest and mathematical
significance will be treated.
MATH 501. Introduction to Analysis (3) Three hours per
week. A study of real numbers and the important theorems of differential and
integral calculus. Proofs are emphasized, and a deeper understanding of calculus
is stressed. Attention is paid to calculus reform and the integrated use of
technology.
MATH 502. Survey of Geometries (3) Three hours per week.
An examination of Euclidean and non-Euclidean geometries. Transformational and
finite geometries.
MATH 503. Probability & Statistics (3) Three hours
per week. Probability theory and its role in decision-making, discrete and
continuous random variables, hypothesis testing, estimation, simple linear
regression, analysis of variance and some nonparametric tests. Attention is paid
to statistics reform and the integrated use of technology.
MATH 504. Special Topics (3; AR) Three hours per week.
May be repeated for credit when topic changes. Course content will vary
depending on needs and interests of students.
MATH 507. Number Theory (3) Three hours per week. An
introduction to classical number theory. Topics include modular arithmetic, the
Chinese Remainder Theorem, primes and primality testing, Diophantine equations,
multiplicative functions and continued fractions.
MATH 510. Seminar in the History of Mathematics (3) Three hours per week. Important episodes, problems and discoveries in
mathematics, with emphasis on the historical and social contexts in which they
occurred.
MATH 515. Combinatorics (3) Three hours per week. A
survey of the essential techniques of combinatorics. Applications motivated by
the fundamental problems of existence, enumeration and optimization.
MATH 520. Linear Algebra (3) Three hours per week.
Applications of concepts in linear algebra to problems in mathematical modeling.
Linear systems, vector spaces and linear transformations. Special attention will
be paid to pedagogical considerations.
MATH 531. Theory of Ordinary Differential Equations (3) Three hours per week. Existence and uniqueness theorems. Qualitative and
analytic study of ordinary differential equations, including a study of first
and second order equations, first order systems and qualitative analysis of
linear and nonlinear systems. Modeling of real world phenomena with ordinary
differential equations.
MATH 600. Thesis Seminar (1-3) One to three hours per
week. Research guidance. May be repeated for credit up to a total of three
semester hours.
MATH 699. Thesis Preparation and Research (1) Master of
Arts in Mathematics students who have not completed their thesis and are not
enrolled in any other graduate course must enroll in MATH 699 each fall and
spring semester until final approval of their thesis. This course is Pass/Fail
and does not count towards any graduate degree. | 677.169 | 1 |
Mathematics
The mathematics curriculum has two primary objectives. The first is to provide students with a thorough grounding in the structure and techniques of the subject area, so that they will be well prepared for future work at the secondary or college level as well as motivated to challenge themselves in these venues. The second is to provide students with an understanding of the utility and power of the subject area and of their current competence and abilities as well as their potential for future development and comprehension.
Towards these objectives, the Mathematics Department faculty promote critical thinking and problem solving skills that will enable students to find success in applying their knowledge of mathematics to other fields. In addition, the faculty develop the skills necessary for students to effectively utilize technology as a mathematical tool for exploration and analysis. Finally, the faculty nurture an appreciation for mathematics as an exact science and of the role it plays in the fields of physical science, art, philosophy, engineering, architecture, and industry.
Mathematics Curriculum Overview
In order to graduate from Avon Old Farms School, students must complete at least three mathematics courses: Algebra 1, Geometry, and Algebra 2 with Trigonometry. Upon completion of Algebra 2 with Trigonometry, students are encouraged to enroll in Advanced Mathematics, Precalculus, or Probability and Statistics. After successfully completing Precalculus, students may elect to take Honors Calculus, Advanced Placement Calculus AB, Advanced Placement Calculus BC, or Advanced Placement Probability and Statistics.
Algebra 1
Algebra 1 introduces the student to fundamental operations using signed numbers and their elementary applications. The goal of Algebra 1 is to develop fluency in working with expressions, equations and variables. Students will extend their experiences with tables, graphs, and learn to solve linear equations, inequalities and systems of linear equations. Students will generate equivalent expressions and begin to apply formulas to methodically solve questions involving motion, speed and distance. Students will simplify polynomials and begin to study and apply strategies to solve quadratic relationships.
Students will use technology to learn, investigate, and develop strategies for analyzing complex situations and mathematical relationships. Topics covered in the course include grouping techniques, exponents, algebraic fractions, linear and quadratic equations, radicals, graphing, inequalities, and the solution of verbal problems.
Algebra 1 Honors
This course is designed for students who have demonstrated a strong ability in previous mathematics courses and who wish to pursue upper-level mathematics courses throughout their academic career. In addition to the topics covered in the regular Algebra 1 course, the honors section studies mathematical modeling, trigonometry, and calculator programming.
Algebra 2 with Trigonometry
This course is a more intensive and extensive study of topics introduced in Algebra 1. The primary objective of the Algebra 2 curriculum is to prepare students for Precalculus or Precalculus Honors. The course is designed to prepare students for college level mathematics and is beneficial for those who will pursue further study in mathematics or related fields. Extensive work is included with equalities, inequalities, absolute value, fractional and negative exponents, radicals, systems of quadratics, logarithms and trigonometric properties. The content of the course is organized around families of functions, including linear, quadratic, exponential, logarithmic, radical and rational functions. Students will learn to represent functions in multiple ways, including verbal descriptions, equations, tables, and graphs. Students will also learn to model real-world situations using functions. To help students prepare for standardized tests, this course provides instruction and practice in a variety of formats. Graphing calculator skills will be taught and used extensively in this course. Throughout this course, students will develop learning strategies, critical thinking skills, and problem solving techniques to prepare for future math courses and college entrance exams.
Algebra 2 with Trigonometry Honors
This course is an extensive, fast-moving study of the fundamental principles of algebra, trigonometry, probability, and statistics to prepare students for Precalculus. Students who earn a high "B" range grade or better in this class usually pursue Honors Precalculus the following year. Topics covered include linear equations, functions, polynomials, complex numbers, quadratic equations, and functions. The honors class will also complete chapters on analytic geometry, exponential functions, trigonometry, sequences, series, and probability. Students completing this class in good standing are prepared to study pre-calculus.
Algebra is the language of calculus. Understanding this, there will be special emphasis early in the year on developing a solid working understanding of the algebraic skills and procedures necessary for success in higher level math courses. Students will learn to define the major concepts in a second year algebra course including polynomials, rational expressions, radical expressions, and complex numbers and then learn how to simplify, add, subtract, multiply and divide these expressions. Other major themes include: solving various types of equations and inequalities, factoring, understanding the concept of a function, and graphing functions on the coordinate plane. Linear and quadratic functions are studied in great detail. Later in the year, students will be introduced to higher degree polynomial functions and associated theorems. Students are introduced to conic sections, exponents and logarithms, right triangle and circular trigonometry, and, if time permits, sequences and series.
Geometry
Geometry's primary objective is the study of Euclidean Geometry as a formal, logical system. Where possible, excursions are made into three-dimensional figures and elementary analytic geometry. Some review of algebraic materials may be included. This course begins with developing visualization and some drawing skills. Both algebraic and geometric models are introduced and are further enhanced throughout the course. Proofs are developed slowly in the first half of the course. Various proof formats, including paragraph, flow-chart, and two-column proofs are presented. Students are expected to be actively involved in their own learning. The use of manipulatives is integrated into this course.
Geometry Honors
The Geometry Honors course begins with a strong development of visualization and drawing skills. Both algebraic and geometric models are introduced and are used throughout the course. Proofs are developed slowly in the first half of the year. Various proof formats, including paragraph, flow chart, and two column proofs, are presented. Students are expected to be actively involved in their own learning. Manipulatives, constructions, and the computer program Geometer's Sketchpad are also integrated into this course.
Advanced Mathematics
This course consists of a more thorough treatment of Trigonometry and other selected topics in Algebra 2 with Trigonometry to prepare students for further study in mathematics. Algebra 2 with Trigonometry is a prerequisite. The primary objective of the Advanced Math curriculum is to prepare students for Precalculus. Integral to the learning process is the systematic review of earlier concepts learned in Algebra 2 with Trigonometry and procedures in which students use previously learned skills to develop proficiency with more advanced concepts. The Advanced Math course includes organizational skills, communication, mathematical tools, calculators, hands on activities and group work.
Precalculus
The primary objective of the Precalculus curriculum is to prepare students for Calculus. Integral to the learning process is the systematic review of earlier concepts learned in Algebra 2 and/or Advanced Math and procedures in which students use previously learned skills to develop proficiency with more advanced concepts, especially Trigonometry. The Precalculus course includes exploration, communication, mathematical tools, manipulatives, calculators, hands on activities and group work.
Precalculus Honors
Designed to prepare the more advanced student for Advanced Placement Calculus, this course provides students an honors level study of trigonometry, advanced functions, analytic geometry, and data analysis. A faster pace also allows for the introduction of topics from calculus earlier in the second semester. Limits, continuity, the definition of the derivative, techniques of differentiation, and applications of the derivative are all explored. Applications and modeling are included throughout the course. Appropriate technology is used regularly for instruction and assessment.
Calculus
This advanced course is an introduction to the fundamental topics comprising calculus. Algebraic, trigonometric, and transcendental functions are studied in the context of differentiation and integration. The Calculus curriculum includes exploration, communication, mathematical tools, manipulatives, calculators, hands on activities and group work. At the conclusion of this course, students should be able to use calculus methods in a variety of applications and problem solving situations.
Calculus Honors
This advanced course is an introduction to the fundamental topics of calculus. Algebraic, trigonometric, and transcendental functions are studied in the context of differentiation and integration. The Honors Calculus curriculum is designed to introduce students to the many application of calculus, learn the fundamental rules of calculus, and develop strong problem solving skills. Students will learn how to use technologies such as the graphing calculator, Mathematica, and Excel to investigate various calculus topics and real world problems. Upon completion of this course, students should be well prepared to move onto a first year college level calculus course.
Probability and Statistics
Less rigorous than Pre-Calculus, the primary objective of Probability and Statistics is to offer students an opportunity to continue their mathematical studies in a new area. This course begins with an overview of statistics and includes an investigation of the fundamental laws of probability. It also includes such topics as distributions, sampling, regression, estimation, and hypothesis testing.
Advanced Placement Calculus AB
This is a rigorous Advanced Placement course designed to prepare students for the AP Calculus AB exam in the spring. The course seeks to develop students' understanding of the concepts of calculus, while providing experience with its methods and applications. A multi-representational approach to calculus is employed with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections between these representations are also explored.
Advanced Placement Calculus BC
This is a rigorous Advanced Placement course that prepares students to take the AP Calculus BC exam in the spring. The course seeks to develop advanced problem solving skills by stressing the application of the concepts covered in the problem solving process. The class requires some vacation assignments that are to reinforce the concepts that have been taught. The class moves quickly and covers all the material outlined by the College Board and is intended for students that have had success in Precalculus or lower levels of Calculus and want to challenge themselves at the highest level.
Advanced Placement Statistics
AP Statistics is the high school equivalent of a one semester, introductory college statistics course. In this rigorous course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance behavior. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-84 graphing calculator, Fathom and Minitab statistical software, and Web-based java applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data. | 677.169 | 1 |
Elementary Statistics - With Cd - 6th edition
Summary: Elementary Statistics is appropriate for a one-semester introductory statistics course, with an algebra prerequisite. ES has a reputation for being thorough and precise, and for using real data extensively. Students find the book readable and clear, and the math level is right for the diverse population that takes the introductory statistics course. The text thoroughly explains and illustrates concepts through an abundance of worked out examples.
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Core Abilities (Note: since this course may be taken in partial fulfillment of the general education requirements, this syllabus includes the following set of core ability goals.)
1. Thinking: Students engage in the process of inquiry and problem solving that involves both critical and creative thinking.
Students will be exposed to the logic of mathematical proof
Students will develop their problem-solving skills
Calculus is a major intellectual development in human history and students will think through the concepts
2. Communication: Students communicate orally and in writing in an appropriate manner both personally and professionally.
Students will develop their skills of written mathematical communication, specifically learning to properly use the language and notation of the Calculus
Students will develop their verbal mathematical communication skills, both in small groups and in class discussions
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
Students will see the importance of integrity regarding their own scholarship
4. Community Involvement: Students demonstrate skills of interdependent group participation and decision-making.
Students will work in groups, learning to share their ideas and skills, and respecting the ideas and skills of others
Specific Course Goals:
1. From the perspective of mathematical content, this course should allow the student to expand and apply skills and knowledge gained in the first semester of Calculus to the topics of integration and applications of integration.
2. The student will gain knowledge and skills, and the ability to apply these, to a variety of situations which might be encountered in the world of mathematics, science, or engineering.
3. The student will further improve his/her ability to communicate mathematical ideas and solutions to problems.
4. The student will improve her/his problem-solving ability.
5. From a most general perspective, the student should see growth in his/her mathematical maturity. The three-semester sequence of calculus courses form the foundation of any serious study of mathematics or other mathematically-oriented disciplines.
Course Philosophy and Procedures:
I am a firm believer in the notion that you as the student must be actively engaged in the learning process and that this is best accomplished by your DOING mathematics. My job here is not to somehow convince you that I know how to do the mathematics included in the course, but to help guide YOU through the material; I am to be a "guide on the side, NOT a sage on the stage". I may not always say things in the way which best leads to your full comprehension, but I will try to do so and I ask that you try to see your learning as something YOU DO rather than as something I do to you. PLEASE feel free to come see me to discuss questions or concerns you may have during the course; I will not bite! PLEASE ask questions in class if you have them; the only dumb question is the one you fail to ask!
Homework: Let me therefore urge you to make it a regular part of your day to try working the homework problems. There will never be enough time for us to go through every listed problem in class, and it is probably unrealistic to think that you will be able to find the time to work through every listed problem, but you should at least spend some time thinking about virtually every problem, and working the more interesting or challenging to completion. The daily homework assignments will not generally be collected or graded. They are intended to structure your learning so that you regularly challenge yourself to see that you understand the material we are looking at. The important thing is that you at least look at all the assigned problems. You should also feel free to work other problems if you deem it necessary for your comprehension of the content.
You should view homework assignments as a test to see how well you understand the material and you should bring to the next class any questions you might have.
Group Work: In general, I think students can benefit greatly by working together on problems. While there is some danger of the "blind leading the blind" syndrome, or of students deceiving themselves into thinking they understand the material better than they actually do, for the most part grappling with ideas and trying to explain them to another student or learning to listen to others explain an idea is a wonderful way to see that you really do understand the material. In class we will spend an occasional day working on a group "lab", and we sill also typically have a group "practice exam" before the individual exams, and I also encourage you to find a "learning group" outside of class.
Portfolio: I will be asking you to keep a PORTFOLIO of your work. This portfolio will be collected twice during the semester, once upon our return from our spring break, on Monday 17 March, and again at the end of the course, on Friday 2 May. Each of these portfolios should be a representative collection of your work during that half of the semester; each collection you turn in should include 5 problems, written up in a finished form, along with a brief discussion of why you chose to include that particular problem. These problems should represent work you are proud of, or problems which brought you to a breakthrough point. Each of these portfolios of your work will be worth 40 points, 8 points per problem. Presumably you will hand in 5 sheets of paper, each of which will include a nicely organized solution to the problem, which might be from homework, or from a lab or worksheet, of from an exam, along with that reflection mentioned above.
Grading: I use a rather traditional Grading Scale: A = 90% (or better), AB = 87%, B = 80%, BC = 77%, C = 70%, CD = 67%, D = 60%. I do try to come up with a mix of points so that exams are not weighted too heavily; about two-thirds of the points during the semester will come from individual, in-class exams - the rest will come from group labs, take-home problems, group practice exams, journals, and portfolios.
Late Assignments: It is rarely much of a problem at the level of a calculus course, but it remains important that students turn in work in a timely manner, so that they do not get behind. Consequently, Late Assignments will be penalized 20% of the possible points for each class period late, up to a maximum of three periods. Assignments more than three days late will not be accepted.
Attendance: I do not prefer to quantify your attendance in terms of a grade, but I can assure you that your chances of success will be much improved by regular attendance.
Americans with Disability Act:
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski in MC 320 (796-3085) within 10 days to discuss your accommodation needs. | 677.169 | 1 |
Organized for use in a lecture-and-computer-lab format, this hands-on book presents the finite element method (FEM) as a tool to find approximate solutions of differential equations, making it a useful resource for students from a variety of disciplines.
The book aims for an appropriate balance among the theory, generality, and practical applications of the FEM. Theoretical details are presented in an informal style appealing to intuition rather than mathematical rigor. To make the concepts clear, all computational details are fully explained and numerous examples are included, showing all calculations. All finite element procedures are implemented in interactive Mathematica notebooks, from which all necessary computations are readily apparent. | 677.169 | 1 |
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examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request.
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Product Synopsis
Written by well-respected authors, the Cambridge Checkpoint Mathematics suite provides a comprehensive structured resource which covers the full Cambridge Secondary 1 Mathematics framework in three stages. This Teacher's Resource for Stage 7 offers advice on how to introduce concepts in the class, and gives ideas for activities to help engage students with the subject matter. Answers to all questions in the Coursebook and Practice Book are also included | 677.169 | 1 |
Objectives
Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. Therefore, no work space is provided, nor does the chapter contain all of the pedagogical features of the text. As a review, this chapter can be assigned at the discretion of the instructor and can also be a valuable reference tool for the student.
This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. If you would like a quick review of arithmetic before attempting the study of algebra, this chapter is recommended reading. If you feel your arithmetic skills are pretty good, then move on to Basic Properties of Real Numbers ((Reference)). However you feel, do not hesitate to use this chapter as a quick reference of arithmetic techniques.
The other chapters include Practice Sets paired with Sample Sets with sufficient space for the student to work out the problems. In addition, these chapters include a Summary of Key Concepts, Exercise Supplements, and Proficiency Exams | 677.169 | 1 |
1567978 / ISBN-13: 9780321567970
Mathematics All Around
"Tom Pirnot" believes that conceptual understanding is the key to a student's success in learning mathematics. He focuses on explaining the thinking ...Show synopsis"Tom Pirnot" believes that conceptual understanding is the key to a student's success in learning mathematics. He focuses on explaining the thinking behind the subject matter, so that students are able to truly understand the material and apply it to their lives. This textbook maintains a conversational tone throughout and focuses on motivating students and the mathematics through current applications. Ultimately, students who use this book will become more educated consumers of the vast amount of technical and mathematical information that they encounter daily, transforming them into mathematically aware citizens.Hide synopsis
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Description:Very good. Annotated Edition. Ships SAME or NEXT business day....Very good67970 Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780321567970 Mathematics All Around
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing stuff | 677.169 | 1 |
Here is the information you need in order to be prepared for class and have a successful year.
Supplies: Starting with the first day of school, you will need pencils, a calculator (TI-84 graphing calculator required for Calculus and suggested for Advanced Math), and a 3-ring binder (with paper and 4 dividers)
Notebooks: You are responsible for keeping aNotebook as follows:
·Section 1 - Class notes: organized by date.
·Section 2- Homework: name, assignment (pg. or worksheet #), date.
·Section 3– Quizzes/tests
·Section 4- Extras
Homework: Homework is assigned on most days. It is essential to your success that you practice the skills you learn in class. Homework is due at the beginning of class the day after it is assigned. Homework may either be collected and graded, or assigned an effort grade.
Notebook: There will be occasional notebook quizzes to check the accuracy of class notes. These quizzes will not be announced in advance and the number of points will vary.
Tests and Quizzes: You will be notified in advance of chapter Tests and Quizzes and are expected to spend time outside of class preparing for them.
Class Rules:
·Bring all materials each day.
· Leaving class for any reason (restroom/locker/etc.) will result in a tardy.
·No eating or drinking in class (except water).
Absence:If you are absent it is your responsibility to get class notes from a classmate and complete any missed assignments. Mrs. Vargo'smake up policy is the same as the school policy (read pg. 6-7 in the student handbook!)
·If you miss class and need help with any new material taught while you were absent, you may make arrangements to come in before or after school for help. Lessons will not be re-taught during class.
·You have two days for every day absent to make up homework assignments.
·If you are only absent on the day of a test or quiz, you must make up the test the day you return.
· If you are absent the day before a test or quiz and no new material was taught, you must take the test as scheduled with the rest of the class.
·Grades will be lowered one letter grade for each late make-up day.
·Make up tests and quizzes may not be taken during class. You must make arrangements to do make-ups before or after school or during study hall. | 677.169 | 1 |
This 14-lesson series introduces each concept in an easy-to-understand way and by using example problems that are worked out step-by-step and line-by-line to completion. Includes Permutations (79 minutes); Combinations #11;(4..
Having trouble engaging your algebra students? This set of PowerPoint® slides highlights student-centered situations to teach algebra. The problems are rigorous enough to require true problem-solving and accessible enough to allow all stude..
Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understanding of key concepts. 13..
GRADES 9-12. Ideal for quick reinforcement or to fill a spare bit of time! The targeted problems directly address Common Core State Standards and Mathematical Practices. Each problem builds problem-solving skills and strengthens understandi..
Everything you need for a class of up to 30 students. Kit contains: 30 Algebra Tile™ Student Sets (each set includes a 35-piece, two-color set of Algebra Tiles™), a 70-piece overhead set of Algebra Tiles™, an instructional ..
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges. | 677.169 | 1 |
This is the first of two courses designed to emphasize topics which are fundamental to the study of calculus. Emphasis is placed on equations and inequalities, functions (linear, polynomial, rational), systems of equations and inequalities, and parametric equations. Upon completion, students should be able to solve practical problems and use appropriate models for analysis and predictions.
This course has been approved to satisfy the Comprehensive Articulation Agreement general education core requirement in natural sciences/mathematics. | 677.169 | 1 |
Book Description: Teacher's Edition. This edition balances the investigative approach that is the heart of the Discovering Mathematics series with an emphasis on developing students' ability to reason deductively. If you are familiar with earlier editions of Discovering Geometry, you'll still find the original and hallmark features, plus improvements based on feedback from many of your colleagues in geometry classes. | 677.169 | 1 |
much
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing stuff. | 677.169 | 1 |
Synopsis
If you are having difficulty learning math, you already know you are not alone. Many people struggle with math. In fact, it is the one discipline in which low grades and low performance are almost universally acceptable because they are so common. For example, a parent is more likely to excuse a lower report card grade in math than in any other subject because that parent probably got lower grades in math when he or she were in school. But why is math so hard to learn? If we look at the nature of learning math it will become easy to see why it is almost a miracle that anyone (without some innate talent) ever learns math. The following "Top 10" can give you insights into how to learn math and help you understand the different pieces that must come together for you to not only learn math but enjoy the journey. 2,636 words.
Found In
eBook Information
ISBN: 9781465934 | 677.169 | 1 |
Introduction to concepts and methods of calculus for students with little or no previous calculus experience. Polynomial and elementary transcendental functions and their applications, derivatives, extremum problems, curve-sketching, approximations; integrals and the fundamental theorem of calculus. M-Th 10.00-12.10 pm
Calculus I
Brief review of high school calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem. Use of symbolic manipulation and graphics software in calculus. M-Th 10.00-12.10 pm
Calculus II
Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and analytic geometry, first and second order ordinary differential equations. Applications to physical sciences. Use of symbolic manipulation and graphics software in calculus. M-Th 1.00-3.10 pm
Calculus, Part II with Probability and Matrices
Functions of several variables, partial derivatives, multiple integrals, differential equations; introduction to linear algebra and matrices with applications to linear programming and Markov processes. Elements of probability and statistics. Applications to social and biological sciences. Use of symbolic manipulation and graphics software in calculus. M-Th 1.00-3.10 pm
Ideas in Mathematics
Topics from among the following: logic, sets, calculus, probability, history and philosophy of mathematics, game theory, geometry, and their relevance to contemporary science and society. M-Th | 677.169 | 1 |
Curriculum: Cambridge IGCSE Mathematics is accepted by universities and employers as proof of mathematical knowledge and understanding. Successful IGCSE candidates gain lifelong skills, including: the development of their mathematical knowledge, confidence by developing a feel for numbers, patterns and relationships, an ability to consider and solve problems and present and interpret results, communication and reason using mathematical concepts and a solid foundation for further study. Pre-AICE 1 focuses on the Algebra I skills and the beginning of Geometry.
Class rules:
Be on time to class (in your seat and quiet when the last bell rings) following "beginning of class procedures".
1st tardy results in a warning,
2nd tardy results in a phone call home.
3rd tardy (and all that follow) results in a referral to student management.
Materials: These need to be replaced if they are lost or used up during the year.
Scientificcalculator (save the directions)
Optional– graphing calculator (TI-83or TI-84 any edition) If you choose to buy another type of graphing calculator you are on your own to learn how to use it.
1½ in. 3-ring binder (to be used for math class only)
Pencil, notebook paper, graph paper
Highlighter
Dry erase markers (blue or black) to donate to the class
Box of tissue to donate to the class
Grading Procedure grading scale
Test/quizzes/projects 65% A 90 – 100
Daily work/ homework 30% B 80 – 89
(Assignments are collected each Wednesday or the day of quiz or test) C 70 – 79
(Bell-work is collected each Friday) 20 pts will be deducted for each day late ---unacceptable---
FCA 5% D 60 – 69
Discipline Procedure
Warning
Timeout in class or other classroom
Parent contact
Referral to dean
Administrative Referral
Make-up work
You are responsible for missed work and tests.
You have the number of days absent to make up assignments i.e. 1 day absent = 1 day to make up work. For foreseen extended absences, arrangements will need to be make IN ADVANCE.
Quizzes will NOT be made up. The test grade earned on the test covering the material missed will count for the quiz grade.
If you miss the day of a test, you must make up the examination the day you return to school. You may receive an alternate test in place of the original (this may or may not be the same format.)
If you are on a field trip you are responsible for all work. If an assignment is due the day you are out it must be turned in before leaving on the field trip. Not after you return. Send it with a friend or bring it to the main office to be put in my box.
A "0" will be entered in the grade book and remain there until the work is turned in.
Extra Help
I am available before school every day EXCET Thursdays and the 1st Wednesday of the month between 8 and 9:15 AM. You may call me at home at 591-2272 any time before 8:30 PM for help or questions. (DO NOT CALL ASKING FOR THE ASSIGNMENT.)
Returned work
You will find graded work in the baskets labeled with each period. It is up to you to get your work between classes or before school. Bell-works are graded but not returned. You may see and go over your graded tests before school, they are not returned because of test security.
.
Cooperative Class Expectations
Ask for and offer help.
Listen carefully and praise my classmates.
Share my ideas and work.
Give my best effort.
Be a good follower and a good leader.
Work hard. I'm here to help you and together we will succeed. We are going to have a great year. God Bless you. | 677.169 | 1 |
Web Site Webmath.com This is a dynamic math website where students enter problems and where the site's math engine solves the problem. Students in most cases are given a step-by-... Curriculum: Mathematics Grades: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
12.
Web Site Prentice Hall Math Textbook Resources This site has middle school and high school lesson quizzes, vocabulary, chapter tests and projects for most chapters in each textbook. In some sections, ther... Curriculum: Mathematics Grades: 6, 7, 8, 9, 10, 11, 12
Web Site Tutorials for the Calculus Phobe Explore a collection of animated calculus tutorials in Flash format. The tutorials that follow explain calculus audio-visually, and are the equivalent of a p... Curriculum: Mathematics Grades: 11, 12, Junior/Community College, University
Web Site Calculus Applets Discover the new way of learning Calculus. All manipula applets are visual and animation-oriented. Moving figures on the screen will help students to grasp ... Curriculum: Mathematics Grades: 9, 10, 11, 12, Junior/Community College, University
Web Site Online Calculus Tutorials From Algebra Review to Multi-Variable Calculus, this website provides step-by-step tutorials for high school and university students. Curriculum: Mathematics Grades: 10, 11, 12, Junior/Community College, University
By Resource Type:
Web Site Document or Handout Image Template Book Video | 677.169 | 1 |
Combinatorial Problems and Exercises
9780821842621
ISBN:
0821842625
Pub Date: 2007 Publisher: American Mathematical Society
Summary: The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems.
Ships From:Boonsboro, MDShipping:Standard, ExpeditedComments:Brand new. We distribute directly for the publisher. The main purpose of this book is to provide... [more] [[ allows the reader to practice the techniques by completing the proof. In the third part, a full solution is provided for each problem. This book will be useful to those students who intend to start research in graph theory, combinatorics or their applications, and for those researchers who feel that combinatorial techniques might help them with their work in other branches of mathematics, computer science, management science, electrical engineering and so on. For background, only the elements of linear algebra, group theory, probability and calculus are needed.[less] | 677.169 | 1 |
This course is designed to assist students whose high school mathematics background is insufficient for the standard first-year mathematics courses. It is primarily intended as a preparation for MATH-035. Topics include: algebraic operations, factoring, exponents and logarithms, polynomials, rational functions, trigonometric functions, and the logarithmic and exponential functions. Graphing and word problems will be stressed. This course is not intended to complete the math/science requirement in the College. Fall.
Credits: 3
Prerequisites: None
Other academic years There is information about this course number in other academic years: | 677.169 | 1 |
Algebra (elementary mathematics)
The elementary algebra east is a branch of the Mathématiques whose object is the study of the laws which govern the numerical quantities. The qualifier of elementary appears at the same time as the modern algebra in order to differentiate it from this one. Today, it is the first approach of the algebra in the school course.
The algebra is different from the arithmetic by the introduction of letters (a, b, c,…, x, y, z,…, \ alpha, \ beta, \ gamma,…) indifferently representing all the numbers and to which are applied same the rules of calculations that if it were about numbers.
It is thus possible to establish laws depending only on the nature of the operations, independently of the numbers.
The resolutions of equations and inequations, the study of the polynomials are applications of the algebra.
Algebraical expressions
An algebraical expression consists of numbers, letters and operational signs: | 677.169 | 1 |
About Me
Wednesday, August 31, 2011
Most math text books have examples that are completely worked out with the solution given. Take a piece of paper and hide the textbook answer and work, but show the question. Redo the problem and then check your work with their work and solution.
2. Study for Tests and Quizzes.
It is easy to just do the review homework and feel like you are ready for the test. You need to do this and more. Study for the test or quiz by going back through problems that have been given and solved in class. Actually redo them and check your work. Studying for math is DOING the MATH.
3. Make sure your homework is correct.
Check your answers with those that are in the back of the book while you are doing your assignment.
4. Do math EVERYDAY.
Do your homework every day. Try not to skip any days of homework. If you are cramming all your work into a short single session you will find this usually ends up in frustration as well as poor long term memory with the topic.
5. Attempt the most difficult questions.
The most difficult questions will usually teach you the most about the material. Never skip them. Try to get the most exposure to these problems as you can. Try to solve them on your own. Revisit them. Go in for help. Ask a question on the problems in class.
6. Take a break.
Give yourself a break when working with math. If you are being efficient, then three fifteen minute sessions in a day are better than one 45 minute session. Stand up. Stretch. Go for a walk. Move your work to a new place. A break is needed when working with math.
7. Have a good attitude.
Never think "I'm terrible at math". You usually meet your own expectations. Believe that you can do it!
8. Go in for help with your teacher and bring a specific question.
When you bring in a specific question to your math teacher they can help you with where you are struggling. The teacher then can typically give you more examples that are similar to what you are struggling with.
9. 5 minutes.
Once your homework is done, then take an extra 5 minutes to look at these possible things: vocabulary, formulas, notes, projects, and book examples.
Wednesday, August 24, 2011
Yesterday I made a math problem so that it took up one whole page of typing paper. I cut it up into 6 equal pieces that were approximately 3 by 3 inches. I put it a random order and put a paper clip on it. I did this for 5 problems in all and 2 sets of each for a total of 10 questions. I have 20 students in my class. So I had my students work in pairs. It is real easy to cut these problems up with a paper cutter. See the above cut out lines that I took with the problem.
Then I put the 5 stations with 2 sets of the same problem around the room. Four people, or two pairs of partners would be at each station. I would then have them start on the problem and set the timer for ONE MINUTE. The partners together would have to unscramble the pieces and then solve the problem. They would write their answer down on their paper. Once they were done, they could check the answer that is provided at each station. After the minute was over and students had checked their answers, I told them to rotate. They went to the next station and we did the process all over again.
I was happy with the outcome because they seemed to enjoy trying to figure out the puzzle and do the math. It also helps the students to MOVE and LEARN. They are moving after each problem. | 677.169 | 1 |
Peltier, Doug
Calculus is a college level class, and as such, most of the emphasis will be placed on how well students do on assessments (tests and quizzes). As a result, student grades are calculated in the following manner: 10% for daily work, and 90% for assessments.
Daily work is collected at the end of every chapter on the day of the chapter test. The students are well aware of this fact, and will probably be scrambling the night before the test to finish any work that remains undone (unless they are not procrastinators, then it will already be done!).
At the bottom of the page you will find the PowerPoint lessons for this class, available usually after the day the material was presented in class, but occasionally the same day. This is the exact same presentation as was given in class, minus any bad jokes and commentary on my part. | 677.169 | 1 |
Personal tools
Sections
Mathematica
Mathematica is a powerful, general-purpose numeric and symbolic computation tool.
Mathematica is a computer algebra system that is widely used in science, engineering, mathematics, finance, and other fields. MATLAB also has a symbolic algebra package, but Mathematica's symbolic computation facilities are more sophisticated and integrated with the rest of its features.
Mathematica has the ability to analytically and numerically solve differential equations using the DSolve and NDSolve commands. As a result, it can an indispensable tool for an instructor wanting to check or generate examples or problems.
Mathematica is not designed primarily for educational purposes, and its LISP-inspired syntax creates a steep learning curve for students and instructors alike. However, since it is widely used in academia and industry it may be beneficial for students to become familiar with its capabilities.
Instructors may find the Manipulate command in Mathematica an especially helpful tool for creating interactive tools for exploring differential equations. The Wolfram Demonstrations Project contains a large number of interactive tools built with the Manipulate (and related) commands. | 677.169 | 1 |
Guides and instructs students on preparing for the SAT mathematics level 1 subject test, providing test-taking strategies and tips, and includes seven full-length practice exams with explanations of each answer.
In this Very Short Introduction, Jacqueline Stedall explores the rich historical and cultural diversity of mathematical endeavour from the distant past to the present day, using illustrative case studies drawn...
From ancient Babylon to the last great unsolved problems, Ian Stewart brings us his definitive history of mathematics. In his famous straightforward style, Professor Stewart explains each major development -... | 677.169 | 1 |
MATH 240
Using a calculator
Solving a system of linear equations on a computer or calculator
is surprisingly difficult.
Inverting a matrix or performing certain other matrix operations
can lead to numerical errors that require a lot of theory to understand.
Our department has an entire undergraduate course,
Math 434, Numerical Linear Algebra,
that covers numerical techniques in linear algebra.
We do not have enough time to discuss numerical algorithms in MATH 240,
and if you do not know the relevant theory,
you must be very cautious and skeptical about the answer
when you just press a button on your calculator.
Solving a system of equations
If you have been trained to believe that
a calculator will always give you the correct answer,
you may be in for a shock
if you try to solve a system of equations
by just plugging the coefficients into your calculator and pressing a button.
Even a system of two equations in two unknowns
can present problems for the program used by your calculator.
Here is one example.
We will try to solve this system of equations.
416785x + 415872y = 1
415872x + 414961y = 0
The coefficients in the problem have six significant digits.
Since the TI-85 calculator stores more than twice that many
significant digits internally,
solving the system would seem to present no problem.
Using the equation solver on the TI-85 gives the following "answer".
You can "check" the calculator answer by substituting it
back into the system.
Be sure to use the values stored in the calculator.
Then, to the limits of the calculator's accuracy,
everything checks out,
and, in fact, both solutions appear to be correct.
To find the exact solution,
we can use elementary row operations on the system of equations.
The first goal is to reduce the size of the numbers,
but retain integer values.
Here are the results.
This is not a problem unique to the TI-85.
Using MATLAB on a SUN workstation also gives
an answer that differs substantially from the correct one.
The difficulties are inherent in the problem.
To look at this problem from the geometric point of view,
we could compute the slope of each line.
To 12 decimal point accuracy, we get
416785 ÷ 415872 = -1.00219538704
415872 ÷ 414961 = -1.00219538704
To most calculators, the lines appear to be parallel,
and so there should be no solution at all!
Because the angle between the two lines is very small,
a small change in the coefficients caused by roundoff error
can make a very large difference in the solution.
From a geometric point of view,
shifting the two lines just a little bit
can make a bit difference in the point of intersection.
Inverting a matrix
In the previous problem,
we were able to find an exact inverse for the coefficient matrix.
To illustrate some of the inherent difficulties
in doing Gaussian elimination using floating point arithmetic,
we will look at the row reduction of a standard "badly behaved" matrix.
The matrix given below is called a Hilbert matrix.
It is a well-known example of a matrix that causes problems
for numerical algorithms.
To help understand the problems,
we will do an exact row reduction,
compared to a row reduction done using floating point arithmetic.
To see how the error in the approximations can be compounded,
we will use a highly simplified example,
in which the floating point arithmetic
is carried out with accuracy to only three significant digits.
In the original matrix, labeled (1),
some of the decimal entries are already inaccurate.
In matrix (3), the three digit computation that produces the
3rd entry in row 4 is this:
.837×10-1 - (.904)(.830×10-1)
= .837×10-1 - .750×10-1
= .870×10-2
Comparing this to the correct value of
1 ÷ 120 = .00833 (to 3 digits)
shows that it has only one correct digit.
In matrix (5), the last entry of row 4 is computed as follows:
.837×10-2 - (.690)(.127×10-1)
= .837×10-2 - .876×10-2
= .006×10-2
Because we have to subtract two values that are nearly equal,
the answer has even less accuracy.
The cumulative errors in reducing just 3 rows
produce a value of -.0000600 instead of
(-1) ÷ 4200 = -.000238 (to 3 digits).
The method for defining a Hilbert matrix can be extended to larger sizes,
and the 10 by 10 Hilbert matrix presents substantial problems
for even a very sophisticated numerical algorithm.
You can experiment on your calculator,
by inverting the Hilbert matrices of larger and larger sizes.
REFERENCES
Yves Nievergelt,
Numerical Linear Algebra on the HP-28 or How to Lie With Supercalculators,
American Mathematical Monthly, (1991), 539-544 | 677.169 | 1 |
Assessment and LEarning in Knowledge Spaces (ALEKS) is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics they are most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics are also retained.
The Basic Algebra courses will be taught using the software ALEKS. It is possible for students to accelerate through the Basic Algebra sequence by completing the courses early and then following the change of section process. This process starts with printing the Math Emporium Course Section Change Form (See below) and going to see your current Basic Algebra instructor. Have the instructor fill out the top of the form and bring the signed form to the Math Department located in MSB 233. | 677.169 | 1 |
Learning Goals and Outcomes
Mathematics Learning Goals
At all levels, Georgetown undergraduates gain knowledge of the following through courses in mathematics:
• Fundamental objects, techniques and theorems in the mathematical sciences, including the fields of analysis, algebra, geometry, and discrete mathematics;
• The principles of mathematical reasoning and their use in understanding, analyzing and developing formal arguments;
• The connections between the mathematical sciences and other scientific and humanistic disciplines;
• The main forces driving the evolution of the mathematical sciences and their past relevance and future potential for the broader society.
Mathematics Learning Outcomes
Through active study of this core body of knowledge, Georgetown mathematics students at all levels develop their ability to:
• Make significant progress on typical mathematical problems previously unfamiliar to them, using appropriate techniques and tools;
• Formulate precise and relevant conjectures based on examples and counterexamples, prove or disprove conjectures, and translate between intuitive understandings and formal definitions and proofs;
• Construct, modify and analyze mathematical models of systems encountered in disciplines such as physics, economics or biology, assess the models' accuracy and usefulness, and draw contextual conclusions from them;
• Clearly communicate mathematical ideas in appropriate contexts both orally and in writing to a range of audiences, including the educated general public.
Statistics Learning Goals
At all levels, Georgetown undergraduates gain knowledge of the following through courses in statistics:
• Fundamentals of probability models and theory underlying statistical methods;
• Principles of statistical reasoning and their use in understanding, analyzing, and developing formal arguments;
• The overall process and particular steps in designing studies, collecting and analyzing data, interpreting and presenting results;
• The role of statistics and its applications in other disciplines, e.g. biological sciences, social sciences, and economics.
Statistics Learning Outcomes
Through the statistics courses they take, Georgetown students at all levels will develop their ability to:
• Choose appropriate statistical methods and apply them in various data analysis problems;
• Use various statistical software to perform data analysis;
• Communicate effectively statistical methods and results in appropriate contexts, both orally and in writing;
• Critically assess the strengths and weaknesses of published studies, and evaluate the validity of reported results. | 677.169 | 1 |
Give your students all the essential tools for a solid introduction to algebra! The skills required to master basic algebra are introduced in Algebra 1 and developed further in the more advanced Algebra 11. A variety of rules, theorems, and processes are presented along with easy-to-follow examples. Games and puzzles use answers to practice problems to reinforce learning and make algebra fun. 48 pages
Last October, Schoodoodle.com introduced supplemental classroom curriculum books in the form of eBooks into our online store and library. We began with 5,000 eBooks for teachers to download, share and use in their classrooms. The demand has been so great- that we have doubled our selection in just a few months.
We now offer over 10,000 titles for educators to choose from that range in all subject areas. Preview the books for free on the sample links, download immediately, and own forever! Each month- we will be featuring new eBooks for you to use to enhance your classroom curriculum but you can view the entire catalog for a range of categories.
*The enhanced eBooks give you the freedom to copy and paste the content of each page into the format that fits your needs. You can post lessons on your class website, make student copies, extract or rotate pages, and edit the contents of the file.
Why eBooks?
eBooks are less costly than traditional books
eBooks are available instantly.
eBooks take up no physical storage space and minimal electronic storage space.
Shop SchooDoodle.com to buy and access free digital ebook reader pdf downloads for children and schools from our online store and library. We offer over 10,000 electronic book titles to download for elementary school, middle school, and high school students. Preview the books for free on the sample links, download immediately, and own forever!
Each month we will be featuring an educational eBook from our catalog for you to use to enhance your classroom curriculum and offer a free download of the book. We now offer over 10,000 electronic book titles to download for elementary school, middle school, and high school students. Preview the books for free on the sample links, download immediately, and own forever! Since we have added this feature, the demand for this technology has grown substantially.
Why are eBooks the smart choice?
1. eBooks are less costly than traditional books
2. eBooks are available instantly
3. eBooks take up no physical storage space and minimal electronic storage space
Our featured eBook this month is Beginning Algebra (Grades 6-8). This 48 page eBook will help you give your students all the essential tools for a solid introduction to algebra! The skills required to master basic algebra are introduced in Algebra I and developed further in the more advanced Algebra II. A variety of rules, theorems, and processes are presented along with easy-to-follow examples. Games and puzzles use answers to practice problems to reinforce learning and make algebra fun. We think you will love this eBook so much that we would like to offer it to you for free.
We have a wide selection of other Pre – Algebra, Beginning Algebra, Algebra II etc. so please see all of our Algebra ebooks that are available for download so teachers and parents can access them any time.
For other subjects and grade levels (K-12) see our entire eBook Catalog. We have 10,000 titles for educators to choose from that range in all subject areas. You can preview the books for free on the sample links, download immediately, and own forever! | 677.169 | 1 |
Book summary
This textbook presents statistics conceptually, avoiding the use of maths other than basic arithmetic, and will, therefore, be appropriate for students who find maths exceedingly difficult. The text explains the basic concepts in a very accessible and jargon-free style. It takes students through certain concepts and statistical tests, with diagrams, examples and explanations throughout. [via] | 677.169 | 1 |
"Thank you for providing families with such a high quality, alternative education for their children. I am most appreciative that it allows for a creative approach to educating the young (and not so young) mind."
This course can be taken as a precursor to Algebra I. The course is a combination of a full pre-algebra course and an introduction to geometry and discrete mathematics. Some topics covered include prime and composite numbers, fractions and decimals, the order of operations, coordinates, exponents, square roots, ratios, algebraic phrases, probability, the Pythagorean Theorem, and more. The text Saxon Algebra ½ Homeschool Edition is included.
Consumer Math
This course is designed to enhance understanding of basic, practical math applications. The course focuses on "real life" processes such as budgeting, compound interest, sales tax, small business management, and data processing to teach algebra, geometry, and statistics. The text Glencoe Mathematics Connections Integrated and Applied is included with this course.
For enrolled students only.
This course covers the following skills: evaluation of expressions involving signed numbers, exponents and roots, properties of real numbers, absolute value and equations and inequalities involving absolute value, scientific notation, unit conversions, solution of equations in one unknown and solution of simultaneous equations, the algebra of polynomials and rational expressions, work problems requiring algebra for their solution, graphical solutions of simultaneous equations, the Pythagorean theorem, algebraic proofs, functions and functional notation, solution of quadratic equations via factoring and completing the square, direct and inverse variation, and exponential growth. The text Saxon Algebra I is included with this course.
This course introduces students to the basic theorems of Euclidean plane geometry and their applications, and explores both plane and solid geometric figures. Students learn how to prove theorems by the axiomatic method, and to use these theorems in solving a variety of problems. Students also learn how to accomplish a variety of geometric constructions. The text Mcdougal- Littell Geometry is included with this course.
In this course, students integrate topics from Algebra I and Geometry and begin the study of trigonometry. The course provides opportunities for continued practice of the fundamental concepts of algebra, geometry, and trigonometry to enable students to develop a foundation for the study of Advanced Mathematics. The text Saxon Algebra II is included with this course.
Prerequisite: Geometry and Algebra I.
Advanced Math prepares the student for further study of mathematics at the college level through a presentation of standard pre-calculus topics, including substantial new material on discrete mathematics and data analysis. The text Saxon Advanced Mathematics is included with this course.
Prerequisite: Algebra II.
Calculus treats all the topics normally covered in an Advanced Placement AB-level calculus program, as well as many of the topics required for a BC-level program. The text begins with a thorough review of those mathematical concepts and skills required for calculus. In the early problem sets, students practice setting up word problems they will later encounter as calculus problems. The problem sets contain multiple-choice and conceptually-oriented problems similar to those found on the AP Calculus examination. Whenever possible, students are provided an intuitive introduction to concepts prior to a rigorous examination of them. Proofs are provided for all important theorems. The text Saxon Calculus is included with this course.
Prerequisite: Advanced Math.
This AP Calculus AB course covers topics typically found in a first-year college Calculus I course and explains topics in differential and integral calculus. This course prepares students to succeed in the Advanced Placement (AP) Calculus AB exam and the subsequent courses. Students will learn calculus by actively becoming engaged with the lectures, readings, animations, activities, and resources in the online textbook. In addition to the online textbook, students will be provided with written materials 6 months; students intending to take the AP exam should enroll by early January-calculus with Trigonometry or the equivalent
AP Calculus BC
This AP Calculus BC course covers topics typically found in a first-year college Calculus I and Calculus II course and advances the student's understanding of concepts normally covered in high school Calculus. Major themes include differential and integral calculus. This course prepares students to take the Advanced Placement (AP) Calculus BC exam. The instructor is the guide for this course, but the student is the learner and will learn calculus by actively becoming engaged with the lectures, readings, animations, activities, and resources in the online textbook and written materials provided 9 months; students intending to take the AP exam should enroll by early Octobercalculus with Trigonometry or AP Caluclus AB or equivalent | 677.169 | 1 |
The School is composed by five set of lectures, designed to introduce young researchers to the more recent advances on geometric and algebraic approaches for integer programming. Each set of lectures will be about six hours long. They will provide the background, introduce the theme, describe the state-of-the-art, and suggest practical exercises. The organizers will try to provide a relaxed atmosphere with enough time for discussion.
Integer programming is a field of optimization with recognized scientific and economical relevance. The usual approach to solve integer programming problems is to use linear programming within a branch-and-bound or branch-and-cut framework, using whenever possible polyhedral results about the set of feasible solutions. Alternative algebraic and geometric approaches have recently emerged that show great promise. In particular, polynomial algorithms for solving integer programs in fixed dimension have recently been developed. This is a hot topic of international research, and the School will be an opportunity to bring up-to-date knowledge to young researchers. | 677.169 | 1 |
ALGEBRA I
2012-2013
Mrs. Cocco
Room C-8
This course is designed to establish a strong foundation in the language of mathematics. Algebra serves as a prerequisite for all secondary mathematics courses. A spiral approach will be given to solving equations. Students will solve equations involving fractions, decimals, and irrational numbers.
Special emphasis will be placed on real-world applications. Students will thoroughly investigate linear and nonlinear equations, graphs and properties. Emphasis will be placed on practical application involving other disciplines and industry.
In addition, this course introduces the study of polynomials, factoring, and special products. Properties of positive exponents are developed with a brief introduction to negative and rational exponents. Rational expressions are explored and are applied to solving fractional equations. This course concludes with the presentation and application of the quadratic formula.
Text: Algebra 1, McDougal Littell
·You will be issued a book at the beginning of the year
·The book should be COVERED to help you protect it.
·You are also responsible for returning the book at the end of the year in the condition you received it—you pay for any damage you cause.
Preparedness for Class
·You are to use a 3-ring binder for this class so that you can keep your notes, homework and handouts in an orderly fashion.
·DATE ALL MATERIAL!!
·You MUST use PENCIL to do math work.I WILL NOT accept work in PEN!!
·You cannot go to your locker once you are in class (even to pick up homework!)BRING EVERYTHING YOU NEED!!!!
Homework Policy
·Homework will be given every other day, for the most part.(See calendar for actual assignments)It will be checked at the start of each period. Your grade will be based on completeness, not accuracy, so it is better to try than to leave answers blank.However, your work must look like you actually tried!
·There will be NO trips to lockers to retrieve homework.It is your job to remember to bring it with you to class.You will receive a zero even if it's done, but in your locker.
·If you have an unexcused absence, your homework for that day is an automatic 0.
·If you have an excused absence and would like credit for the homework that was due while you were absent, please show it to me when you return to class the next day.
·Upon returning from an excused absence, it is your responsibility to find out the assignment you missed and have it done in a timely manner.
·If you are going to miss class for a field trip or school activity you are to show me any work that is due for that period before you miss it (even if that means coming in before school).And if you miss class for an activity and homework is assigned, it is up to you to find out the assignment as it is still due the next day.
Tests & Quizzes
·Tests will be given either at the end of each chapter or halfway through for long chapters.
·Quizzes will be given approximately once a week (about 2 or 3 sections)
·Partial credit will be given if I can follow your train of thought and your work is correct for what you did
·If you miss a test or quiz you will take a different version than the rest of the class.You have 5 days to make up a missed test or quiz on your own time (NOT IN CLASS!)
·There will be a midterm in January and a final in June.They will be averaged to give you a 5th marking period grade.
·NOTE:If you have completed all of you homework throughout the marking period, I will drop your lowest quiz score.
Grading System
·I will be using a point system for your marking period grade.You and I will both keep a running tally of your grades that we always know where you stand in my class.
·The total amount of points will vary by marking period but the items will always be worth the following:
Test: 100 pointsQuiz: 50 pointsHomework: 10 points
Extra Credit:Extra credit will be available on some quizzes and tests.Also, coming to extra help will count as extra credit.
Extra Help:I am available for extra help most days after school between 2:25 – 2:45 PM. | 677.169 | 1 |
Let me explain: one the one hand, linear algebra and calculus are enough to consider a lot of non-trivial problems and describe basic issues in many areas. On the other hand, the various areas of mathematics tend to interact intensely with each other, which is what makes math so cool. So it's going to be difficult to direct you to a specific area, since chances are that a reference that is advanced enough will not be shy about using much more advanced notions (check out the math articles on wikipedia to get an idea of what I mean; even innocuous sounding ones can get pretty intense).
I do want to encourage you to give in to your curiosity: but instead of picking a specific subject, you would be much better off picking up specific references that are written more specifically for your level. There are many of those, look for general math books, e.g. from the AMS and MAA. "Proofs from THE BOOK" might be a bit intense, but roughly at the right level.
Since the various areas of math tend to riff off each other as I mentioned, the last thing you want to do is get specialized too early anyway, so generalist books are better for you now. | 677.169 | 1 |
Synopsis:Stuck On Algebra is a classroom-proven interactive Algebra workstation that keeps students on task doing traditional Algebra in a classic gaming model combining an unbending standard of proficiency with the forgiving and encouraging spirit of "failure without consequence". The result: steady improvement and repeated small successes, the addictive formula of video games without any dilution of the Algebra experience.
Background: SOA is the second generation of a system last sold in the early 90s. More than one educator who used that system in the 90s has sought me out in recent years to ask if it were still available. SOA is available now for beta testing here.
Software In Brief: SOA offers: step-by-step guidance and correction of basic Algebra I problems entered by the student or generated by the application; solved solutions with explanations of generated problems; unassisted exams on a hierarchy of Algebra topics.
Transformations SOA transforms learning mathematics in several important ways:
1. Thanks to step-by-step checking, weak arithmetic skills do not prevent the learner from succeeding with Algebra. Those skills improve as mistakes are caught. The student must work to figure out what they did wrong and correct it. Progress is slower at first, but they are working on Algebra instead of yet another tedious worksheet of arithmetic, so the learner's motivation to persevere is strong.
2. Assistance available in Training Modes lets students of any ability experience the pleasure of solving Algebra puzzles and enjoy math in its own right. They may make more mistakes getting there, but that only increases the satisfaction of finally succeeding and draws them into further study.
3. With SOA correcting all the work, tracking student progress, and offering first-level assistance when students get stuck, the teacher has more time to work with students individually or in small groups.
4. In Mission Mode learners must meet a fixed standard of mastery by passing unassisted, "no second chance" challenges. Missions become available only as prerequisite missions are passed, so the independent learner has a structure they can follow. For any student, Missions draw learners into ever more high-quality practice as they attempt repeatedly to pass the unassisted challenges, encouraged by getting closer each time to succeeding.
Summary The system works for several reasons.
First, Algebra is easy but there is a lot of it and it is cumulative. Algebra requires fluent application of many easy rules, which in turn requires a substantial quantity of high-quality practice to make those rules second-nature. With SOA students get more practice with ever-present feedback and assistance.
Second, Algebra is fun for any student as long as they are given the fighting chance to solve problems on their own. SOA's instant feedback, detailed hints, and solved examples give them that chance.
Third, the stigma of failure is lifted without compromising the standard of proficiency that must be met. The satisfaction of small successes and evidence of steady improvement even as they fail at exams draws learners into further practice and eventual mastery. This is precisely the addictive formula of computer gaming. | 677.169 | 1 |
MBF3C Grade 11 College Course Description
This course enables students to broaden their understanding of mathematics as a problem solving tool in the real world. Students will extend their understanding of quadratic relations; investigate situations involving exponential growth; solve problems involving compound interest; solve financial problems connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating data involving one variable; connect probability and statistics; and solve problems in geometry and trigonometry. Students will consolidate their mathematical skills as they solve problems and
communicate their thinking | 677.169 | 1 |
Introductory TechnicalTechnical Mathematics, 5E provides current and practical vocational/technical applications of mathematical concepts for today?s sophisticated trade and technical work environments. Each unit provides a unique learning experience by featuring practical math concepts alongside step-by-step examples and problems drawn from various occupations that illustrate on-the-job applications of math. Enhancements to the Fifth Edition include a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a sec... MOREtion that supplements the basics of working with spreadsheets for graphing. Introductory Technical Mathematics, 5th Edition provides current and practical vocational and technical math applications for today's sophisticated trade and technical work environments. Each unit delivers practical math concepts alongside step-by-step examples and problems drawn from various occupations. The plentiful examples and problem sets emphasize on-the-job applications of math.Enhancements to the fifth edition include improved algebra coverage, a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a section that supplements the basics of working with spreadsheets for graphing. | 677.169 | 1 |
Nelson Functions 11 provides 100% coverage of the NEW Ontario curriculum for Grade 11 University (MCR 3U) while preparing students for success in Grade 12 and beyond. Key Features & Benefits include:
• Skills and Concepts Review at the beginning of every chapter
• Multiple solved exam...
Nelson Principles of Mathematics 10 ensures students build a solid foundation of learning so they are prepared for success in senior level courses. The program supports the diverse needs of students (through multiple entry points to help a varying range of learners), and offers extensive supp...
Big Ideas from Dr. Small provides math teachers with what they need to know to teach the curriculum while focusing on the big ideas for each math concept. Each book includes hundreds of practical activities and follow-up questions to use in the classroom. The accompanying Facilitator's Guide ...
The Mathematics Teacher eMentor DVD is a flexible, interactive professional learning resource that brings the expertise of leading Canadian math educator, Dr. Marian Small, to teachers across Canada.
With DVDs for K-3, Grades 4-6, and Grades 7-9, the Mathematics Teacher eMentor provides the full s...
More Good Questions, written specifically for secondary mathematics teachers, presents two powerful and universal strategies that teachers can use to differentiate instruction across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert ... | 677.169 | 1 |
Representation Standard
for Grades 9–12
Instructional
programs from prekindergarten through grade 12 should enable all students
to—
create and use representations to organize, record, and communicate
mathematical ideas;
select, apply, and translate among mathematical representations
to solve problems;
use representations to model and interpret physical, social,
and mathematical phenomena.
If mathematics is the "science of patterns" (Steen 1988), representations are
the means by which those patterns are recorded and analyzed. As students
become mathematically sophisticated, they develop an increasingly large
repertoire of mathematical representations and the knowledge of how to
use them productively. This knowledge includes choosing specific representations
in order to gain particular insights or achieve particular ends.
The importance of representations can be seen in every section of this chapter.
If large or small numbers are expressed in scientific notation, their
magnitudes are easier to compare and they can more readily be used in
computations. Representation is pervasive in algebra. Graphs convey particular
kinds of information visually, whereas symbolic expressions may be easier
to manipulate, analyze, and transform. Mathematical modeling requires
representations, as illustrated in the "drug dosage" problem and in the
"pipe offset" problem. The use of matrices to represent transformations
in the plane illustrates how geometric operations can be represented visually
yet also be amenable to symbolic representation and manipulation in a
way that helps students understand them. The various methods for representing
data sets further demonstrate the centrality of this topic.
p.
360
A wide variety of representations can be seen in the examples in this chapter.
By using various representations for the "counting rectangles" problem
in the "Problem Solving" section, students could find different solutions
and compare them. The use of algebraic symbolism to explain a striking
graphical phenomenon is central to the "string traversing tiles" task
in the "Communication" section. Representations facilitate reasoning and
are the tools of proof: they are used to examine statistical relationships
and to establish the validity of a builder's shortcut. They are at the
core of communication and support the development of understanding in
Marta's and Nancy's work on the "string traversing tiles" problem. Although
at one level the story of Mr. Robinson's class is about connections, at
another level it is about representation: one group of students places
coordinates that "make things eeeasy," the class gains insights from dynamic
representations of geometric objects, and the students produce proofs
in coordinate and Euclidean geometry. A major lesson of that story is
that different representations support different ways of thinking about
and manipulating mathematical objects. An object can be better understood
when viewed through multiple lenses. »
What should representation
look like in grades 9 through 12?
In grades 9–12, students' knowledge and use of representations should
expand in scope and complexity. As they study new content, for example,
students will encounter many new representations for mathematical concepts.
They will need to be able to convert flexibly among these representations.
Much of the power of mathematics comes from being able to view and operate
on objects from different perspectives.
In elementary school, students most often use representations to reason about
objects and actions they can perceive directly. In the middle grades,
students increasingly create and use mathematical representations for
objects that are not perceived directly, such as rational numbers or rates.
By high school, students are working with such increasingly abstract entities
as functions, matrices, and equations. Using various representations of
these objects, students should be able to recognize common mathematical
structures across different contexts. For example, the sum of the first
n odd natural numbers, the areas of square gardens, and the
distance traveled by a vehicle that starts at rest and accelerates at
a constant rate can be represented by functions of the form f(x) = ax2.
The fact that these situations can be represented by the same class of
functions implies that they are alike in some fundamental mathematical
way. Students are ready in high school to see similarity in the underlying
structure of mathematical objects that appear contextually different but
whose representations look quite similar.
p.
361
High school students should be able to create and interpret models of more-complex
phenomena, drawn from a wider range of contexts, by identifying essential
features of a situation and by finding representations that capture mathematical
relationships among those features. They should recognize, for example,
that phenomena with periodic features often are best modeled by trigonometric
functions and that population growth tends to be exponential, or logistic.
They will learn » to describe some real-world
phenomena with iterative and recursive representations.
Consider the graph of the concentration of CO2
in the atmosphere as a function of time and latitude during the period
from 1986 through 1991 (see fig. 7.39) (Sarmiento 1993). Teachers might
use an example such as this to help students understand and interpret
several aspects of representation. Students could discuss the trends in
the change in concentration of CO2 as
a function of time as well as latitude. Doing so would draw on their knowledge
about classes of functions and their ability to interpret three-dimensional
graphs. They should be able to see a roughly linear increase across time,
coupled with a sinusoidal fluctuation with the seasons. Focusing on the
change in the character of the graph as a function of latitude, students
should note that the amplitude of the sinusoidal function lessens from
north to south. Students can test whether the trends they observe in the
graph correspond to recent theoretical work on CO2
concentration in the atmosphere. For example, the author of the article
attributes the sinusoidal fluctuation to seasonal variations in the amount
of photosynthesis taking place in the terrestrial biosphere. Students
could discuss the differences in amplitude across seasons in the Northern
and Southern Hemispheres.
Fig. 7.39. A three-dimensional graph
of the concentration of C02
in the atmosphere as a function of time and latitude (Adapted
from Sarmiento [1993])
Electronic technologies
provide access to problems and methods that until recently were difficult
to explore meaningfully in high school. In order to use the technologies
effectively, students will need to become familiar with the representations
commonly used in technological settings. For example, solving equations
or multiplying matrices using a computer algebra system calls for learning
how to input and interpret information in formats used by the system.
Many software tools that students might use include special icons and
symbols that carry particular meaning or are needed to operate the tool;
students will need to learn about these representations and distinguish
them from the mathematical objects they are manipulating.
What should be the teacher's role in developing representation in grades
9 through 12?
p.
362
An important part of learning mathematics is learning to use the language, conventions,
and representations of mathematics. Teachers should introduce students
to conventional mathematical representations »
and help them use those representations effectively by building
on the students' personal and idiosyncratic representations when necessary.
It is important for teachers to highlight ways in which different representations
of the same objects can convey different information and to emphasize
the importance of selecting representations suited to the particular mathematical
tasks at hand (Yerushalmy and Schwartz 1993; Moschkovich, Schoenfeld,
and Arcavi 1993). For example, tables of values are often useful for quick
reference, but they provide little information about the nature of the
function represented. Consider the table in the "Algebra" section in this
chapter that gives the number of minutes of daylight in Chicago every
other day for the year 2000. The values in the table suggest that the
function is initially increasing and then becomes decreasing. Knowledge
of the context of a graph of those values suggests that the behavior is
actually periodic. Similarly, algebraic and graphical representations
of functions may provide different information. Some global properties
of functions, such as asymptotic behavior or the rate of growth of a function,
are often most readily apparent from graphs. But information about specific
aspects of a function—the exact value of f() or exact values of
x where f(x)has a maximum or a minimum—may best
be determined using an algebraic representation of the function. Suppose
g(x) is given by the equation g(x) = f(x)
+ 1, for all x. The analytic definitions of f(x) and
g(x) may offer the most-effective ways of computing specific
values of f(x) and g(x), but graphing the function
reveals that the "shape" of g(x) is precisely the same as that
of f(x)—that the graph of g(x) is obtained by
translating the graph of f(x) one unit upward.
As in all instruction, what matters is what the student sees, hears, and understands.
Often, students interpret what teachers may consider wonderfully lucid
presentations in ways that are very different from those their teachers
intended (Confrey 1990; Smith, diSessa, and Roschelle 1993). Or they may
invent representations of content that are idiosyncratic and have personal
meaning but do not look at all like conventional mathematical representations
(Confrey, 1991; Hall et al. 1989). Part of the teacher's role
is to help students connect their personal images to more-conventional
representations. One very useful window into students' thinking is student-generated
representations. To illustrate this point, consider the following problem
(adapted from Hughes-Hallett et al. [1994, p. 6]) that might be presented
to a tenth-grade class:
A flight from SeaTac Airport near Seattle, Washington, to LAX Airport
in Los Angeles has to circle LAX several times before being allowed
to land. Plot a graph of the distance of the plane from Seattle against
time from the moment of takeoff until landing.
p.
363
Students could work individually or in pairs to produce distance-versus-time
graphs for this problem, and teachers could ask them to present and defend
those graphs to their classmates. Graphs produced by this class, or perhaps
by students in other classes, could be handed out for careful critique
and comment. When they perform critiques, students get a considerable
amount of practice in communicating mathematics as well as in constructing
and improving on representations, and the teacher gets information that
can be helpful in assessment. One representation of the flight that a
student might produce is shown in figure 7.40. »
Fig. 7.40. A representation that
a student might produce of an airplane's distance from
its take-off point against the time from takeoff to landing
This representation indicates a number of interesting and not uncommon misunderstandings,
in which literal features of the story (the plane flying at constant height
or circling around the airport) are converted inappropriately into features
of the graph (Dugdale 1993; Leinhardt, Zaslavsky, and Stein 1990).
Representations of this type can provoke interesting classroom conversations,
revealing what the students really understand about graphing. This revelation
puts the teacher in a better position to move the class toward a more nearly
accurate representation, as sketched in figure 7.41.
Fig. 7.41. A more nearly accurate
representation of the airplane's distance from its take-off
point against the time from takeoff to landing
Mathematics is one of humankind's greatest cultural achievements. It is
the "language of science," providing a means by which the world around us
can be represented and understood. The mathematical representations that
high school students learn afford them the opportunity to understand the
power and beauty of mathematics and equip them to use representations in
their personal lives, in the workplace, and in further study. | 677.169 | 1 |
Teaching Conic Sections
Teaching Conic Sections
So I currently teach a precalc class and new this year we are required to teach conic section.
We cover parabolas, circles, ellipses, and hyperbolas. Since I haven't taught this before, I was wondering if anyone has suggestions on how to teach it? The book we use has a bunch of formulas, but I'm looking for a way to teach it to my students without using all the formulas so they don't have to memorize a bunch of formulas before their exam. What has worked for others?
You should be able to design good lessons directly based on the book sections. As long as you use a Pre-Calculus book you will have rich enough information available.
Be sure to demonstrate the conic sections using a realistic three-dimensional model. Also use the definitions of each conic section and the distance formula to derive the equation for each conic section, and include the analytical cartesian graph for each.
You are right on-target about not just giving a bunch of formulas. The demonstration and the derivations are important for learning and understanding.
Teaching Conic Sections
As a student who struggled through conic sections, I found that by exploring how they were really just variations of the of the same things cemented my understanding of the topic. So if I were in your shoes I would try to show the similarities and differences of the different sections. Specifically between the hyperbola and parabola and the circle and ellipse.
As someone who not long ago learnt Conic Sections, I found the derivations of the formula much easier than remembering them. It was good to see the formulas at first but I much preferred the derivations.
As above said, use a 3D model as well. The 2D drawing didn't really do it justice for me.
I was definitely going to derive the formulas using the distance formula and talk about applications. I wouldn't scratch formulas altogether, but our book has like 8 different formulas, which isn't fair to give all of them to my students if I don't give them on an exam.
Something one of my physics professors said to our class is recalled to me by this thread. He said students of today are so used to tv games, comics, etc. rather than playing with things with their hands, that they can't visualize 3d objects anymore. He was of course exaggerating. I think it quite odd if a student can't visualize what's going on with conic sections, so yes a model would be quite good. Maybe you could get someone to cut it at all the right angles.
Also, the old books on geometry, particularly solid geometry, should be good with conic sections, so maybe go down to the library and have a look at them.
Ah yes, I have a fun experiment using that! You should certainly teach that!
Here it goes: Dandelin was a Belgian, and some people decided to celebrate him. So what they did was the following. They made an ice-cream cone, they put a small biscuit in there (they made it like an ellipse so it would fit inside the cone). And they they put a ball of ice-cream in the cone. Then they would sell it to people.I always tought that it was very clever, and it was quite the financial succes too!did they then discover another, smaller, ice-cream (just like discovering another layer of chocolates when you finish the first layer!), which touched the other focus on the other side of the biscuit? | 677.169 | 1 |
In this limits worksheet, students apply L'Hopital's rule to solve four limits problems. They solve a total of eleven short answer problems. The final seven problems ask students to find the asymptotes of functions.
In this limiting reagent and percent yield worksheet, students fill in 6 blanks with terms related to limiting reagents and percent yield. They determine if 6 statements are true or false, they match 5 terms with their definitions and they solve 2 problems related to percent yield and limiting reagents.
Students examine the importance of limiting power in governments. In this government lesson, students investigate the importance of placing limits on government by looking at the US Constitution. They look at ways that being an active citizen benefits the common good and study the definition of philanthropy.
In this limits and continuity test, learners solve 8 multiple choice questions. They define the words limits and continuity. Students determine the limits of 8 functions. Learners find the value for a constant in one function, and prove one function is continuous at x=0. 4 questions require students to graph functions. There are 25 questions in all (plus one extra credit question).
In this infinite limit instructional activity, students compute horizontal and vertical asymptotes. They use trigonometric functions to find the limits of functions and compare results. This two-page instructional activity contains examples and explanations and fourteen problems.
In this successive approximations activity, students use the Babylonian algorithm to determine the roots of given numbers. They identify the limits of a function, and compute the rate of change in a linear function. This two-page activity contains explanations, examples, and approximately ten problems. | 677.169 | 1 |
PUMP Algebra Curriculum Home Page
This page is very out of date and is currently being modified. In the
meantime, please go to Carnegie Learning to learn
more about currently available cognitive tutors for mathematics and
writing.
Who are we?
The PUMP(Pittsburgh Urban Mathematics Project)
Algebra Project is a collaboration between the ACT
Research Group and the PACT
Center at Carnegie Mellon University, and a group of teachers
in the Pittsburgh Public Schools. It is an attempt to make high school
Algebra accessible to all students through the use of situational curriculum
materials and an intelligent computer based tutoring system.
The high school tutor and course materials are now called "Cognitive
Tutor Algebra" and are being marketed by the PACT Center's spin-off
company, Carnegie
Learning. The PACT Center is currently developing tutors for
Middle School math.
The development of Algebra throughout the curriculum is based on the
students' own informal knowledge of mathematics and on problem situations.
Modelling situations such as the Nintendo Problem, shown above, students
begin to construct intuitive understandings of and connections between
multiple representations of functions. From the beginning of the course
students are asked to make the connections between the various representations
and to construct each representation based on their understanding of the
problem situation.
A mere listing of topics covered does not adequately provide the necessary
framework for the curriculum. Consequently, we use a matrix which attempts
to show the development of the curriculum in a more meaningful way; however,
a three dimensional framework showing the multiple representations as the
core which expands from the first quadrant with simple direct variation
to mx+b to all four quadrants to systems to data analysis to quadratics
would probably be more appropriate.
Currently students work in their regular classrooms three days a week on
the curriculum. The other two class periods are spent in the computer lab
working on the computer tutors. (See the PAT
tutor). The classroom curriculum is reproduced for each student on
loose-leaf notebook paper with space for them to write their responses
on the actual workbook. ALL answers must be written in complete sentences.
Homework is also reproduced on loose-leaf. TI-81 scientific calculators
are provided by the school for use in the classroom. Each student can be
issued a scientific calculator to use on homework.
The U.S. Shirts
Problem is a sample three day lesson module from the first quarter
of the classroom curriculum. Teachers are encouraged to read over the problem
situation at the beginning of the period and then give the students time
to work in cooperative groups to solve the problem. Groups are given overlays
to describe the problem and asked to present their results to the rest
of the class.
Learning in Cooperative Groups
The PUMP project is committed not only to providing the opportunity
for all students to enroll in Algebra, but also to providing the students
with the human and technological support to enable them to be successful
in Algebra. This support includes the computer tutors, the support of the
Chapter One reading specialist, after school tutoring, Family Algebra Nights,
the inclusion of Special Education students and teachers, support for the
teachers including summer workshops and on-going help, and new assessment
strategies.
Family Algebra Night
Student assessment is a major area of emphasis. The first
semester final exam and the year
end final exam from the1993-94 school year are presented to the new
students at the beginning of the school year along with level 4 student
responses in order to clearly communicate our expectations to the students.
Students are assessed on their performance on group tasks in the classroom,
individual on demand performance tasks, portfolios, and their work on the
computer tutors, as well as on more the traditional homework and tests.
At the end of each grading period students are given an individual on-demand
performance task similar to the situations that they have worked on in
the classroom. Each of these requires the student to do a mathematical
analysis of a situation and to produce a writen report based on their analysis.
At the end of the first and third grading periods, these tasks are graded
by the individual teachers; but at the end of each semester these tasks
are graded using the New
Standards Type Grading Conference Model. | 677.169 | 1 |
Lab Math 9
This course is structure to reinforce Core Curriculum Content Standards in numerical operations, data analysis, geometric reasoning, and algebra in preparation for the HSPA and SAT.
Preparedness for Class
·Please use a 3-ring binder for this class so that you can keep your notes and handouts in an orderly fashion.
·You MUST use PENCIL to do math work.I WILL NOT accept work in PEN!!
Tests & Quizzes
·Tests will be given either at the end of each concept.You will get the whole period to complete and check over a test.
·Quizzes will be given approximately once a week and will take half a period.
·Quizzes will be open notebook!
·Partial credit will be given if I can follow your train of thought and your work is correct for what you did
·If you miss a test or quiz, excused or unexcused, you will make it up upon your return.However, you will take a different version than the rest of the class.You have 5 days to make up a missed test or quiz on your own time (NOT IN CLASS!)
·There will be a midterm in January and a final in June.They will be averaged to give you a 5th marking period grade.
Projects
·We will be doing a number of different projects throughout the year.Each one will have a different point value.That information will be given with the directions for the project.
Homework
·There is (usually) no homework in this class!!(I reserve the right to give homework, if necessary)
Grading System
·I will be using a point system for your marking period grade.You and I will both keep a running tally of your grades that we always know where you stand in my class.
·The total amount of points will vary by marking period but the items will always be worth the following:
Test: 100 pointsQuiz: 50 pointsClasswork: 20 points
Extra Credit:Extra credit will be available on tests.Also, coming to extra help will count as extra credit.
Extra Help:I am available for extra help most days after school between 2:25 – 2:45 PM
Contact Information
Phone: 732-222-9300 x3890 (voicemail)Email: [email protected]
School Rules:Review school handbook for school rules.
Ways to be successful:
1.Be on time2. Never laugh at a classmate
3.Raise hand to ask or answer questions4. Watch your language
Please sign below acknowledging that you have read and are aware of the information on the syllabus. | 677.169 | 1 |
Welcome to Calculus! This semester will be a
challenging one for you, but hopefully, with my suggestions, you will be able
to successfully get through this class!
In order to succeed, you will have to know some
things even before you walk into your Calculus classroom on the first
day. First off, sit towards the front. If you do this, you will be
forced to pay attention. Secondly, make sure you get to know the people
that sit around you. If you are outgoing, strive to know the majority of
the people in the class. This will make class time more enjoyable for you
but will also help you with your grades. If you have trouble with
something, you will have a peer to ask for help out of class. Lastly,
when your professor gives you the syllabus for the semester, start right
away! Start to do some of the assigned problems. If they don't make
any sense to you, at least read the material you will be going over in class
the next day thouroughly.
There have been many things that I have discovered
over the course of the semester that could be of value to you. First,
always keep up with your assignments. Have your assignment done so that
you can follow along when your professor lectures about the topic. Some
of the assigned problems will be difficult and you will not be able to
understand them. When this comes up, make sure that you ask
questions. The best way is to ask questions while in class. If
class time runs out, do not just forget about the problems you had on the
assignment, go in and ask your professor during his/her office hours. In
addition to doing your assignments, take your own notes from the book.
This will help you to understand topics covered in lecture better. For
me, this technique really worked. Once I began to take my own notes in addition
to the notes I took from my professor's lecture, I did a lot better, especially
on my weekly quizzes. Lastly, everyone messes up sometimes. If you
get a bad grade on a quiz or an exam, make sure you know all the mistakes you
made and why. Chances are, you will see problems that you had trouble
with on comprehensive tests. Learn from your mistakes, and you will do
better the next time you have the opportunity.
I hope some of my suggestions help you during your
semester in Calculus. Good luck! | 677.169 | 1 |
Trigonometric Derivatives
In this lecture you will cover Trigonometric Derivatives with Professor Switkes. You will start off by learning the Six Basic Trigonometric Functions as well as their Patterns. This lecture is finished off with six fully worked out video examples.
This content requires Javascript to be available and enabled in your browser.
You can use the
derivative formulas for
and
to derive the derivative formulas for the other trigonometric
functions.
Trigonometric Derivatives
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. | 677.169 | 1 |
Authors
Why a liberal arts mathematics book with a quantitative literacy focus?
How do you engage students with the study of math? Crauder, Evans, Johnson, and Noell have found the answer: Help them become intelligent consumers of the quantitative data to which they are exposed every day—in the news, on TV, and on the Internet.
In an age of record credit card debt, opinion polls, and questionable statistics, too few students have mastered the basic mathematical concepts required to think about and evaluate data. Quantitative Literacy: Thinking Between the Lines develops the idea of rates of change as a key concept in helping students make good personal, financial, and political decisions.
The goal of Quantitative Literacy is a more informed generation of college students who think critically about the data provided to them, the images shown to them, the facts presented to them, and the offers made to them. Quantitative Literacy shows students the mathematics that matters to them: their bank account, their medical tests, their daily news feed. It also develops their mathematical thinking, helping them to understand the difference between truthful and misleading mathematical reporting.
It's All in the Examples…
After taking your course and working with Quantitative Literacy, students will be equipped to think about and answer all of the following questions:
Will the Atkins Diet really help me lose weight?
How do I use logic to get the best results from a Google search?
Is the local carpet store trying to fool me into thinking their prices are lower because they quote price by the square foot instead of the square yard?
How far can I go on this tank of gas?
How do I interpret the results of my medical tests?
How can businesspeople and politicians use graphs and charts to mislead me?
Will inflation affect my savings and the age at which I can retire?
How do I avoid getting tricked by a Ponzi scheme?
I want to buy a new car in two years. How much do I need to save each month to achieve my goal? How much car can I really afford?
Why are games of chance so financially risky?
Does the golden rectangle explain the beauty of some paintings and architecture?
LearningCurve A research-based breakthrough in adaptive quizzing available in MathPortal. For more productive classtime and better grades. Simple to assign and simple to use. See for yourself. | 677.169 | 1 |
Perform basic calculations involving the above mentioned notions, both in concrete cases and in more general and abstract cases.
Describe the main ideas in proofs involving the notions above, like for instance the impossibility of trisecting the angle and doubling the cube.
Contact Information
[email protected]
Course offered (semester)
Spring
Language of Instruction
English
Aim and Content
The course covers basic theory of groups and permutations, normal subgroups, group homeomorphisms and factor groups, group actions and Sylow Theory. In addition, the course includes the basic theory of rings and fields, polynomial rings, ideals and factor rings. Studies also include field extensions, finite fields and unique factorisation domains. In the latter, the focus is on groups of utomorphisms of fields, including the Galois theory necessary to show the insolvability of the general quintic by radicals. | 677.169 | 1 |
mathematic... mathematical statistics and to information theory. The effective construction of probability spaces receives particular attention. Author Alfred Rényi—former Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theory—considered effective construction of probability spaces particularly important to applying methods and results of probability theory to other branches of mathematics. Professor Rényi discusses basic theorems of probability theory in terms specific to the theorem in question, rather than in the most general form. His rigorous treatment also covers the mathematical notions of experiments and independence, the laws of chance for independent random variables, and the effects of dependence. Two brief appendixes offer helpful background in measure theory and functional analysis.
Bonus Editorial Feature:
Alfred Renyi (1921–1970) was one of the giants of twentieth-century mathematics who, during his relatively short life, made major contributions to combinatorics, graph theory, number theory, and other fields.
Reviewing Probability Theory and Foundations of Probability simultaneously for the Bulletin of the American Mathematical Society in 1973, Alberto R. Galmarino wrote: "Both books complement each other well and have, as said before, little overlap. They represent nearly opposite approaches to the question of how the theory should be presented to beginners. Rényi excels in both approaches. Probability Theory is an imposing textbook. Foundations is a masterpiece." In the Author's Own Words: "If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy."
"Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?" — Alfred Rényi | 677.169 | 1 |
MTH 5020
Basics
Office Hours
MW: 10am-11am
TH: 2pm-3pm
or by appointment
Prerequisites:
Successful completion of MTH 1610 or successful completion of the MTH 1610 Place-Out Test administered by the Department of Mathematical and Computer Sciences, or successful completion of a course accepted for transfer as MTH 1610 by the Department of Mathematical and Computer Sciences or the College.
Requirements:
Pens preferred; graph paper, and a scientific calculator; that is, a calculator that can handle numbers in scientific notation and has [yx], [π], and [!] keys. (Cell-phone calculators, generally, are not scientific.) CELL PHONES ARE TO BE SHUT OFF AT THE BEGINNING OF CLASS (unless a prior arrangement with me has been made).
Course Overview:
This graduate course is designed to deepen and extend prospective teachers' understanding of the concepts underlying the school mathematics curriculum in grades PK-5. Teachers working in the diverse contexts of school mathematics classrooms must possess not only sound understanding of mathematical ideas, but of the processes by which this understanding develops and in which this understanding is applied. Therefore, how one does mathematics in this class is as important as the mathematical ideas themselves.
In this course, students will:
Pose and solve problems, individually, and in groups, in class and outside of class;
Describe and analyze their work and the work of others, including the mathematical thinking of children as seen in written and video cases drawn from elementary classrooms, both orally and in writing;
Use a variety of tools, including manipulative models and technology, to solve problems;
Demonstrate working knowledge of the big mathematical ideas of the course.
Examine records of elementary classroom practice – videos and samples of children's written work – to analyze children's understanding of the mathematical ideas listed in above.
Classroom Environment:
It is absolutely critical that we create a productive classroom environment that is friendly, non-judgmental, gentle and relaxed so that all class members will feel sufficiently safe to offer suggestions even when they are not absolutely sure that they are correct. So, take care with each other's feelings. Give each other permission to be unsure, and encouragement to take chances and make guesses. That's how we will all learn best. And besides, it is more fun that way.
We will be doing mathematics "one problem at a time." A "problem" is a mathematical situation for which you know no solution. An "exercise" is an opportunity to practice a known procedure. We will be exploring a lot of problems, and in the process will learn many useful strategies for solving them. The goal is to understand and explain why things are true, often in several different ways. After each class, your task is to review your notes, make sense of as much as you can and mark the parts about which you are still confused. Then ask about them with your groupmates or me. In this class, everything can make sense! ! This course does not follow a textbook, so I suggest that you keep a loose-leaf notebook that contains an accurate record of all in and out of class activities. You will refer to it frequently as your prepare your assignments and use it for the in-class exams. They are open-book!
The Mathematical "Big Ideas" of This Course:
Mathematical problem-solving, reasoning, and communication;
Proportional Reasoning;
Patterns and their identification, representation, analysis, generalization, and use;
Descriptive Statistics;
Probability;
Mathematical Disposition (This is, participating in the individual, small-group, and whole-class activities and discussions that constitute the daily work of the course; offering mathematical ideas for discussion and analysis by others, both orally and in writing; demonstrating intellectual commitment to learning and teaching mathematics.
As part of the learning process in our classroom, everyone is expected to observe the professional skills you make use of every day in your workplace. The classroom environment is one where a feeling of safety and security is necessary. Being considerate of others, their opinions and points of view is essential and expected. An atmosphere of equality,
respect and consideration are all considered part of professionalism. Behaviors that would indicate you are acting in a professional manner would include (and are not limited to):
relevant and appropriate participation in class discussions;
avoiding the use of iPods, computers, cell phones and text messaging;
preparation for class through reading all assigned material and handing assignments in on time;
use of active listening skills (even if you disagree with someone's point of view);
attentiveness when someone else is speaking and
an attitude that reflects openness and receptivity to learning and the learning process.
Part of your responsibilities as members of this classroom community includes recognizing the importance and responsibility you hold in facilitating the learning of your fellow classmates.
Attendance:
Successful completion of this course does not depend only on scores on assessments. It depends, in large part, on having participated in the set of class activities that comprise the course. Therefore, prompt attendance is required. I do understand that there might be times when you must miss class. If you must miss all or part of a class, use the office hours, phone number or e-mail address provided on page 1 to discuss the reasons with me beforehand. Whenever you miss class, you must do a 2 - 3 page "make-up" of the material that was missed. This involves writing your own set of notes about what happened that day and the results that were found in class. (This way, your personal set of class notes will be complete for use on the exams.) The "make-up" must be completed within a couple weeks of the absence. More than three absences will lower your grade by one letter, unless special arrangements are made with the instructor.
(Regular tardiness will be interpreted as a lack of intellectual commitment to the course, and will prevent a student from earning an "A.")
Assessment and Grading: Assessment in any mathematics class is the process of gathering and reporting evidence of students' developing mathematical proficiency. In this class a database of evidence, collected from a variety of sources and built throughout the semester, will be summarized as a letter grade, as described next.
1. What are the characteristics of a student who will earn a grade of "B" or better in this class?
Such a student will have, by the end of the course, provided consistent evidence of having reached an appropriate level of mathematical proficiency. Mathematical proficiency is defined as:
Conceptual understanding of the big ideas that underlie the school mathematics curriculum, and fluency with the procedures, skills and tools used to do mathematics.
The strategic competence needed to tackle novel mathematical problems, including the problems of understanding the mathematical thinking of children, and the adaptive reasoning needed to explain and justify one's own methods and solutions, and the methods and solutions offered by others;
A productive disposition toward doing and learning mathematics. A prospective teacher has a productive disposition if she views mathematics as a sensible and meaningful discipline, and if she sees herself as capable of making sense of her own mathematical ideas and those offered by children, through persistent and diligent effort.
2. How does an "A" student differ from a "B" student?
An "A" student will have distinguished herself by:
Providing convincing evidence of a level of mathematical proficiency that goes well beyond the standard set for the course;
Participating consistently in the individual, small-group, and whole-class activities and discussions that constitute the daily work of the course;
Regularly offering mathematical ideas for discussion and analysis by others, both orally and in writing;
Demonstrating, through attendance, promptness, and attitude, the intellectual commitment to learning at the heart of outstanding teaching.
3. What are the characteristics of a "C" student?
Such a student will have, by the end of the course, provided some evidence of mathematical proficiency, but not at the consistent level required to earn a grade of "B" or better. She might fall short of that standard, and earn the minimum passing grade for the course, if she:
Demonstrates proficiency in some but not all of the sections of the course;
Participates, but only intermittently, in class activities and discussions;
Demonstrates, through poor attendance, excessive tardiness, missing or late written work, or poor attitude, a lack of intellectual commitment to learning and, by extension, to teaching.
4. Why no "D" grades?
This course is required for prospective teachers, and a licensure recommendation is based on, among other things, grades of "C" or better in all required courses. A student who does not earn a grade of "C" or better will have to repeat the course, so a grade of "D" would be meaningless. A student who does not demonstrate the minimum characteristics of a "C" student, as described above, will receive a grade of "F."
5. How can a student in this class provide evidence of mathematical proficiency and commitment to teaching?
The instructor will give students opportunities throughout the semester to demonstrate mathematical proficiency, by assigning mathematical tasks to be completed in writing. The students' written work will be assessed using the attached scoring guides. These mathematical tasks will be of five types:
Embedded tasks: instructional tasks for which the student composes an individual, written response in class.
A Midterm and Comprehensive Final comprised of tasks similar to the embedded tasks described above.
Homework:
Homework will be assigned when appropriate. Sometimes, homework will be graded for completion, other times it will be graded more rigorously.
Reading Responses: Students will be assigned weekly readings that will usually be about 15-20 pages. Students will be asked to respond to the readings in writing either on-line through "Just In Time Teaching" or through a written assignment.
The instructor will also gather, in a systematic if not exhaustive way, evidence of mathematical proficiency from students' daily work in class. Therefore, participation in class discussions is a good way to meet or exceed the requirements of the course.
Grading Criteria for MTH 2620
Here is how the final course grade will be calculated. Performance on the AMTs and the Final Exam are weighted very heavily. If your actual assessments don't fit into the attached rubric then the instructor will make a judgment call.
AMT "M" or "IP" grade
An AMT will be given a grade of M when all problems meet expectations. AMTs that do not meet this standard will be given a grade of IP. Students are expected to revise and resubmit their work until they get a grade of M for each of their AMTs. Revisions will be considered late if they are turned in more than a week after they are returned. Late papers, including late revisions, will cause the numeric grade for the assignment to be lowered.
Numeric Grade:
The following two components will determine a student's numeric grade for the semester.
AMTs: Each problem on the first submission will be graded using the attached rubric. The numeric score for the AMT will be the average of the scores for the first submission. Re-writes of the AMT will not affect the numeric score. The semester AMT numeric score will be the average of the individual AMT scores.
Exams: Exam problems will also be graded on the attached rubric. The exam numeric score for the semester will be the average of the scores for the individual problems. The semester exam numeric score will be the average of the two individual exam scores.
Religious Holidays:
Observance of religious holidays follows College policy, which is posted on the web at in the Academic and Campus Policies for Students section. Each student is responsible for understanding and abiding by the policy.
Americans with Disabilities AccommodationsAcademic Dishonesty:
An act of Academic Dishonesty may lead to sanctions including a reduction in grade, probation, suspension or expulsion. See the Student Handbook at in the Academic and Campus Policies for Students section. | 677.169 | 1 |
Demystified
Unlike most books on algebra, this guide lets readers master algebra one simple step at a time--at their own speed. "Algebra Demystified" is loaded ...Show synopsisUnlike most books on algebra, this guide lets readers master algebra one simple step at a time--at their own speed. "Algebra Demystified" is loaded with diagrams to reinforce mathematical concepts, along with exercise sets, chapter ending quizzes, and final exams to master the material Algebra Demystified
Some but not many penciled in answers, but I have an eraser(haha). The book was in tact and just what I needed to advance myself and with any textbook, to move to the next level.
Very Satisfied!! I give it a Five star rating!:) | 677.169 | 1 |
High School Curriculum: Mathematics
Mathematics
Aims and philosophy
The ultimate aim of the Mathematics Department is to maximize the mathematical potential
of each student, regardless of ability. The department strives to make teaching
informative, interesting and inspiring. Specifically, we aim to strengthen and develop
mathematical knowledge and skills, develop the ability to think logically, help
to understand the relevance and application of mathematics in a real-world context,
and help appreciate the power and beauty of mathematics. Equally important is to
enable the acquisition of a suitable foundation in the subject in order to facilitate
further study in mathematics or related subjects.
Curriculum by year-group
Grades 7 – 9:
In grade 7, basic skills are reviewed and consolidated, and students are thereby
encouraged to develop their understanding of the principles involved and their appreciation
of patterns and relationships in mathematics. During grade 8 and into grade 9, students
are set into ability groups. Familiar topics are explored more deeply and new concepts
are introduced. Emphasis is placed on developing a feel for 'number' and interpreting
the reasonableness of results obtained in calculations. At all times, ways of applying
mathematics to everyday situations are investigated, as well as the role of mathematics
in the world in general. As grade 9 progresses, more abstract areas are explored
more fully, especially Algebra.
At the conclusion of these three years, students will hopefully have built a strong
foundation in the major areas of Arithmetic, Algebra, Geometry, Statistics and Probability.
Grades 10 and 11: Edexcel IGCSE Mathematics (4400)
All EIS-J students follow the Edexcel IGCSE syllabus which is offered at both Higher
and Foundation levels. The ability range is wide, and following the same setting
principle as in grades 8 and 9, students are set into four Higher groups and two
Foundation groups in each grade. It is expected that the most able students, especially
those in the two top groups, will be able to achieve excellent or very good grades,
and they consistently meet these expectations. Proportionally very few Higher students
attain less than a 'C' grade (grading is A* to D), and this grade is also attainable
by some Foundation students (grading for this level is C to G).
IGCSE Mathematics can be broadly divided into four main distinct, but at times inter-related,
areas of study: Number, Algebra, Shape and Space, and Data Handling. The aims and
objectives for each level are similar, although the Higher level syllabus is technically
more demanding, especially in the use of Algebra as a tool in solving a wide variety
of problems. In both courses, the skills of interpreting the question and making
the correct decision about which method of solution is applicable, receive particular
attention. There is no coursework component on this course and it is fully expected
that students make appropriate use of a scientific calculator throughout.
Grades 12 and 13: IBDP Mathematics Higher Level, Mathematics Standard
Level, or Mathematical Studies Standard Level
These grades follow the IB diploma programme in Mathematics which includes study
at one of three levels: Mathematics Higher Level, Mathematics Standard Level, or
Mathematical Studies Standard Level. The three levels accommodate different levels
of ability, previous exam success and importantly, whether mathematics will play
a significant role, or not, in any future higher education course undertaken by
a student.
The Mathematics Higher Level course is very demanding and suitable only for the
very best students of this subject. It facilitates entry into courses with a high
mathematical content. To add to the depth of study at this level, the group of core
topics studied is supplemented by an option topic selected from a list of four advanced
and interesting areas of work.
Students on the Mathematics Standard Level course are mathematically competent,
previously demonstrating good skills and achieving good results. They study the
same core topics as on the Higher Level course but not to the same depth. On both
of these courses students must submit a portfolio for internal assessment, consisting
of two pieces of work representing two different types of task.
The Mathematical Studies Standard Level course offers a less demanding study of
the subject and is suitable for students who have previously struggled with mathematics
and/or for those whose may not be required to study the subject at such an intense
level. However, it is challenging in its own right, and should certainly not be
considered as an easy option. It includes useful practical applications, and students
must submit a project for internal assessment. | 677.169 | 1 |
Wiki's calculus page gives a good Earth-from-space overview, and its topic-specific pages cover a lot of the material, but there's only the vaguest of hints of the order in which things go. It's still far better than Mathworld's page, though.
Concentrate on the theory behind calculus and DO NOT skip on the proofs. Once you understand the fundamental theorem of calculus everything under it falls into place. Calculus, like many other areas of math, is a large amount of memorization, and an even larger amount of understanding what you're memorizing.
Well, I already know most basic stuff for differentiation and integration (most of calc 1). So, I'm not necessarily looking for an overview of calculus, but something that I could use to study all the stuff I don't already know. Fill in the gaps/gaping holes. The wikibooks and wikisource articles look good. I wouldn't mind delving into a bit of calc 3.
In my opinion, Calc 3 is really simple. Once you have Calc 1 and 2 down, as well as an understanding of Linear Algebra concepts, I'd say you could learn it pretty quickly, if you aren't treated as an idiot.
I've found that reading the calculus textbook I was given as part of my AP Calc class is extremely useful. More useful than the teacher. I don't do the homework, I don't listen to the lessons (You probably shouldn't follow my example, but...), but when it comes for test time, I have pretty much perfect accuracy. It's pretty intuitive, once you understand what you're doing.
A conceptual understanding could definitely come that quickly, but I think you would have a hard time solving any real problems. Plus, once you get up to stuff like calculus of variations you won't have a solid foundation of understanding.
I recommend Mathematical Methods in the Physical Sciences by Mary L Boas as the most practical math textbook I've read. (get it cheap used~$20)
A conceptual understanding could definitely come that quickly, but I think you would have a hard time solving any real problems. Plus, once you get up to stuff like calculus of variations you won't have a solid foundation of understanding.
It could take you an hour to learn how to use a saw, hammer, and tape measure. But building a house could take a lifetime.
Ya calculus is pretty difficult than other topics but there are many websites available online from where you can take reference and in my opinion hard copy is the best option and for that you can refer to Dr.R.D>Sharma's latest edition. | 677.169 | 1 |
Applied Math Courseware - Metals/Welding
Description
This program provides career-based math activities related to occupational training in Metals & Welding. In addition to helping students improve their basic math skills, they will learn how these skills are used in the workplace. This multimedia presentation is packed with colorful graphics, stimulating background music, helpful math aids, and numerous skill-building activities. Over 100 reproducible activities are included in the comprehensive User's Guide. Students are first assessed using a job specific diagnostic test. The assessment is followed with a math review. There is a unit of job-related word problems. You can view and print activities. You can also view, edit, and print the student's work, as well as add you own math problems to the program. Each student works at his own speed at the computer. | 677.169 | 1 |
This course begins with a brief introduction to writing programs in a higher level language, such as Matlab. Students are taught fundamental principles regarding machine representation of numbers, types of computational errors, and propagation of errors. The numerical methods include finding zeros of functions, solving systems of linear equations, interpolation and approximation of functions, numerical integration and differentiation, and solving initial value problems of ordinary differential equations.
This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results, as well as writing programs to implement the numerical methods with a software package, such as Matlab.
Bisection Method: use the bisection method to solve the equation f(x)=0 and estimate the number of iterations in the algorithm to achieve desired accuracy with the given tolerance;
One-Point Iteration: use the iterative method to find the fixed point of the function f(x), and analyze the error of the algorithm after n steps;
Higher-order Rootfinding Methods: use Newton's method, Newton-Raphson's method, or the secant method to solve the equation f(x)=0 within the given tolerance;
Aitken Extrapolation: understand the order of a convergent sequence and use Aitken's method to accelerate the convergence of the sequence, as well as determining the order of convergence using the iterative method combined with the Taylor formula;
Roots of Polynomials: combine Horner's method with Muller's method to compute roots of a polynomial and analyze whether a numerical root is truly a complex root, or if its imaginary part results from numerical errors.
Newton Divided Differences: derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations;
Newton-Cotes Integration Methods: use the closed Newton-Cotes formula, including the Trapezoidal rule and Simpson's rule, to approximate definite integrals; use the Lagrange polynomial to estimate the degree of accuracy; derive the composite numerical integration using the closed Newton-Cotes formula;
Richardson Extrapolation: use Richardson's extrapolation to derive higher order approximation formulas for numerical differentiation and integration; | 677.169 | 1 |
amental Mathematics Through Applications
Fundamental Mathematics through Applications focuses on relevant content, motivating real-world applications, examples, and exercises demonstrating ...Show synopsisFundamental Mathematics through Applications focuses on relevant content, motivating real-world applications, examples, and exercises demonstrating how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format pairing an example with a corresponding practice exercise encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section incorporating related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and historical connections. Compelling Historical Notes give students further evidence that mathematics grew out of a universal need to find efficient solutions to everyday problems. Plenty of practice exercises provide ample opportunity for students to thoroughly master basic mathematics skills and develop confidence in their understanding.Hide synopsis
Description:New. 0321228308 Purchased as new and in great condition. We...New. 0321228308 | 677.169 | 1 |
Applied math means that mathematics is applied to any field of science, engineering, or even business and economics. If a mathematical topic (e.g. calculus) can be used to solve a certain real-world practical topic such as estimating the peak of growth of bacteria, i.e. using differential equation, then you have now applied mathematics. | 677.169 | 1 |
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Mathematics: Applications and Concepts is a three-course middle school series intended to bridge the gap from elementary mathematics to Algebra 1. The program is designed to motivate your students, enable them to see the usefulness of mathematics in the world around them, enhance their fluency in the language of mathematics, and prepare them for success in algebra and geometry. | 677.169 | 1 |
Maths Year 11
Year 11 is a very busy year at CHSG in the Mathematics Faculty! For 2012-13 there will be three opportunities for students to sit a GCSE in Mathematics; in November, March and in June 2013. Revision for the GCSE exams starts almost immediately from the beginning of Year 11, working towards either a Mock exam in November or the early-entry GCSE itself for a select few students. The majority of girls will sit the final GCSE in March 2013, with an option to re-sit in June if they are close to the next grade up. Students will be given many revision materials over the course of year 11, but one they have access to already is
Areas studied
Number & Problem Solving
Algebra
Geometry & Measures
Data Handling/Statistics
Skills
During GCSE Mathematics students will be taught skills that enable them to function in other subjects and in everyday life. In particular, students will be taught how to present and analyse data accurately, they will be shown how to calculate percentages quickly and efficiently in their heads and also how and when it is appropriate to use their calculators. They will study and learn how to convert between widely used measures including metric and imperial measures, and they will also learn how to problem solve and how to present their findings in a meaningful way. They will also learn to use algebra and geometry to generalize and to solve problems. The skills learnt during GCSE Mathematics prepare students for life after Year 11 and for those pupils that wish to continue studying the subject post-16 and take A level Mathematics, their GCSE studies will have prepared them for the rigours, as well as the beauty, of the subject.
Setting
Students are set according to their potential, based on prior results in tests and teacher assessments. We are combining both types of assessment to provide a rounded view of individual student understanding so that they are placed in the group that will best meet their Mathematical needs. They are also set challenging yet achievable targets based upon their last exam result. Students will be in classes of no more than 30 students, and in lower ability groups, sometimes less than 15 per class. There will be opportunities throughout the year for pupils to move groups, according to their progress. Teachers will discuss movements at Mathematics Faculty meetings and decide if a move is in the best interest of the student.
Homework
Students will be set one piece of homework a week. Homework may be from the MyMaths website, which is marked automatically and immediately online, with a written piece of work lat east once a fortnight. Both pieces will be designed to extend or consolidate class work, or will be revision work. Students should get written feedback from their teacher on their homework once a fortnight. In year 11, students will be given past papers to complete in the Spring term in preparation for their GCSE exam.
Assessment & Reporting
Students are assessed using a variety of methods with homework and class work being an important part of this. They will have a formal exam at the end of Year 9 and Year 10 to look at progress from previous years. There will also be interim reports throughout the year, as well as an annual full report according to the whole school timetable. Parents can contact class teachers at any time to get an update on their daughter's progress.
How parents can help
Ensuring that students come equipped to their lessons – students will need their own geometry set and a calculator for both class work and homework
Checking that students are completing homework tasks to the best of their ability and encouraging them to seek support in plenty of time if they are struggling
Giving opportunities to work out how much change you should get in a shop, or to estimate shopping bills – it's a good mental Maths workout!
In Year 11, students are given a MathsWatch revision CD Rom – please encourage them to use it and ask them to show you how it works, its just like having a private tutor at home, but for free!
All pupils have access to MyMaths – they can revise or study independently at any time to complement their studies. It has a GCSE Statistics section too.
Most importantly, be positive about Mathematics at home – students that hear positive things about the subject at home are more likely to develop a positive attitude to it themselves!
GCSE Revision - February 2012
All year 11 students that are to take the GCSE examination on Monday 5th March please find below revision lists for your information and attention. | 677.169 | 1 |
Grade Descriptors
Thorough knowledge and understanding; successfully applied mathematical principles in a sophisticated and accurate manner in a wide variety of contexts.
Successful application of mathematical principles to solve a range of challenging problems. Clear integration of knowledge, understanding and skills from different areas. Comprehensive responses containing all necessary detail.
Thorough knowledge and comprehensive understanding of the syllabus.
B
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
Broad knowledge and understanding; applied mathematical principles in a variety of contexts, although some responses lacked detail or contained minor errors.
Successful application of mathematical principles to solve a variety of problems. Some integration of knowledge, understanding and skills from different areas. Some responses lacked necessary detail or contained minor errors.
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
C
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
Satisfactory knowledge and understanding of the syllabus; applied mathematical principles and processes in performing routine tasks to a satisfactory level, although some responses lacked detail; several significant errors.
Satisfactory application of mathematical principles to solve some problems. Satisfactory integration of knowledge, understanding and skills from different areas, when given some direction.
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
D
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to apply mathematical principles in straightforward contexts; many significant errors.
Limited application of mathematical principles to solve problems.
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
E
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level.
Very limited knowledge of the syllabus; difficulty applying mathematical principles even at a basic level.
Limited application of mathematical principles to solve even the most basic problems.
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level. | 677.169 | 1 |
7
Hello, in this blog I am going to look back on all of the topics we have covered so far in this semester which are: real numbers, order of operations, evaluating, translating, solving 1-step equations, solving 2-step equations, solving literal equations, CLT, exponents, and distributive property. I feel that I get real numbers really well, but sometimes I can get a little confused, but not a lot. Order of operations, evaluating, exponents, and distributive property all come easy to me really good! For the rest of them they are kind of confusing to me, but I understand them in the end. Yes, I have been thinking about semester exams, what I think about them is I am nervous like everyone else is because I don't want to fail them and do bad. Exams always get me nervous because I don't want to do bad on them and then have them bring my grades down. Three things that I could start doing now to help get ready for exams is start studying, get all of the papers needed to study for the exams, and just prepare myself.
Thanks for listening! | 677.169 | 1 |
Calculus Latin, calculus, a small stone used for counting of calculus. Cal broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
In American mathematics education, precalculus or Algebra 3 in some areas, an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra and Trigonometry. Precalculus prepares students for calculus the same way as pre algebra prepares students for Algebra I. While pre algebra A lower level class might focus on topics used in a wider selection of higher mathematical areas, such as matrices which are used in business.
With the same design and feature sets as the market leading Precalculus, 8/e, this addition to the Larson Precalculus series provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, this text contains the features that have made Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. In addition to a brief algebra review and the core precalculus topics, PRECALCULUS WITH LIMITS covers analytic geometry in three dimensions and introduces concepts covered in calculus.
This market-leading text continues to provide both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a one- or two-term course that prepares students to study calculus, the new Eighth Edition retains the features that have made PRECALCULUS a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises.
Traditionally studied after Algebra II, this mathematical field covers advanced algebra, trigonometry, exponents, logarithms, and much more. These interrelated topics are essential for solving calculus problems, and by themselves are powerful methods for describing the real world, permeating all areas of science and every branch of mathematics. Little wonder, then, that precalculus is a core course in high schools throughout the country and an important review subject in college. Unfortunately, many students struggle in precalculus because they fail to see the links between different topics—between one approach to finding an answer and a startlingly different, often miraculously simpler, technique. As a result, they lose out on the enjoyment and fascination of mastering an amazingly useful tool box of problem-solving strategies. And even if you're not planning to take calculus, understanding the fundamentals of precalculus can give you a versatile set of skills that can be applied to a wide range of fields—from computer science and engineering to business and health care. Mathematics Describing the Real World: Precalculus and Trigonometry is your unrivaled introduction to this crucial subject, taught by award-winning Professor Bruce Edwards of the University of Florida. Professor Edwards is coauthor of one of the most widely used textbooks on precalculus and an expert in getting students over the trouble spots of this challenging phase of their mathematics education.
Full of relevant and current real-world applications, Stefan Waner and Steven Costenoble's FINITE MATHEMATICS AND FINITE MATHEMATICS AND APPLIED CALCULUS, Fifth Edition connects with all types of teaching and learning styles. Resources like the accompanying website allow the text to support a range of course formats, from traditional lectures to strictly online courses.
This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed.
Finite Mathematics and Calculus with Applications, Ninth Edition, by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to get involved with the material, such as "Your Turn" exercises and "Apply It" vignettes that encourage active participation.
Clear provides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics.Designed for the two-semester Applied Calculus course, this graphing calculator-dependent text uses an innovative approach that includes real-life applications and technology such as graphing utilities and Excel spreadsheets to help students learn mathematical skills that they will draw on in their lives and careers. | 677.169 | 1 |
Dojo Toolkit Graphing Calculator Project Readme
Author: Jason Hays
Trac ID: jason_hays22
Contents:
Expressions
Variables, Functions, and uninitializing variables
toFrac in GraphPro
Numbers and bases
Graphing equations
Substitutes for hard to type characters
Making Functions
Decimal points, commas, and semicolons in different languages
Important mathematical functions
---------------Expressions----------------
The calculator has the ability to simplify a valid expression.
With Augmented Mathematical Syntax, users are allowed to use nonstandard operators in their expressions. Those operators include ^, !, and radical.
^ is used for exponentiation.
It is a binary operator, which means it needs a number on both the left and right side (like multiplication and division)
2^5 is an example of valid use of ^, and represents two to the power of five.
! is used for factorial.
It supports numbers that are not whole numbers through the use of the gamma function. It uses the number on its left side. Both 2! and 2.6! are examples of valid input in America. (2,6! is valid in some nations)
radicals can be used for either square root or various other roots.
to use it as a square root sign, there should only be a number on its right. If you put a number on the left as well, then it will use that number as the root.
To evaluate an expression, type in a valid expression, such as 2*(10+5), into the input box. If you are using GraphPro, then it is the smaller text box.
After you have chosen an expression, press Enter on either your keyboard or on the lower right of the calculator.
If it did not evaluate, make sure you correctly closed your parentheses.
In the Standard calculator, the answer will appear in the input box, in GraphPro, the answer will appear in the larger text box above.
On the keyboard, you can navigate through your previous inputs with the up and down arrow keys.
If you enter an operator when the textbox is empty or highlighted (like *) then Ans* should appear. That means the answer you got before will be multiplied by whatever you input next.
So try Ans*3. Whenever you start the calculator, Ans is set to zero.
--------------Variables, Functions, and uninitializing variables----------------
A variable is basically something that stores a value. If you saw Ans in the previous example, you've also seen a variable.
If you want to store your own number somewhere, you'll need to use the = operator.
Valid variable and function names include cannot start with numbers, do not include spaces, but can start with the alphabet (a-z or A-Z) and can have numbers within the names "var1" is a valid name
Input "myVar = 2" into the textbox and press "Enter." You've just saved a variable. Now if you ever type myVar into an expression, 2 will appear (unless you change it to something else).
Variables are best used to store Ans. Ans is overridden whenever you evaluate an expression, so it is good to store the value of Ans somewhere else before it is overridden.
If you want a variable (like myVar) to become empty, or undefined, you just need to set it equal to undefined.
Now try "myVar = undefined" Now myVar is no longer defined.
Functions are very useful for finding answers and gathering data.
You can use functions by inputting their name and their arguments.
For this example, I'll be using the functions named "sqrt" and "pow"
sqrt is a function with one argument. That argument has a name too, its name is 'x.' x is a very common name amongst built in functions
So, let's run a function. Input "sqrt" then input a left parenthesis (all arguments of a function go within parentheses). Now type a value for x, like 2.
Now close the parentheses with the right parenthesis. If you used 2, you should have "sqrt(2)" in the text box. If you press enter, you should get the square root of 2 back from the calculator.
Now for "pow" it has two arguments 'x' and 'y'
Type in "pow(" and pick a value for 'x' (I am picking 2 again)
but now, you need to separate the value you gave x with a list separator. Depending on your location, it is either a comma or a semicolon. I'm in America, and I use commas.
by this point, I have "pow(2,"
Now we need a value for 'y' (I'm using 3). Put a ')' and now I have 'pow(2,3)'
Press Enter, and, following my example, you should get 8
In this calculator, there are several ways to input arguments.
You've already seen the first way, just input numbers in a specific order based on the names.
The second way is with an arbitrary order, and storage.
With 'pow' I can input "pow(y=3, x=2)" and get the exact answer as before. x and y will retain their assigned values, so you will need to set them to undefined it you want to try the next way.
The third way is to let the calculator ask you for the values. Input "pow()" If the values have been assigned globally, then it will use those values, but otherwise, it will ask for values of x and y. They will not be stored globally this way.
I'll go ahead and mention that because of the way the calculator parses, underscores should not be used to name a variable like _#_ (where # is an integer of any length)
---------------toFrac()----------------
toFrac is a function that takes one parameter, x, and converts it to a fraction for you. It is only in GraphPro, not the Standard mode.
It will try to simplify pi, square roots, and rational numbers where the denominator is less than a set bound (100 right now).
Immediately after the calculator starts, toFrac may seen slow, but it just needs to finish loading when the calculator starts. After that, it will respond without delay.
For an example, input "toFrac(.5)" or (,5 for some). It will return "1/2"
For a more complicated example, input "toFrac(atan(1))" to get back "pi/4" (atan is also known as "arc tangent" or "inverse tangent")
--------------Numbers and bases----------------
This calculator supports multiple bases, and not only that, but non integer versions of multiple bases.
What is a base? Well, the numbers you know and love are base 10. That means that you count to all of the numbers up until 10 before you move on to add to the tenths place.
So, what about base 2? All of the numbers up until 2 are 0 and 1. If you want to type a base 2 number into the calculator, simply input "0b" (meaning base 2) followed by some number of 1's and 0's. 0b101 is 5 in base 10
Hexadecimal is 0x, and octal is 0o, but i won't go into too much detail on those here.
If you want an arbitrary integer base, type the number in the correct base, insert '#' and put the radix on the end. ".1#3" is the same as 1/3 in base 10
Because there is not yet cause for it, you cannot have a base that is not a whole number.
--------------Graphing Equations----------------
First thing is first, in GraphPro only, the "Graph" button in the top left corner opens the Graph Window
So, now you should see a single text box adjacent to "y="
Type the right side of the equation using 'x' as the independent variable.
"sin(x)" for example. To Graph it, make sure the checkbox to the left of the equation is selected, and press the Draw Selected button.
You can change the color in the color tab. By default, it is black. Under window options, you can change the window size and x/y boundaries
Let's add a second function. Go to the Add Function button, select the mode you want, and press Create. Another input box will appear.
If you selected x= as the Mode, then y is the independent variable for the line (an example is "x=sin(y)").
If you want to erase, check the checkboxes you want to erase, and press "Erase Selected"
And similarly, Delete Selected will delete the chosen functions
"Close" will terminate the Graph Window completely
---------------Substitutes for hard to type characters---------------
Some characters are not simple to add in for keyboard users, so there are substitutes that are much easier to add into the text box.
pi or PI can be used in place of the special character for it.
For epsilon, eps or E can be used.
radical has replacement functions. sqrt(x) or pow(x,y) can be used instead.
--------------Making Functions-----------------
My favorite part. Before we start, I'll mention that Augmented Mathematical Syntax is allowed in the Function Generator (yay).
Ok, now the bad news: to prevent some security issues, keywords new and delete are forbidden.
Sorry, it is a math calculator, not a game container; not that that would be so bad, but it is to keep it from being used for some evil purposes.
Ok, onto function making. Most JavaScript arithmetic is supported here, but, some syntax was overlapping mathematical syntax, so ++Variable no longer increases the contents of Variable because of ++1, but Variable++ does increase it (same deal with --)
Strings have incredibly limited support. Objects have near zero support
So, let's make a Function:
Press the "Func" button. A Function Window should pop up.
Enter a name into the "functionName" box. (it must follow the name guidelines in the variables section) I'm putting myFunc
Enter the variables you want into the arguments box (I'll put "x,y" so I have two arguments x and y)
Now enter the giant text box.
Type "return " and then the expression you want to give to the calculator. I'm putting "return x*2 + y/2"
Then press Save. Now your function should appear in the functionName list and you can call it in the Calculator.
If you want to Delete a function you made, select it in the function Name list, and then press Delete.
If you altered a previously saved function (and haven't saved over the old one) you can reset the text back to its original state with the Reset button.
Clear will empty out all of the text boxes in the Function Window
Close terminates the Function Window
---------------Decimal points, commas, and semicolons in different languages----------------
In America, 3.5 is three and one half. Comma is used to separate function parameters and list members.
In some nations, 3,5 is three and one half. In lists, ;'s are used to separate its members.
So, when you evaluate expressions, 3,5 will be valid, but in the function generator, some ambiguous texts prevent me from allowing the conversion of that format to JavaScript. So I cannot parse it in the Function Generator.
And here is my example:
var i = 3,5;
b = 2;
I cannot discern whether the semicolon between i and b are list separators or the JavaScript character for end the line. b could be intended as a global variable, and i is a local variable, but I don't know that. So language conversion isn't supported in Function Making.
--------------Important mathematical Functions---------------
Here is a list of functions you may find useful and their variable arguments:
sqrt(x) returns the square root of x
x is in radians for all trig functions
sin(x) returns the sine of x
asin(x) returns the arc sine of x
cos(x) returns the cosine of x
acos(x) returns the arc cosine of x
tan(x) returns the tangent of x
atan(x) returns the arc tangent of x
atan2(y, x) returns the arc tangent of y and x
Round(x) returns the rounded integer form of x
Int(x) Cuts off the decimal digits of x
Ceil(x) If x has decimal digits, get the next highest integer
ln(x) return the natural log of x
log(x) return log base 10 of x
pow(x, y) return x to the power of y
permutations(n, r) get the permutations for n choose r
P(n, r) see permutations
combinations(n, r) get the combinations for n choose r
C(n, r) see combinations
toRadix(number, baseOut) convert a number to a different base (baseOut)
toBin(number) convert number to a binary number
toOct(number) convert number to an octal number
toHex(number) convert number to a hexadecimal number | 677.169 | 1 |
THE NEMETH CODE TUTORIAL FOR THE BRAILLE LITE
The Problem
For individuals who cannot read print symbols, the study of
mathematics poses an extreme challenge. In order for a person who
reads braille to succeed in the study of mathematics, a necessary
condition is mastery of the Nemeth Code, a complex braille code
used to display braille equivalents of print math symbols found
in all fields of mathematics. Unfortunately, many teachers of
students with visual disabilities are ill prepared to provide
effective instruction in this braille code. Therefore, legions of
academically able blind students cannot read or write the Nemeth
Code, and are forced to listen to the contents of math
instructional materials and attempt to carry out mathematical
operations mentally. It is virtually impossible to achieve
mathematical literacy through this ill-advised approach.
The inability to master the concepts underpinning the study of
mathematics is a decades-long stumbling block which will
constrain the individual in many aspects of life, limiting
educational and vocational choices, as well as potential earning
capacity. To rectify this untenable situation, the staff of
Research and Development Institute is engaged in the development
of a tutorial which will provide an effective, independent method
for blind students to study the Nemeth Code. This groundbreaking
effort, never before attempted by any other group, holds the
promise of providing a solution to the intractable problem of
mathematical illiteracy among blind students.
The Braille Lite
The interactive Nemeth Code Tutorial has been designed to be
used with the Braille Lite, a hand-held computer specifically
designed for use by blind persons which combines synthetic speech
and a 20 or 40 cell electronic refreshable braille display. The
device is small and lightweight, and operates on standard
household current or a rechargeable nickel-cadmium battery which
provides thirty hours of operation between charges. The braille
display is designed to show braille symbols in a series of cells.
Each cell is composed of eight tiny pins, housed in small holes,
which "pop up" when stimulated electronically. As the Braille
Lite sends signals to each cell, the appropriate pins move up
slightly out of their holes, tactually perceivable by the braille
reader. To move to the next set of braille symbols after reading
a line of braille cells, a key is pressed and the next set of
braille symbols appears instantaneously. Following this
procedure, the reader can move forward and backward through a
file. The Braille Lite also has speech capability, enabling the
user to simultaneously listen to information and read braille.
This marriage of synthetic speech and refreshable braille is the
most expeditious combination for a tactile reader to learn the
code of braille mathematics.
The Tutorial
Special delimiters have been programmed into the software to
cause the Braille Lite to speak Nemeth Code correctly,
distinguishing mathematical notation from the code used in
literary braille. This is the capability of the software which
makes it extraordinarily valuable to the learner. No other device
exists that speaks braille mathematics correctly, enabling the
learner to compare spoken Nemeth Code symbols to their display on
the electronic braille array. This makes learning to read and
write the symbols remarkably efficient.
The tutorial content is divided into lessons which include
basic concepts initially, and progressively more sophisticated
notation in successive lessons. The scope of the notation
includes that which is found in all mathematics courses up to and
including calculus. Lesson material can be heard by the learner
as well as read on the braille display. Each lesson contains
explanatory material describing the rules governing various
topics within the Nemeth Code and examples of Nemeth Code
expressions. Following the explanatory section of each lesson,
three sets of interactive exercises are presented to the learner,
providing immediate feedback; this is a major strength of this
tutorial. In the first exercise set, the learner is presented
with spoken mathematics notation which is to be brailled. After
the "judge" command is invoked, the Braille Lite announces the
number of errors, and marks the first error by raising two pins
below it on the braille display. The learner is then given
limitless opportunities to correct those errors. There is also a
command which can be used to toggle between the incorrect and the
correct answer, providing the opportunity for direct
comparison.
The second set of exercises emphasizes reading of Nemeth Code
symbols. The learner is instructed to read braille shown on the
display. The "judge" command causes the Braille Lite to speak the
displayed symbols, either one symbol at a time or one line at a
time, enabling the learner to compare the correct spoken
equivalent to his or her answer.
Proofreading exercises are presented in the third set, where
correct spoken symbols are supplied along with a display of
braille symbols which contain errors. The learner is instructed
to find and correct the errors. The 'judge" command can be
invoked to indicate errors. A "show answer" function enables the
learner to toggle the braille display between the correct answer
and the answer which contains errors. | 677.169 | 1 |
amount of math in materials science/engineering?
amount of math in materials science/engineering?
Hi, I was just looking over the "course calendar" for a materials science/engineering program at the University of Toronto ( I find it strange that there is only ONE required math course throughout all 4 years. I know that there is some physics involved with materials science, so how much math is generally "required" in this field? will there be algebra? the expectations only seem to be a course in calculus, but I'm pretty sure that I'll need more than that. thanksthanks. to clarify, by algebra, I meant linear algebra.. et c. I don't know "college algebra" is supposed to be but linear algebra is usually taken after or concurrently with calculus
amount of math in materials science/engineering?
Hello,
I am a materials science/engineering major (along with a double major in physics) at a major research university in the US. For MSE I had to take calc I, calc II, calc III (sometimes called multivariable), diff. eq., linear algebra and a stat class.
You need differential equations for things like solid state diffusion (you need it for all of physics really); you need calc III for stuff like thermo and magnetic properties; you need lin. alg. for analyzing crystal lattices as well as quantum mechanics which materials scientists DO NEED TO BE PROFICIENT WITH. And you need the others in order to learn the above subjects, they're the base.
I would encourage you to take as much math as possible; I would also encourage you to double major or minor in physics or chem. Every time I tell a mat sci prof my major, they say something to the effect of "I wish I had done something like that." Materials science is getting evermore fundamental. And physics or chemistry will give you an advantage.
thanks, it was precisely the information I was looking for. I'm taking spivak-style calculus courses and a more theoretical linear algebra course right now. I really like it, but is it necessary? should I look at the more computational side of math rather than the proof/theoretical side of math? I've heard some people say "if you need calculus for physics, spivak isn't your book" - I'm thinking if this applies. | 677.169 | 1 |
All the key areas of the SAT of Mathematics are covered in this iTooch SAT Math app including Numbers and Operations, Algebra, Geometry and Statistics. Short and helpful chapter summaries review key facts and over 1,400 example problems give students plenty of practice so that the methodology of working through problems is clear. Thanks to this app, future exposure to complex SAT math structures should seem less daunting.
This app allows you to cover a spectrum of problems; you can make sure you've got the basics covered and stretch yourself with some of the more difficult questions. Real-world problems are used in many cases, so that the importance of learning these skills is clear. It can be used to help students prepare for the SAT and/or review high-school level math concepts in general in a fun and interactive way.
Apps automatically sync in the background in order to load new activities whenever an Internet connection is available.
Meet the SAT Math Team:
Hannah Kirk
SAT Math author, Hannah Kirk, is a British mathematics graduate with a professional background in research. She holds a BSc Economics and Mathematics from the University of the West of England and an MSc Econometrics from the University of Manchester. Her research interests revolve around international development issues. Hannah has experience as a private tutor of mathematics for pupils undertaking the equivalent high school graduation exam in England.
Eileen Heyes
SAT Math editor, Eileen Heyes has a BA in journalism from California State University, Long Beach. She wrote and edited at newspapers for 30 years while trying to decide what she wanted to be when she grew up. She is the author of three nonfiction books for teens and two mysteries for children. In learning the storytelling craft, she has studied screenwriting and improv, earned a certificate in Documentary Arts, and volunteered in the street cast of a Renaissance Faire. She takes it all back into the classroom as a writer-in-residence with the United Arts Council of Wake County, North Carolina. Originally from Los Angeles, she now lives in Raleigh with her brilliant husband and one of her two interesting, articulate sons. | 677.169 | 1 |
Pre-Algebra Guide (Android) app for $0.99
This complete PRE-Algebra GUIDE provides more than 325 rules, definitions, and examples, including number lines, integers, rational numbers, scientific notation, median, like terms, equations, the Pythagorean Theorem, and much more. Each of 44 different steps builds upon another, giving you a solid foundation in basic Algebra for further studies and real-world applications. | 677.169 | 1 |
USEFUL LINKS:
STUDENT LEARNING OUTCOMES
Upon successful completion of Math 250, the student
should be able to:
1. State and apply basic definitions, properties,
and theorems of first semester Calculus.
2. Model and solve problems using derivatives of algebraic and transcendental
functions.
3. Analyze and sketch graphs using the principles of calculus.
4. Evaluate limits, derivatives, definite and indefinite integrals graphically,
algebraically, and/or using the formal definitions.
STUDENT LEARNING OBJECTIVES:
Student will review the concepts of absolute
value inequalities, functions, combinations of functions and composite functions.
Student will evaluate limits using the limit
theorems, the definition, and demonstrate the concept of continuity.
Student will find the derivative (first and
higher order) using rules, theorems and definition. Interpret as slope, rate
of change, velocity, and acceleration.
Student will learn and demonstrate techniques
of approximation, and the differential. | 677.169 | 1 |
Word Problems
Since arithmetic and geometric series are common menu items that everyone loves, they show up a lot in word problems. Unlike hotdogs and burgers, the word problems usually provide some individual quantities. They ask you to compute a related...
Please purchase the full module to see the rest of this course
Purchase the Series Pass and get full access to this Calculus chapter. No limits found here. | 677.169 | 1 |
Elementary Statistics - Updated Solution Manual - 10th edition
Summary: Addison-Wesley is proud to celebrate the Tenth Edition of Elementary Statistics. This text is highly regarded because of its engaging and understandable introduction to statistics. The author's commitment to providing student-friendly guidance through the material and giving students opportunities to apply their newly learned skills in a real-world context has made Elementary Statistics the #1 best-seller in the market. Students learning from Elementary Statisti...show morecs should have completed an elementary algebra course. Although formulas and formal procedures can be found throughout the text, the emphasis is on development of statistical literacy and critical thinking. ...show less
0321470400 THIS BOOK IS IN STOCK & WILL SHIP SAME DAY!USED BOOK WITH CLEAN PAGES,LIGHT WEAR TO COVER.THIS BOOK IS IN VERY GOOD CONDITION AND NO MISSING PAGES OR ANYTHING THAT WOULD COMPROMISE THE LEGI...show moreBILITY OR UNDERSTANDING OF THE TEXT.FREE TRACKING NUMBER PROVIDED IMMEDIATELY UPON PURCHASE SO YOU CAN TRACK YOUR PURCHASE WITH EASE.WE SHIP 6 DAYS A WEEK TWICE A DAY! GUARANTEED A++CUSTOMER SERVICE0321470400 | 677.169 | 1 |
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how is doing operations (adding, subtracting , multiplying, and dividing ) with rational expressions similar or different from doing operations with fractions | 677.169 | 1 |
Download "Frankestein" by Mary Shelley. for FREE. Read/write reviews, email this book to a friend and more...
FrankesteinComments for "Frankestein"
Fluid mechanics is an essential subject taught at degree level on engineering and science courses.
The book is complimentary follow up for the book "Engineering Fluid mechanics" also published on BOOKBOON, presenting the solutions to tutorial problems, to help students check if their solution method is correct, and if not, they can see the full solution hence giving them further practice in...
Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems in most topics in basic algebra. The problems have a wide variation in difficulty, which is indicated by the number of stars.
This is an HTML version of the ebook and may not be properly formatted. Please view the PDF version for the original work.
An excerpt is a selected passage of a larger piece, hence this is not the complete book. | 677.169 | 1 |
Description: This course is an introduction to modern geometry of
high-dimensional convex bodies. We are going to study the distances
between convex bodies, sections and projections, approximation of
systems of functions etc. In these problems the precise structure of
a convex body is usually unknown, so the probabilistic methods will
play a crucial role. In particular, to find a section of a convex
body with certain nice properties, one can consider a random section
and show that the property is satisfied with positive probability.
This approach allows to prove the celebrated Dvoretzky theorem: any
high-dimensional convex body possesses a section of a large
dimension, which is close to an ellipsoid. The existence of an
ellipsoidal section is a surprising result even for simplest convex
bodies, such as cubes or cross-polytopes.
We shall consider the properties of random convex bodies, the
connection between the volume of a body and the structure of its
sections and different applications of convex geometry techniques to
Analysis. | 677.169 | 1 |
North Carolina Modules (NC1, NC2, NC3, NC4, NC5)
North Carolina has recently emerged as a leader with regard to state
curriculum and assessment standards. The North Carolina Standard Course
of Study, which dates back to 1898, is revised periodically to reflect
changing needs of students and society. The latest revision adopts a
philosophy of competency-based curriculum.
In the early 1990's, the N.C. Department of Public Instruction (NCDPI)
produced an outline of competency goals by grade for mathematics, as well as
specific objectives and assessment measures pertaining to these goals. The
NCDPI also developed hundreds of problems which serve as sample measures and
provide a foundation for classroom instruction and assessment.
The North Carolina Math Objectives database (NC1) contains 1749
of those problems and 260 accompanying diagrams. The material spans skills
and concepts from 6th grade through high school (including calculus) and
includes multiple-choice, free-response, and open-ended problems. Teachers
in North Carolina will immediately see the benefit of having the problems in
a computer database. Teachers from around the country will certainly appreciate the wide
range of topics and the high-quality sample items for regular instruction
and assessment.
The North Carolina Elementary Math database (NC2) contains 1316
problems and 925 pictures taken from the state's released "Testlets" for
grades 3 through 5. The problems are organized by grade, and then by topic.
Although most problems are multiple-choice, there are some open-ended
questions available for each grade level.
The North Carolina Algebra I database (NC3) contains 2126
original multiple-choice problems and 600 pictures for the Algebra I
End-of-Course test. The original problems were authored by Susan Fink, a
respected math teacher from Forsyth County Schools (Winston-Salem), and are
drawing rave reviews from teachers across the state. All problems are cross referenced to the 1992 NC goals and objectives,
as well as to the ojectives enacted in 1998.
The North Carolina Reading database (NC4) contains 929 problems
based on more than 100 reading passages. The database contains all problems from
the North Carolina Dept of Public Instruction's testlets for grades 3 through 8,
and is organized by grade.
Finally, the North Carolina Math Testlets database (NC5) contains
1713 problems and 635 accompanying diagrams. This database is a continuation of
the NC2 database, as it includes all problems from the state's testlets
for grades 6 through 8, and Algebra I. The problems are organized by grade and
then by topic, and each grade includes a section of open-ended questions.
The North Carolina modules are available in packages at reduced prices for
North Carolina schools. NC schools, please contact EducAide for special
pricing information. | 677.169 | 1 |
Book DescriptionMore About the Author
Product Description
Review
Second Edition S. Lang Introduction to Linear Algebra "Excellent! Rigorous yet straightforward, all answers included!"—Dr. J. Adam, Old Dominion University
--This text refers to an out of print or unavailable edition of this title.
Inside This Book(Learn More)
Browse and search another edition of this book.
First Sentence
The concept of a vector is basic for the study of functions of several variables. Read the first page
This text is intended for a one semester introductory course in Linear Algebra at the sophomore level geared toward mathematics majors and motivated students. It was originally extracted from Lang "Linear Algebra," and is now in its second edition (a vast improvement over the first: Lang rarely does the increasingly popular token update).
The text takes a theoretical approach to the subject, and the only applications the reader can expect to see are to other interesting areas of mathematics. With the exception of the last chapter, these are left in the exercises, and Lang does not push them vary far.
The trend in most Linear Algebra texts at this level that attempt to appeal to a large audience (such as engineering students) is away from the Definition-Theorem-Proof approach and towards a less formal presentation based around ideas, discussions as proofs, and applications. I prefer the former approach, which Lang is very much in the tradition of, and believe that the way to teach students how to write rigorous and presentable proofs is by making them read and study them. In fact, I learned how to write proofs from studying this text and working all of Lang's well-chosen exercises.
"Introduction to Linear Algebra" starts at the basics with no prior assumptions on the material the reader knows (the Calculus is used only occasionally in the exercises): the first chapter is on points, vectors, and planes in the Euclidean space, R^n. After that is a chapter introducing matricies, inversion, systems of linear equations, and Gaussian elimination. While the book does spend adequate time on how to perform Gaussian elimination and matrix inversion, it also gives all the proofs that these methods work.
The bulk of the theoretical material comes in Chapters III through V, which respectively present the theories of vector spaces, linear mappings, and composite and inverse mappings. The approach is rigorous, but by no means inaccessible. As is necessary in a course like this, time is spent on establishing clear and solid proofs of basic results that will be treated as almost trivial ("you can show it on your homework to convince yourselves") in more advanced classes - c.f. Lang's "Undergraduate Algebra."
The next two chapters cover scalar products and determinants, and have a somewhat more computational feel to them. There is much theory in the sections on scalar products, but a big focus is also the Gramm-Schmidt method for finding an orthonormal basis. Many of the determinant proofs are in the 2 x 2 and 3 x 3 case to avoid bringing in the full formalism and notation of determinants in general.
The text concludes with what is its most difficult chapter, the one on eigenvectors and eigenvalues. It is the most, however, for applications to physics, and interest applications comprise the last half of the chapter.
If you are ordering this text used, I recommend you take care to find the second edition. The first edition was significantly shorter and covered less material.
This is an introductory text, and not for learning the material that would be included in a second course or part of the algebra sequence at the junior/senior level. For those purposes, I recommend Lang's "Linear Algebra." Portions bear strong (often exact) resemblance to the book at present consideration, but the most basic material is missing and much advanced material is included.
In conclusion, I highly recommend this text for a motivated student who wants a first exposure to Linear Algebra. The text isn't always easy reading, and parts may be a tough climb for readers without much exposure to this type of reading. The experience, however, is well worth it; in mathematics, one really only learns as much as one sweats, so to speak.
15 of 15 people found the following review helpful
5.0 out of 5 starsA wonderful book and benchmark test for students26 April 2000
By A Customer - Published on Amazon.com
Format:Hardcover
This is a wonderful book for freshmen/sophomores. Being a senior now, it's easier to evaluate the quality of the text and judge it's worth compared to other books. I really don't think there's a better book on linear algebra at this level. Everything in here is well motivated, organized and as rigorous as possible for an intro book. That's not to say that there's not room for improvement as far as motivation goes, but what he has certainly suffices. Even if you don't get everything in here on your first pass, this book provides a good benchmark test - if you can get through it in good shape, then you are probably well prepared to begin upper level work. If you can't, then you should probably try again before attempting a serious course in, say, group theory or topology. Linear algebra provides the ideal subject matter with which to introduce the student to rigorous proof techniques, because it has so many easily visualized yet useful examples. So if you can't follow the proofs here, don't expect to follow the proofs in a more abstract course. If there's any other book that I might use in this one's place, it would actually be Lang's "Linear Algebra," which I find to be more cohesive and motivated, although more difficult.
This text is well written and is motivated by theory. Better suited as a supplemental text, as opposed to a required course text. As for the self acclaimed "smart" reviewer from Irvine, A grades in mathematics do not mean that you have mastered the subject. The school which you attend also affects your grades. Not to mention, linear algebra is usually a bridge to higher mathematics, grades in calculus, and diff equs don't really matter. If you are having trouble with this text or the course associated with it, chances are that you will have a very, very hard time in more mathematical courses such as abstract algebra and classical analysis. Calculus 1, 2, 3, and diff equs are just applications of mathematical theory. It is doubtful that after this sequence that the student even knows the definition of a limit of a function in a single variable which is ironic, for what is calculus but the study of limits. For example, the derivative is the limit of the difference quotient, the Riemann integral is the limit of Riemann sums, etc...
The point is that linear algebra, at the theoretical level, is a bridge to higher mathematics. This is a good text to use in order to cross that bridge. Serge Lang is a great mathematician, he was recently given an award from the AMS for his achievements in writing textbooks. My favorite linear algebra text is 'Linear Algebra' by Hoffman/Kunze. For people who lack in mathematical ability and wish for a more applied introduction to linear algebra, 'Linear Algebra and its Applications' by Gilbert Strang. If the reader from Irvine or anyone having difficulty with this beautiful subject wishes for a even simpler text, there is 'Elementary Linear Algebra' by Bernard Kolman.
Amongst other great works by Serge Lang, I believe that 'Algebra' is a classic which should be in the library of any mathematics student and professor. | 677.169 | 1 |
Developing Skills in Algebra
Developing Skills in Algebra is designed for the
student who needs a comprehensive review of the topics from elementary and
intermediate algebra. This textbook uses the topics covered by many schools
in an intermediate algebra course. Within the reader friendly styled text,
students will find the algebraic skills necessary to prepare them for courses
in college algebra and trigonometry. New topics are presented with expanded
explanations, a progression of examples and colorful diagrams, aiding visual
learners in their understanding of formulas. To help build a strong foundation
and ensure understanding, students will have plenty of opportunity for practice
before proceeding to the next concept. | 677.169 | 1 |
Equations, Roots & Exponents Mastery DVD A 12-lesson pre-algebra program that teaches selected critical concepts, skills, and problem-solving strategies needed to recognize and work with different types of equations problems. | 677.169 | 1 |
MATH 211
Fundamental Mathematics I
CR:
3.0
Prerequisite: not open to first-year students. A course for prospective elementary teachers covering the methods of instruction of mathematics and emphasizing a hands-on approach. topics include number systems, elementary number theory, ratio, proportion, and percent.
Course Overview
Students in the mathematical programs analyze and solve problems in a variety of environments while improving and extending their logical skills. Major programs may be elected which emphasize abstract or applied mathematics.
A student may earn either a Bachelor of Arts or a Bachelor of Science degree in mathematics. Interdepartmental majors are offered in mathematical economics and mathematics-physics. Students interested in any of these majors are encouraged to consult the department chair for advising assistance.
Note: No more than two 300-level courses may be double-counted for a mathematics major and a statistics minor. No 300-level course may be double-counted for a mathematics minor and a statistics minor.
Teacher Licensure Students seeking teacher licensure in secondary mathematics must include MATH 310 and MATH 333 in their major program. In addition, one course in statistics (MATH 106, MATH 205, or MATH 304) must be included in the major program. | 677.169 | 1 |
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