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Math in Our World - 2nd edition
ISBN13:978-0077356651 ISBN10: 0077356659 This edition has also been released as: ISBN13: 978-0072982534 ISBN10: 0072982535
Summary: The author team of Dave Sobecki, Angela Matthews, and Allan Bluman have worked together to create the second edition of Mathematics in Our World, an engaging text catered to the needs of todays liberal arts mathematics students. This revision focuses strict attention to a clear and friendly writing style, integration of numerous relevant real-world examples and applications, and implementation of the step-by-step approach used for years in Blumans Elementary Statistics: A Step by Ste...show morep Approach. The result is an exceptionally engaging text that is able to both effectively and creatively convey the basic concepts fundamental to a liberal arts math curriculum for even the most hesitant student |
Useful Mathematical and Physical Formulae is a compact volume presented in a concise manner for general use. Collected in this book are commonly used formulae for studies such as quadratics, calculus, and trigonometry; in addition are simplified explanations of Newton's Laws of Gravity and Snell's Laws of Refraction. A glossary, a table of mathematical and physical constants, and a listing of Imperial and Metric conversions are also included.
Praise
"The fascinating, informative Wooden Books series blends ancient wisdom and modern knowledge. The books . . . will stimulate more thinking and subsequent 'Eureka' moments than a dozen novels laced with narrative innovation and postmodern stylings."—The Atlanta Journal-Constitution |
Mathematics for Elementary School TeachersIntended for the one- or two-semester course required of Education majors, Mathematics for Elementary School Teachers, 4/e, offers pre-service teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect content to the hands-on activities in the corresponding Explorations Manual. In addition to presenting real-world problems that require active learning, Bassarear demonstrates that there may be many paths to finding a solution--and even more than one answer. With this exposure, future teachers are better prepared to assess student needs using diverse approaches. |
The Online Mathematics Subject Tree
Math Societies
· AMATYC – The American Mathematical Association of Two Year Colleges is an organization that was founded in 1974. This organization works specifically with promoting math studies in two year colleges.
· AMS – The American Mathematical Society promotes mathematical education and research through educational publications, journals, conferences and more.
· MAA – The Mathematical Association of America focuses on mathematics at the undergraduate college level.
· EMS – The European Mathematical Society Publishing House is associated with all journals and publications relating to applied mathematics.
· Mathematician Biographies – Categorize the mathematician by date, or arrange them alphabetically. This mathematician index houses one of the best collection of biographies and information on mathematical geniuses.
· Famous Mathematicians – Houses profiles and biographies of mathematicians all throughout the world, this index is arranged alphabetically.
Math Education Websites
· Math Education Resources – A wonderful collection for both educators and students interested in learning math. The websites listed all contain math resources aimed to educate students of all math levels and concentrations.
· Mathematical Resources on the Internet – A huge collection of mathematical help. Arranged by different categories including math journals, mathematics websites, math discussion groups, math references and more, this website should definitely be bookmarked and saved.
· Mathematical Journals – A list of mathematical journals that are published on the web. Includes mathematical journals from all over the world.
· Electronic Math Journals – In addition to a complete listing of mathematical journals on the internet , there is a huge section for printed mathematical journals and where you can find these publications.
· Math Crony – Available as a free trial, this math software helps students learn basic math skills such as multiplication, long division and more.
· Math Calculators and Tools – Free calculators, conversion tools, and other download able programs aimed at making math education easier for students of all ages.
· Online Math Calculators and Solvers – Including graphing software, time calculators, logarithmic equation solvers and more, this collection of math software and tools covers just about every math topic and field. |
Summary: David Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, Sixth Edition, focuses on teaching mathematics by using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected books. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greate...show morer emphasis. Many sections now contain more examples and exercises involving applications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes. This Enhanced Edition includes instant access to Enhanced WebAssign the most widely-used and reliable homework system. Enhanced WebAssign presents thousands of problems, links to relevant textbook sections, video examples, problem-specific tutorials, and more, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help users learn the basics of WebAssign quicklyly used. Book only -- does NOT include access card. Ships same day or next business day. Free USPS Tracking Number. Excellent Customer Service. Ships from TN
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Quick Review Math Handbook Hot Words, Hot Topics, Book 1
9780078600838
ISBN:
0078600839
Pub Date: 2003 Publisher: Glencoe/McGraw-Hill
Summary: The one-stop reference resource for teachers, students, and parents! "Quick Review Math Handbook: Hot Words, Hot Topics" (available in English and Spanish) provides your students and their parents with a comprehensive reference of important mathematical terms and concepts to help them build their mathematics literacy. The easy-to-use format allows parents to help their children with homework assignments and test prep...aration.
McGraw-Hill Staff is the author of Quick Review Math Handbook Hot Words, Hot Topics, Book 1, published 2003 under ISBN 9780078600838 and 0078600839. Three hundred eighty three Quick Review Math Handbook Hot Words, Hot Topics, Book 1 textbooks are available for sale on ValoreBooks.com, two hundred eighty one used from the cheapest price of $0.01, or buy new starting at $6.00.[read more [more |
About a year ago I took a Linear Algebra class that was required for my degree. Unfortunately that class had an unidentified pre-requisite and started at a much higher level then I really needed. Going in I had no prior experience with linear algebra. I can definitely see how understanding linear algebra would be a very good thing to have in my field so I've been trying to piece it together ever since and have felt like I'm close but I just don't quite get it. I understand that linear algebra is a way to solve a lot of equations rapidly... In my mind this seems like that means finding values for the variables... but it didn't seem like we ever did... Instead we were doing things like multiplication of matrices and that made no sense. Or we would apply advance algorithms to get the matrix into certain forms which the reason for never made sense to me. So what does it mean to solve a system of equations? What are some real world examples that might make understanding linear algebra easier? Why are orthogonal and other types of matrices so special? Any insights, examples, suggestions are greatly appreciated!
As the question stands, it is way to vast to tackle in a single post. (Although I have seen heroic answers to vast questions before.) Have you already tried reading the wikipedia page on linear algebra? Also this page should deal with your question about solving equations and its relationship to linear algebra.
–
RaskolnikovMar 12 '11 at 19:08
2 Answers
I'm not going to try and answer all of your questions because it's really a very broad question. I will at least give you a start and then the best thing you can do is either take another course or open a book and learn some things, coming back to ask more specific questions along the way.
Surely you are familiar with equations like $5x = 6$ where we want to find all solutions $x$ where $x$ is in some field, say in this case the real numbers. In this case every nonzero element has an inverse so you can multiply by $1/5$ to get $x = 5/6$.
Although linear algebra isn't really just about solving equations, that's where it starts. It's called linear because we only want to solve equations that are linear in the unknown variable. The simplest case would be something like
$$
x + y = 4,
2x - y = -1
$$
Actually we can just write this in matrix form. If you remember how to multiply a matrix, then we can write this system as $Ax = b$:
The reason why we multiply matrices is because we want to solve $Ax = b$ by multiplying by the inverse of $A$ to get $x = A^{-1}b$. Of course, not all matrices have inverses. So the set of all $n\times n$ matrices, with addition and multiplication is a ring but not a field. A ring is sort of like a field but now we remove the requirement where inverses exist for all nonzero elements. Also matrix multiplication is not commutative: $AB$ is not necessarily equal to $BA$.
In the above case $A$ does have an inverse, and you can multiply on the left by $A^{-1}$ (see if you can find it) to get the solution to this system of equations.
Thus we have found: multiplication of matrices helps us solve equations.
However, we are only beginning because finding the inverse of a matrix is tricky, so we study the different ways to represent matrices and calculate with matrices in order to more efficiently move them around. This is a bit vague but intentionally so since there is so much mathematics going on in the background which you need to learn.
Linear algebra is really about vector spaces. To appreciate the idea of a vector space you should first get some experience with abstraction by doing hundreds of problems. A vector space is just a set of elements together with addition and scalar multiplication that satisfy certain axioms. It turns out that matrices correspond to maps between vector spaces in a chosen basis of that space. This may not make too much sense to you now, but the important point is that putting matrices in different forms corresponds to changing the basis of the vector space in different ways.
The reason why we like to use vector spaces is because then we can concentrate on the algebraic properties of vector spaces without having to worry about specific numbers or equations, which then can be applied to all sorts of problems which have little do with solving equations.
The best thing you can do to understand linear algebra is to take a course/read a book and just start solving problems. It is impossible to really understand what it is about first and then practice doing it. The understanding comes with the practice.
Linear algebra is not necessarily about solving linear equations rapidly. Indeed, most algebraist don't care for speed except for mathematicians in numerics and computer algebra.
Linear Algebra is taught because of two dual reasons (i) it is best understood (ii) it is omnipresent within any higher mathematics.
So, constructs from linear de facto appear in any science that does anything beyond simple pen-and-paper-computation. Most prominent examples where linear algebra is used 'immediatly' compromise computer graphics and modeling biological/chemical/social systems, not to forget linear optimization or numerical linear algebra. |
MATLAB Student Version
04/01/03
Students in engineering, math or science have a new technical computing resource designed for their needs. The MathWorks' MATLAB Student Version includes full-featured versions of MATLAB and Simulink, the software products used by engineers, scientists and mathematicians at leading universities, research labs, technology companies and government labs. MATLAB integrates computation, data analysis, visualization and programming in one environment. Simulink is one of the leading interactive environments for modeling, simulating and analyzing dynamic systems. In addition, there is no difference between the student and professional versions of the program, which, according to the company, is important because students are learning skills with the same tools they may use in a professional arena. The program also comes with MATLAB and Simulink books to help students get started. This product has a special student price of $99. The MathWorks, (508) 647-7000 |
Product Description Using methods such as Socratic dialogue, ample discussion, and integration of other subjects, it teaches the ways in which these dialectic students learn best. Example scenarios, exercises, points to remember, quotes, charts, and thorough lessons will help students grasp the concepts presented, and be able to apply them! Grades 8 & up. 324 pages, softcover.
Product Reviews
The Discovery of Deduction: An Introduction to Formal Logic
3
5
1
1
great content but wordy
I think this text is technically very useful as it covers the basics of formal logic in a comprehensive manner. My major concern is the amount of text (a small font is used) if this book is aimed at the 12 - 15 year old age group, especially if the group is not academically strong. A lot of students will be put of just because of the amount of text they are presented with. I think this textbook is an excellent resource for a teacher or someone wishing to teach themselves. I would not recommend it for use with children in the 12-15 year old age group unless they are great readers and motivated academically.
February 24, 2012 |
Precalculus: Concepts Through Functions A Right Triangle - 2nd edition
Summary: Pre-calculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, Second Edition embodies Sullivan/Sullivan's hallmarks accuracy, precision, depth, strong student support, and abundant exercises while exposing readers to functions in the first chapter. To ensure that students master basic skills and develop the conceptual understanding they need for the course, this text focuses on the fundamentals: preparing for class, practicing their homework, a...show morend reviewing the concepts. After using this book, students will have a solid understanding of algebra and functions so that they are prepared for subsequent courses, such as finite mathematics, business mathematics, and engineering calculus. KEY TOPICS: Functions and Their Graphs; Linear and Quadratic Functions; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Trigonometric Functions; Analytic Trigonometry; Applications of Trigonometric Functions; Polar Coordinates; Vectors; Analytic Geometry; Systems of Equations and Inequalities; Sequences; Induction; the Binomial Theorem; Counting and Probability; A Preview of Calculus: The Limit; Derivative, and Integral of a Function MARKET: For all readers interested in pre-calculus1645081 used book - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front or back
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cara cara membuat curriculum vitaeDedication
To Jessica Alexander and Uriel Avalos in gratitude for their invaluable work in preparing this text for
publication.
Ann Xavier Gantert
The author has been associated with mathematics education in New York State as a teacher and an
author throughout the many changes of the past fifty years. She has worked as a consultant to the
Mathematics Bureau of the Department of Education in the development and writing of Sequential
Mathematics and has been a coauthor of Amsco's Integrated Mathematics series, which accompanied that
course of study.
Reviewers:
Richard Auclair
Mathematics Teacher
La Salle School
Albany, NY
Domenic D'Orazio
Mathematics Teacher
Midwood High School
Brooklyn, NY
Steven J. Balasiano
Assistant Principal,
Supervision Mathematics
Canarsie High School
Brooklyn, NY
Debbie Calvino
Mathematics Supervisor,
Grades 7–12
Valley Central High School
Montgomery, NY
George Drakatos
Mathematics Teacher
Baldwin Senior High School
Baldwin, NY
Ronald Hattar
Mathematics Chairperson
Eastchester High School
Eastchester, NY
Raymond Scacalossi Jr.
Mathematics Coordinator
Manhasset High School
Manhasset, NY
Text Designer: Nesbitt Graphics, Inc.
Compositor: ICC Macmillan
Cover Design by Meghan J. Shupe
Cover Art by Radius Images (RM)
Please visit our Web site at:
When ordering this book, please specify:...
PREFACE
Algebra 2 and Trigonometry is a new text for a course in intermediate algebra and
trigonometry that continues the approach that has made Amsco a leader in presenting mathematics in a modern, integrated manner. Over the last decade, this
approach has undergone numerous changes and refinements to keep pace with
ever-changing technology.
This textbook is the final book in the three-part series in which Amsco parallels
the integrated approach to the teaching of high school mathematics promoted by
the National Council of Teachers of Mathematics in its Principles and Standards for
School Mathematics and mandated by the New York State Board of Regents in the
Mathematics Core Curriculum. The text presents a range of materials and explanations that are guidelines for achieving a high level of excellence in their understanding of mathematics.
In this book:
✔
The real numbers are reviewed and the understanding of operations with irrational numbers, particularly radicals, is expanded.
✔
The graphing calculator continues to be used as a routine tool in the study of
mathematics. Its use enables the student to solve problems that require computation
that more realistically reflects the real world. The use of the calculator replaces the
need for tables in the study of trigonometry and logarithms.
✔
Coordinate geometry continues to be an integral part of the visualization of
algebraic and trigonometric relationships.
✔
Functions represent a unifying concept throughout. The algebraic functions
introduced in Integrated Algebra 1 are reviewed, and exponential, logarithmic, and
trigonometric functions are presented.
✔
Algebraic skills from Integrated Algebra 1 are maintained, strengthened, and
expanded as both a holistic approach to mathematics and as a bridge to advanced
studies.
✔
Statistics includes the use of the graphing calculator to reexamine range, quartiles, and interquartile range, to introduce measures of dispersion such as variance
and standard deviation, and to determine the curve that best represents a set of
bivariate data. |
presenting problem solving in purposeful and meaningful contexts, MATHEMATICAL EXCURSIONS, 2/e, provides users in the Liberal Arts course with a glimpse into the nature of mathematics and how it is used to understand our world. Highlights of the book include the proven Aufmann Interactive Method and multi-part Excursion exercises that emphasize collaborative learning. An extensive technology program provides users with a comprehensive set of support tools. This Enhanced Edition includes instant access to WebAssignŽ, the most widely-used and reliable homework system. WebAssignŽ presents over 500 problems, as well as links to relevant book sections, that help users grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this book. This guide contains instructions to help users learn the basics of WebAssign quickly. |
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$205Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management.
The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization.
Concepts of Combinatorial Optimization, is divided into three parts:
On the complexity of combinatorial optimization problems, that presents basics about worst-case and randomized complexity;
Classical solution methods, that presents the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming;
Elements from mathematical programming, that presents fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field. |
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Overview
Written by an experienced author team with expertise in the use of technology and NCTN guidelines, this book provides an emphasis on multiple representations of concepts and an abundance of worked examples. Rich exercises include graphical and data-based problems, and interesting real-life applications in biology, business, chemistry, economics, engineering, finance, physics, the social sciences and statistics.
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A college level calculus text focusing on the appropriate use of technology in combination with standard analytic techniques. The full array of calculator functions are introduced from the beginning, with graphical, numerical, algebraic/analytic, and communication techniques emphasized throughout. Applications are explored in various fields and some 3800 exercises are offered. Requires exposure to algebra, geometry, and trigonometry, although the first chapter reviews this |
Spring 2014 MTH55 Elementary Algebra (5 units)
Section 0831 Begins: January 21, 2014 Ends: May 23, 2014
Course Description
This course will cover the topics of operations with real numbers, solution techniques of single variable linear equations and inequalities, graphing linear equations in two variables, solving systems of linear equations, simplifying and combining polynomials, calculating roots and radicals, and solving quadratic equations. Students will: learn to solve applied problems using linear equations, use slope to graph two-variable linear equations, solve applied problems using two variables, and solve quadratic equations by factoring and using the Quadratic Formula.
Instructor: Michelle Snider
Email: msnider@mendocino.edu
Textbook Information: An electronic textbook is available on the MyMathLab website. Access to this website requires an access code which costs about $90. You may purchase a textbook if desired.
Estimated Time per Week: Students can expect to spend approximately 3 hours per week, per unit reading, writing, and taking quizzes and participating in online class discussions.
Special Requirements: Log into Etudes the first day of class to find class requirements and information regarding MyMathLab, the website where the class will be held.
Assignments & Tests: All assignments and tests will be found on the MyMathLab website
Additional Comments: The entire course will be conducted online at the Pearson's MyMathLab website. Students are required to have Internet access, an active email account, and purchase an access code for the MyMathLab website.
New to ETUDES:
Here is an
Online Orientation (Flash presentation opens in a new window)
that will show you the basics of how to use ETUDES. Here is a
flash tutorial (Flash presentation opens in a new window)
that demonstrates the log in protocol. Be sure to check System
Requirements before getting started with ETUDES. You need to do this
on each computer you use while taking a class through ETUDES.
ETUDES Course: You will log into the
Etudes classroom with the log-in information provided below.
First 2 letters of first name +
First 2 letters of last name +
Last 5 digits of Student COLLEAGUE ID
(Type using all lower case letters)
Example: Jose A. Garcia
Student ID: 1021945
Username = joga21945 |
Review of Foerster's Algebra 1 with a Home Study Companion − Algebra 1 by David Chandler
As of this writing (2008), some of the most popular and respected algebra 1 programs among homeschoolers are:
Saxon math,
Harold Jacob's Algebra,
Teaching Textbooks Algebra 1.
I certainly recognize each program has its followers and its good points − yet they do have their drawbacks as well.
For example, Teaching Textbooks is known for its thoroughness and being a very very comprehensive program since all solutions are provided in full on a DVD. However, people also generally consider it as not challenging.
Saxon math employs an incremental approach that introduces a new concept every day (every lesson). Many kids grow bored on it, or they can't get the concepts when new stuff comes along so soon.
Harold Jacob writes in a different, lighthearted style, with some cartoons. This book is praised a lot by homeschoolers as very interesting. People say it's good for kids who have intuition with math. But did you know what Jacobs himself recommends as a followup to his algebra program? Paul Foerster's Algebra II, Trig, and Calculus.
So I want to present another alternative: start using Paul Foerster's texts at Algebra 1 level, alongside with the Home Study Companion video lessons made by David Chandler.
I feel this option, in general, is EXCELLENT, because of the quality of the text and of the video lessons. It serves BEST those students who don't mind − or who even want to have something a little challenging − and who want to gain a very strong background in mathematics.
For the rest of this review, I will now present some details from both the book and the video lessons.
Foerster's Algebra texts are exceptional in several ways. Many people keep give them high acclaim. Look at for example Foerster's algebra 1 review written by the folks at MathematicallyCorrect, or the comparison chart at MathematicallyCorrect.com that compares several algebra 1 texts from well-known publishers. FACE recommends Foerster's texts in its Noah plan.
Personally, I have to praise the book as well. After seeing a competitor product (traditional algebra 1 text) that starts every lesson with a confusing real-life example, Foerster's Algebra 1 looked fantastically clear, teaching the concepts and techniques in small steps, allowing for plenty of practice. The book is very comprehensive, very logical, and often goes deeper into the topics than some other books.
And it's not just that. The way concepts are presented, developed, and practiced, he has managed to weave algebra 1 topics into a connected body of knowledge. Everything new is based on previously learned concepts, and connections between the concepts are emphasized. The text just reads great.
For example, in the whole book, Foerster has a UNIFYING THEME: that of an expression. In his own words:
For increasingly complex expressions, students do these three things:
Write an expression representing a variable quantity in some real-world situation,
Find the value of the expression when x is known,
Find x when the value of the expression is known.
In each lesson, after the main part of explaining the concept, the text presents several examples. Foerster intends the student to cover the answers to these examples, then try to solve the problems, and then uncover the solutions. Each lesson has plenty of practice problems (BTW it's not intended that every student work every problem). The end of each chapter has a section of applications via numerous word problems.
His word problems are excellent. They are multi-step problems, and are not just the typical knock-off problem categories (D=RT problems, work problems, mixture problems, etc.) with the numbers changed. The
mathematics needed to attack the problems vary from problem to
problem, and the student needs to combine techniques he's learned. He is teaching the student how to think
analytically.
Yet I have to mention this also: the examples in the lessons full of word problems are written so that the many questions in the examples actually guide you step-by-step in how to think and build your equation. You will not see that in every algebra text.
Foerster doesn't forget humor, either. He has livened up the word problems with clever character names
and silly puns. In general, his writing style is warm and approachable by students.
David Chandler, the author of the Homeschool Companion to Foerster's algebra 1, points out a few other good points of this text and Foerster's other books:
They have a real sense of "authorship." Most math textbooks seem
to be written by a committee controlled by the publishers. Paul
Foerster is an ex-engineer turned teacher who has an intimate sense of
the usefulness and power of mathematics as a tool for solving
real-world problems. His writing comes across like a conversation
with a real author. He is also a good writer!
He has a good balance between rigor and intuition. It is more
important at the introductory level to have an intuitive grasp of an
issue (negative numbers, distributive law, etc.) and how to use them
in a problem-solving context than to see rigorous proofs of
mathematical properties. The rigor is not brushed aside: it is simply
handled in a balanced way.
Some people may object to the untraditional sequence of topics, where quadratic equations are presented about in the middle of the whole text, instead of near the end.
Foerster himself mentions this in the foreword and says:
"This ... is made possible by technology, specifically, the use of calculators to evaluate radicals. As a result, students are able to work more realistic word problems in which answers are decimals."
Quadratic equations are presented in the 6th chapter of a total of 14 chapters. In chapter 6, students learn to complete the square, which is then used to prove the quadratic formula, and applications follow. Solving quadratic equations by factoring is much later, in chapter 10. This approach allows for the inclusion of quadratic equations in the problem solving sections of the second half of the book − and remember, the word problems in the various chapters are excellent!
Home Study Companion − Algebra 1 by David Chandler
Who is David Chandler? He is a mathematics teacher with BS in physics, MA in
Education, and MS in Mathematics Harvey Mudd College, Claremont Graduate University, and
California Polytechnic University). He's been teaching for 30 years in public, private, international, and charter schools at all levels from 2nd graders on up, through the full high school and junior college math and physics curriculum.
David Chandler has put together A Home Study Companion - Algebra 1, which consists of whiteboard video lessons to accompany every lesson in Foerster's Algebra 1 book. You can fast forward or rewind these lessons at will, to find the exact spot you're looking for.
In these lessons, he usually presents the concept at hand, just like a normal teacher would do in class. He then goes through and explains in detail several examples from the corresponding lesson in Foerster's book.
In essence, you get to listen to an excellent, experienced math teacher explain the complete Algebra 1 class: the concepts and solved examples.
Below are some screenshots. Click them to enlarge.
David Chandler is not just doing example problems from the book. He is actually TEACHING you a complete lesson on the concept at hand. Based on his teaching experience, he is very conscious of
the areas where students have conceptual difficulties and points out ways they can build intuition for what is going on behind the equations.
For example, Chandler explains and justifies the distributive property in more detail than the book itself. He constantly "throws in" or explains little "tricks of the trade", such as which of the x-terms you should get rid of in the equation with x-terms on both sides (for example 5x + 9 = 7x − 6), or where did the plus-minus ( ±) sign suddenly come from. Or, he takes little sidesteps to point out connections: "In fact, you've seen this before:.... ".
He mentions the "customary" ways of writing mathematics. For example, while solving a certain problem from the book, he changes the variable from x to t because it is the customary variable for time. After Chapter 6, he's even added a lesson of his own (outside of Foerster's) called "Getting Fluent", which explores ways that you can write down your equation solving more efficiently − the way mathematicians are accustomed to doing it.
All in all, Chandler "expands" the presentation of the topics and the example solutions as compared to the concise explanations in Foerster's text, adding in more detailed explanations. You'll also see exactly what buttons to push on the calculator in those problems that require such. Chandler talks and writes fairly slowly (view the sample video below) so your student should be able to keep up easily. Algebra isn't a speed contest anyway!
You could easily use these video lessons to accompany some other algebra text, as well. The example problems he uses are fully written out on the video.
Solutions manual (ISBN 9780201861006) is more difficult to find. To buy this directly from Pearson/Prentice Hall, you need to sign up with their "Oasis" program and provide proof that you are homeschooling. Once that is done, you will have an account and can order teacher as well as student resources. |
This applet demonstrates an exponential growth model which plots population P_i for i=1 to i=600 given user input for the initial population P_0 and growth rate G. The difference equation used is P_(i... More: lessons, discussions, ratings, reviews,...
This applet demonstrates a logistic growth model which plots population P_i for i = 1 to i = 600 given user input for the initial population P_0, growth rate G and carrying capacity CC. The difference... More: lessons, discussions, ratings, reviews,...
The FTC applet assists students in understanding the concept of the area under a curve. As x is changed, the curve f(x) is drawn and the area between the curve and the x axis is shaded blue. To the |
Success in your calculus course starts here! JamesStewartThis fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.
The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print media and technology products for successful teaching and learning. |
MATH 090. Fundamentals ofMATH 099. Intermediate1000-2000 Level Courses
MATH 1040- College Algebra.An in-depth study of algebraic equations and inequalities. Comprehension of the underlying algebraic structure will be stressed as well as appropriate algebraic skills. The study will include polynomials, rational, exponential, and logarithmic functions as well as systems of equations/inequalities. Prerequisite: Online Math Placement Testfor College Algebra of 50% or higher.
MATH 1050 Elementary Functions for Calculus (Precalculus). An intensive study of the elementary funtions required for calculus. These functions will include polynomial, rational, exponential, logarithmic, and trigonometric functions. Emphasis is on their algebraic structure and graphs. Analysis of conic sections and analytic geometry will be included. Prerequisite: MATH 1040- College Algebra or Onine Math Placement Test for Precalculus of 70% or higher.
MATH 1120 Calculus for Business & Economics.Calculus for the business and economics students. Prer., MATH 1040 or Math Placement Tests for College Algrebra at 87% or higher AND 50% or higher on the Calculus for Business and Economics Test
MATH 1310. Calculus I with Precalculus, Part A. See MATH 1350 for calculus topics covered. Algebraic and elementary function topics are covered throughout, as needed. MATH 1301 and MATH 1320 together are equivalent to MATH 1305. The sequence MATH 1310-1320 is designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for MATH 1305. Prer., 4 years high school math (algebra, geometry, trigonometry or their equivalents). Credit not granted for this course and MATH 1350.
MATH 1320. Calculus I with Precalculus, Part B.Continuation of MATH 1310. See MATH 1350 for calculus topics covered. Algebraic and trigonometric topics are studied throughout, as needed. Prer., MATH 1310. Credit not granted for this course and MATH 1350.
MATH 1330. Calculus for Life Sciences. A systematic introduction to calculus concepts useful in the life sciences, such as rates of change, limits, differentiation and integration, with emphasis on applications in the life sciences and the areas connected to modeling biological processes, such as differential equations and dynamical systems. Students may not take MATH 1330 and MATH 1350 and receive credit for both. Req., MATH 1050 or score 20 or more on the Algebra Placement Exam and score 10 or more on the Calculus Readiness Exam.
MATH 1350. Calculus I.Selected topics in analytical geometry and calculus. Rates of change of functions, limits, derivatives of algebraic and transcendental functions, applications of derivatives, and integration. Prer., MATH 1050 or Online Math Placement Testsfor College Algebra at 87% or higher AND 50% or higher on the Calculus Test.
MATH 2150 Discrete Mathematics.Introduction to most of the important topics of discrete mathematics, including set theory, logic, number theory, recursion, combinatorics, and graph theory. Much emphasis will be focused on the ideas and methods of mathematical proofs, including induction and contradiction. Prer., MATH 1350.
MATH 2650. Intro to Computational Math. one (1) credit hour. An introduction to the use of computers in mathematics using the MATLAB computer algebra system. Representation of equations and functions using arrays. Visualization of data and functions. MATLAB programs including: general program organization, subprograms, files, and built-in mathematical functions. Prer., MATH 2350
3000 Level Courses
MATH 3010. Mathematics for Elementary Teachers I.Covers the whole number, integer, and rational number systems that are of prime importance to the elementary teacher. For students planning on elementary teacher certification.
MATH 3020. Mathematics for Elementary Teachers II. Intuitive and logical development of the fundamental ideas of geometry such as parallelism, congruence, and measurement. Includes study of plane analytical geometry. For students planning on elementary teacher certification.
MATH 3110. Theory of Numbers.A careful study, with emphasis on proofs, of the following topics associated with the set of integer: divisibility, congruences, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes. Prer., MATH 1360 and MATH 2150.
MATH 3410. Estimation, Convergence and Approximation. Sequences, numerical series, and power series. Integrals and the analysis of functions defined by integrals. This course provides a thorough introduction to proofs in analysis, and is strongly recommended for students planning to take MATH 4310. Prer., MATH 2350.
MATH 3810. Introduction to Probability and Statistics.The axioms of probability and conditional probability will be studied as well as the development, applications and simulation of discrete and continuous probability distributions. Also, expectation, variance, correlation, sum and joint distributions of random variables will be studied. The Law of Large Numbers and the Central Limit Theorem will be developed. Applications to statistics will include regression, confidence intervals, and hypothesis testing. Prer., MATH 2350.
4000/5000 Level Courses
MATH 4050/5050. Topics in Mathematics Secondary Classroom.The topics covered will vary from one offering to the next. Topics will be chosen to meet the needs of secondary mathematics teachers for additional training to teach to the Colorado Model Content Standards. Prer., one semester of calculus, or instructor approval.
MATH 4100/5100. Technology in Mathematics Teaching and Curriculum. Methodology for using technology as a teaching/learning tool for high school and college math courses. Use of graphing calculators, computer algebra systems, computer geometry systems and the internet will be emphasized. Students are required to develop and present a portfolio of in-depth projects. Prer., MATH 1360.
MATH 4140. Modern Algebra I.A careful study of the elementary theory of groups, rings, and fields. Mappings such as homomorphisms and isomorphisms are considered. The student will be expected to prove theorems. Prer., MATH 2150 and MATH 3130. One of MATH 3110, MATH 3500, or MATH 3510 (preferably MATH 3110) is strongly recommended.
MATH 4250/5250. Introduction to Chaotic Dynamical Systems.Introduction to dynamical systems or processes in motion, that are defined in discrete time by iteration of simple functions, or in continuous time by differential equations. Emphasis on understanding chaotic behavior that occurs when a simple non-linear function is iterated. Topics include orbits, graphical analysis, fixed and periodic points, bifurcations, symbolic dynamics, chaos, fractals, and Julia sets. Prer., MATH 2350.
MATH 4670/5670. Scientific Computation.Description and analysis of algorithms used for numerical solutions of partial differential equations of importance in science and engineering. The main emphasis is on theoretical analysis, but some practical computations are included. Prer., MATH 2350, MATH 3130, MATH 3400, and CS 1150 or equivalent.
MATH 4830/5830. Linear Statistical Models. Methods and results of linear algebra are developed to formulate and study a fundamental and widely applied area of statistics. Topics include generalized inverses, multivariate normal distribution and the general linear model. Applications focus on model building, design models, and computing methods. The "Statistical Analysis System" (software) is introduced as a tool for doing computations. Prer., MATH 3810 or ECE 3610, or MATH 3100 and MATH 3130.
MATH 5270. Algebraic Coding Theory.The basic ideas of the theory of error-correcting codes are presented. We will study some important examples and give applications. These codes are important for the digital transmission of data. Prer., MATH 4140.
MATH 5910/6910. Theory of Probability I.Theoretical approach to probability. Measure theory is given form within a large body of probabilistic examples, ideas and applications. Weak and strong laws of large numbers, central limit theory, recurrence, Martingales. Prer., MATH 4310.
MATH 5920/6920. Theory of Probability II.Probability theory for sequences of dependent random variables, with the major focus on martingale theory and its applications. Prer., MATH 5910/6910.
MATH 6310. Mathematics and Economics for K-12 Teachers. Designed to provide K-12 teachers with various methods and concepts from mathematics and economics which can be incorporated into K-12 mathematics or economics curricula. Not an option for MATH majors or graduate students. Meets with ECON 6310.
7000 - 9000 Level Courses
MATH 7000. Master's Thesis.
MATH 8000. PhD Dissertation. Enrollment is limited to those students who are in the PhD program in Applied Science, Mathematics, and have primary thesis advisor in the Department of Mathematics. Prer., Consent of instructor. |
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Master introductory surveying with Schaum's--the high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams!
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Schaum's Outlines contain hundreds of solutions to problems covered in any college course. This guide, which can be used with any text book or can stand alone, contains a list of key definitions, a summary of major concepts, and step by step |
and Middle School Mathematics is designed for pre-service or in-service teachers. It combines up-to-date technology and research with a vibrant writing style to help teachers grasp curriculum, teaching, and assessment issues as they relate to secondary and middle school mathematics. The third edition offers a balance of theory and practice, including a wealth of examples and descriptions of student work, classroom situations, and technology usage to assist any teacher in visualizing high-quality mathematics instruction in the middle and secondary classroom. |
This text gives a comprehensive survey of modern techniques in the theoretical study of partialdifferentialequations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: 1) representation formulas for solutions, 2) theory for linear partialdifferentialequations, and 3) theory for nonlinear partialdifferentialequations.... |
A bridge to upper-level math, BJU Press' Fundamentals of Math Grade 7 textbook will ensure students have a solid foundation in the skills they'll need for 8th grade and beyond! Whole numbers, decimals, number theory, fractions, rational numbers, percents, measurement, geometry, area/volume, probability/statistics, integers, algebra, relations/functions, and logic/set theory are all taught in detail with review to keep concepts fresh. Integrating biblical principles with "Math in Use" segments, students are taught to see God as involved in all subjects, while problem solving sections allow for thinking skill development as students use problem solving methods to reach a solution. Chapters include clear explanations of new concepts, plenty of practice, "skill check" reviews, example problems, and a cumulative review of the new concept. 676 pages, softcover.
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Fundamentals of Math 7 StudentText (2nd Edition)
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Math Fundamentals of Math 7 StudentText (2nd Edition).
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We used the DVD's for BJU. I have to say my children did not find them easy to watch. They felt the instructor was quite boring. My husband felt that a lot of the lessons should have been simplified for better understanding. He often stopped the DVD to teach them an easier way to work the problems. |
Project Laboratory in Mathematics
it like to do mathematical research? The "Project Laboratory in Mathematics" course from MIT's OpenCourseWare provides some fine insights into this endeavor. The course was originally developed by Professor Haynes Miller and features information about how to help students "explore puzzling and complex mathematical situations." The site includes selected video lectures from the course, instructor insights, and a selection of projects and examples, such as "The Dynamics of Successive Differences Over Z and R." Also, the site includes information on how to customize this course for a variety of settings, along with examples of classroom activities and helpful resources.Thu, 20 Feb 2014 14:22:52 Moving |
Mathematics
Contents:
RAND has explored, among other math-related topics, mathematics curricula in primary education and the role of mathematics in innovation, e.g., in the evaluation of new medical technologies or the development of methodologies such as game theory.
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A first-year algebra curriculum that blends tutoring software with conventional textbook learning had a positive effect for high school algebra students. Researchers found significant improvements—a change equivalent to moving from the 50th percentile to the 58th on an algebra posttest.
Students who had taken occupationally focused career and technical education (CTE) courses in addition to their regular academic courses had similar learning gains to those who had only taken academic courses: an academic curriculum that includes CTE courses neither bolstered nor curtailed the acquisition of math skills.
This paper describes a new approach and associated search schemes for optimization under uncertainty. Analysts can apply this method to a problem with a significantly larger number of decision variables, uncertain parameters, and uncertain scenarios.
Comparative effectiveness research will be hard to use appropriately because context and emotion often dominate a patient's rational decisionmaking and because therapies are provided in different health care environments, making small differences between therapies basically meaningless.
Electronic searches typically yield far more citations than are relevant, and reviewers spend a substantial amount of time screening titles and abstracts to identify potential studies eligible for inclusion in a review.
On May 14, 2009, Titus Galama discussed the reality of U.S. competitiveness in science and technology and whether gains by China, India, and other nations are affecting America's chances of remaining a scientific leaderThe mean value of travel time savings obtained from a random parameters logit model estimated using the respondents who received the D-efficient design survey was closer to what is typically found in the literature.
This randomized, controlled field trial estimated the causal impact of a technology-based geometry curriculum on students' geometry achievement, as well as their attitudes toward mathematics and technologyEngland reformed its elementary math curriculum in 1999 to improve educational outcomes. Evaluations of the reforms were generally positive, but the evidence of success and value for money was more difficult to confirm.
The U.S. Department of Education has awarded the RAND Corporation a $6 million grant to conduct a five-year study of the effectiveness of a technology-based mathematics curriculum created by Carnegie Learning, Inc., of Pittsburgh.
Using longitudinal data from a cohort of middle school students from a large school district, researchers estimate separate "value-added" teacher effects for two subscales of a mathematics assessment under a variety of statistical models varying in form and degree of control for student background characteristics.
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Researcher Spotlight
Research Programmer
Tim Colvin is a senior research programmer at RAND with an interest in applied mathematics, numerical analysis, probability, mathematical modeling, quantitative analysis, databases, logistics, surveys and survey programming. He has authored and co-authored several books, chapters, and journal… |
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This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers. While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating systems; details refer to IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C. Other implementations of the graphics routines are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST |
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Prentice Hall Mathematics Course 1:
A combination of rational numbers, patterns, geometry and integers in preparation for one- and two-step equations and inequalities.
Guided Problem Solving strategies throughout the text provide students with the tools they need to be effective and independent learners. An emphasis on fractions solidifies student understanding of rational number operations preparing them to apply these skills to algebraic equations. Activity Labs throughout the text provide hands-on, minds-on experiences reaching all types of |
Description: The aim is to highlight and explain some areas commonly found difficult, such as calculus, and to ease the transition from school level to university level mathematics, where sometimes the subject matter is similar, but the emphasis is usually different. |
Description
With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.
The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in aAbout the author
Mary Jane Sterling is professor ofmathematics at Bradley University.She is the author of many booksincluding Algebra I For Dummies, 2nd Edition and Algebra Workbook |
Basic Math & Pre-Algebra for Dummies
Overview
Tips for simplifying tricky operations
Get the skills you need to solve problems and equations and be ready for algebra class
Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.
* Understand fractions, decimals, and percents
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Unravel algebra word problems
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Grasp prime numbers, factors, and multiples
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Work with graphs and measures
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Solve single and multiple variable equations260425
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Online Support for Math Classes
The following courses are taught through online resources:
Course Code
Course Title
Math 060
Prealgebra
Math 070
Elementary Algebra
Math 080
Geometry
Math 110
Intermediate Algebra
Math 111
Business and Consumer Mathematics
Math 114
Applied Mathematics I
Math 116
Applied Mathematics II
Math 122
Trigonometry
Math 125
Quantitative Literacy
Math 128
Foundations of Mathematics for Elementary Teachers
Math 129
Foundations of Mathematics for Elementary Teachers II
Math 140
College Algebra
Math 143
Finite Math
Math 149
Precalculus
Math 250
Calculus
Math 251
Calculus II
Math 252
Calculus III
To access these classes:
1. Navigate to my.oakton.edu (available as the myOakton link on the top of this Web page). Enter your username and password. |
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student's skills in logic and reasoning.
Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.
Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.
Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.
Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.
Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.
Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson's Rule to approximate an area beneath a curve.
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.
Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios.
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There are twelve study units in this module.
In the first two, you'll revise and extend the basic mathematical knowledge and skills in basic algebra and graphs that should mainly be familiar to you. This revision material should help you identify and fill any gaps in your previous knowledge, and develop your basic mathematical skills to the level that you'll need in the rest of the module. Much of the material in these two units will be available online, so you can make a start on your revision even before the module begins, if you wish. The first two units also teach you about communicating mathematics, and introduce you to the mathematical software that you'll use in the module.
In the remaining study units you'll cover these topics:
Functions: these provide a means of representing situations where one quantity depends on another. For example, the distance travelled by a car depends on the time that it has been travelling. You need to know about functions before you can study calculus.
Trigonometry: you'll revise the relationships between the angles and side lengths of triangles, and the definitions of the trigonometric functions sine, cosine and tangent for angles of any size. You'll learn many useful properties of these functions, which are used to model a wide range of cyclical phenomena, such as rotating objects, and waves.
Vectors: these are quantities that have both a size and a direction. You'll learn about the mathematics of vectors, and how to use them to model a variety of physical quantities, such as speed in a particular direction.
Calculus: this is one of the most important and widely applicable topics in mathematics. It is concerned with quantities that change continuously, such as the distance travelled by, and the speed of, a moving object. You'll be introduced to differentiation and integration, and learn how to use calculus to model a range of different situations and to solve problems from areas such as physics and economics.
Matrices: these are arrays of numbers, which can be manipulated mathematically in various ways. They're used extensively in both pure mathematics and mathematical applications.
Sequences: you'll learn how to work with some commonly occurring types of number sequences, such as those in which each number is obtained by multiplying the previous number by a constant.
Complex numbers: these form an intriguing set of numbers that includes all the usual numbers, and also many `imaginary' numbers, such as the square root of minus one. They have many uses in applied mathematics, as well as being the basis of some fascinating pure mathematics.
You'll work mainly from the module books, which are available in various electronic formats as well as in print. You can view many of the worked examples in the books in an alternative video format, in which tutors work through and discuss the examples. You'll also use specially-designed software applications to help you understand the concepts taught, and you'll learn to use a mathematics computer package to solve problems. There are many online interactive practice questions to help you consolidate your learning.
The module includes a large amount of online study material, and requires you to use mathematical software frequently, so you'll need regular access to a suitable personal computer.
Samples of the study material, including example assessment questions, are available at our MathsChoices website.
You will learn
Successful study of this module should begin to develop your skills in:
expressing problems in mathematical language
using mathematical techniques to find solutions to problems
communicating mathematical ideas clearly and succinctly.
Entry
This is a key introductory Level 1 module. Level 1 modules provide core subject knowledge and study skills needed for both higher education and distance learning, to help you progress to modules at Level 2.
Although many of these topics are revised, consolidated and extended in the module, we recommend that you have some previous knowledge of:
coordinates of points in the plane, and the equations of straight lines and parabolas.
geometry of plane figures, such as the sizes of angles, alternate and corresponding angles, the areas of shapes, similar and congruent shapes, and the properties of triangles, rectangles and circles
geometry of solid figures, such as volumes and other properties of cuboids and cylinders
simple inequalities
trigonometric ratios – sine, cosine and tangent
logarithms and the rules for manipulating them.
A mathematical A-level, or a high grade in GCSE mathematics (or the equivalent), would normally provide this. If you are not familiar with the majority of the topics listed above, we recommend that you study our Level 1 module Discovering mathematics (MU123) before this module.
Essential mathematics 1 is designed to be taken either as your first university-level mathematics module or following on from Discovering mathematics (MU123).
Essential mathematics 2 (MST125) – available from October 2014 – is designed to follow on from Essential mathematics 1. However, if you have plenty of study time and a high level of confidence and fluency with algebraic manipulation you could study both modules in one year.
If you have any doubt about the level of study, or about choosing the most suitable mathematics module with which to start, please contact our Student Registration & Enquiry Service. or look at our MathsChoices website. The MathsChoices website also contains a self-assessment quiz to help you decide if Essential mathematics 1 is the right module for you.
Preparatory work
The first two units of the module help you to revise, consolidate and extend the basic mathematical knowledge and skills that are required in the rest of the module. Much of the material in these first two units will be available online before the module begins, and it would be a good idea to start working through it as soon as you can, to make sure that you're as well prepared as possible for the main work in the module. Working through this material will also help you confirm whether this is a suitable module for you: if you find that most of it is unfamiliar to you, we recommend that you consider taking Discovering mathematics (MU123) first.
If you wish to do some extra preparation before starting on the study material, then we suggest that you work through a GCSE Mathematics Higher Level, or equivalent, text book, which may be available online or in a local library. You could also use a book or website to familiarise yourself with the first core module (C1 – the first pure maths module) of AS-Level Mathematics, or equivalent. This will contain some topics which you are not expected to have studied before you start this module but, if you can do some work on those as well, it may help you to get a head start with your studies. The MathsChoices website contains further suggestions for help on topics you may need to practice, for example algebra and trigonometry.
Regulations
As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are
available on our Essential documents website.
If you have a disability
By its nature mathematics is a visual subject, and this module will contain considerable amounts of mathematical notation and graphs, and other forms of diagram. If you have a visual impairment or limited manual dexterity you may experience difficulties with some of the activities and assessment questions which involve the interactive use of ICT or which have a high graphical content.
It is important to note that use of the online activities and resources, which include on-screen dynamically-changing graphs and mathematical notation, will be an integral part of your study. You will need to spend considerable amounts of time using a personal computer, and some of your assignments will be interactive and online.
Written transcripts of any audio components and Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader (and mathematical notation may be particularly difficult to read in this way). and website, including access to computer applications and to optional online tutorials.
You will need
We recommend a basic scientific Casio `Natural' calculator. The module website includes a calculator guide with references to this series of calculators. Note that programmable calculators are not permitted in the final examination, and many graphing calculators are also programmable since 2007 you should have no problems completing the online activities.
If you've got a netbook, tablet or other mobile computing device you may have difficulties with some software, check our Technical requirements section.
If you use an Apple Mac you will need OS X 10.6 or later is particularly concerned to help you with your study methods. We may also be able to offer group tutorials (online or face-to-face), that you are encouraged, but not obliged, to attend. The locations of face-to-face tutorials will depend on the distribution of students taking the module.
Assessment
The assessment details for this moduleFuture availability
The details given here are for the module that starts in October 2014 and February 2015. We expect it to be available twice a year.
Students also studied |
Welcome to the new BBA Math Wiki!
Please be patient with us as we gather and build our materials
The mission of Burr & Burton Academy's Math Department is to provide all students with a mathematical experience that strives to extend their motivation and abilities for an ever-changing world. This goal is achieved as students engage in rich curricula guided by dynamic teachers in distinct courses that offer appropriate rigor and opportunities.
All Burr and Burton Academy Math students will:
have strong number sense
have an appropriate mathematical vocabulary
have a functional connection between mathematics and the real world
have a framework for disciplined, logical thinking that allows them to be creative and agile problem solvers
have the ability to effectively communicate their mathematical thinking
Calculation Nation
Looking for an interesting alternative to some of your less productive internet tendencies, give these games a try.
Technology
The Burr & Burton Math Department believes that technology should be used responsibly in the teaching and learning of mathematics. Technology cannot become a substitute for computational fluency or basic understanding; but the ability to model, extend, and automate is immensely valuable in creating new and exciting opportunities.
Graphing calculators, dynamic geometry software, and other tools will be used in all Burr & Burton math classes. Exactly when and how often will vary by teacher and course.
For all students that anticipate years of studies, culminating with Calculus (which we hope is ALL of you), we recommend the purchase of the.
I
Article...
Information from Gay Dillin, Media Relations Manager at NCTM. NCTM Releases new landmark publication: Focus in High School Mathematics: Reasoning and Sense Making
RESTON, Va., October 6, 2009-The National Council of Teachers of Mathematics (NCTM) today released Focus in High School Mathematics: Reasoning and Sense Making, which suggests practical changes to the high school mathematics curriculum to refocus learning on reasoning and sense making. This shift is not a minor refinement but constitutes a substantial rethinking of the high school math curriculum.
"Reasoning and sense making are at the heart of mathematics from early childhood through adulthood," said NCTM President Henry (Hank) Kepner. "A high school mathematics curriculum based on reasoning and sense making will prepare students for higher learning, career success, and productive citizenship."
NCTM's new publication suggests that the more mathematics instruction builds on what students have previously learned, the more students will be able to learn and retain as they progress from prekindergarten through college. Additionally, focusing on reasoning and sense making has the potential to give coherence to the curriculum and streamline it to improve students' learning of important mathematics. A focus on mathematical reasoning and sense making also helps students to use mathematics more effectively in making wise decisions in the workplace and as citizens.
Reasoning is the process of drawing conclusions based on evidence or stated assumptions-extending the knowledge that one has at a given moment. Sense making is developing understanding of a situation, concept, or context by connecting it with existing knowledge or experience.
The first volume in a series of companion books will also be published this month. Focus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability will be followed by books that offer examples of ways to make reasoning and sense making central in algebra and geometry. Focus in High School Mathematics: Reasoning and Sense Making was developed with the involvement of high school teachers, mathematics educators, an administrator, mathematicians, and a statistician.
Learn more about Focus in High School Mathematics: Reasoning and Sense Making |
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Course Goals
Introduce students to integral calculus (including elementary first order differential equations); see topics 1, 2 and 3 below in Topics Covered below for specific topics.
Introduce students to the application of the integral calculus and differential equations in science and engineering; see topics 2 and 3 below in Topics Covered
Introduction students to series of constants and functions, and the notions of approximation and convergence
Develop student mathematical modeling and problem solving skills.
Develop student ability to use a computer algebra system (CAS) to aid
in the analysis of quantitative problems. This includes (but is certainly
not limited to) mastery of the commands listed in Performance Standards
below.
Develop student ability to communicate mathematically.
Introduce applications of mathematics, especially to science and engineering.
Textbook and other required materials
Textbook: Thomas' Calculus - Early Transcendentals
Twelfth Edition - Weir, Hass Supplement: Just in Time - bundled with text. DE Problem supplement: 2004-05 version from Angel Computer Usage: Maple14 must be available on your laptop
Course Topics
Note: The Fall quarter class is predomiantly Advanced Placement Freshman.
However, some time will be spent reviewing some topics and getting up to speed
in Maple. Student taking the course later in the will have already been instructed
in Maple in a prior course.
Course Requirements and Policies
Computer Policy
Students will be expected to demonstrate a minimal level of competency with a relevant computer algebra system. The computer algebra system will be an integral part of the course and will be used regularly in class work, in homework assignments and during quizzes/exams. Students will also be expected to demonstrate the ability to perform certain elementary computations by hand. (See Performance Standards below.)
Performance Standards
With regard to be "by hands" computational skills, each student should
Final Exam Policy
The final exam will consist of two parts. The first part will be "by hands" (paper, pencil). No computing devices (calculators/computers) will be allowed during the first part of the final exam. This part of the exam will cover both computational fundamentals as well as some conceptual interpretation, though the level of difficulty and depth of conceptual interpretation must take into account that this part of the exam will be shorter than the second part of the exam. The laptop, starting with a blank Maple work sheet, and a calculator, may be used during the second part of the exam. No "cheat sheets", prepared Maple worksheets or prepared program on the calculator may be used. The second part of the exams will cover all skills: concepts, calculation, modeling, problem solving, and interpretation.
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the grading scheme, based on the various course components.
the number and format of hour exams, quizzes, homework assignments, in class assignments, and projects,
the policies governing the work items above, e.g., whether the computer will be used, what collaboration is allowed, and the format of assignments.
all policies for classroom procedure, including group work, class participation, laptop use and attendance*.
*Note that most instructors will enforce some type of grade penalty for students with more than four unexcused absences. |
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CTY Math Coordinator's Handbook
Introduction
The CTY math staff is a very close, family-like group, and a large
number of staff members return year after year. This makes it possible
for many of the important details of the mechanics of CTY math to be
passed along informally, as a sort of "apprenticeship" which occurs
during the course of the summers. Usually, this works beautifully,
because most instructors have been TAs, and most coordinators have
been instructors. However, when someone lacking this experience is
hired as a math coordinator (as has happened a few times), there is no
single, comprehensive information source which this person can use as
a guide. The pre-calculus instructor's handbook does not cover many
aspects of the coordinator's job, and the coordinator's job
description is not sufficiently specific. The new coordinator must
repeat, in only a few days, the development of methods and ideas that
previous math coordinators have already worked out over the course of
several years. This is clearly not an efficient training technique!
To help new coordinators manage this uncomfortable situation, this
handbook gives a detailed explanation of the activities,
responsibilities, and overall role of the CTY math coordinator. It
discusses some of the major decisions that a coordinator will have to
make, and points out aspects of the job which may vary from site to
site. Topics are organized by the time period in which they occur.
The handbook is pretty useful as a checklist for the experienced
coordinator, as well. After all, there's a lot of stuff to remember!
Authors
The Math Coordinator's Handbook was written by Ari Rapkin, with help
and suggestions from Martha Meadows, Mike Brandstein, and Shermann
Min. Collectively, their experience as math coordinators spans five
CTY sites and a total of nearly twenty years.
Beginning of summer
Placement testing materials
Make sure there are enough ADT's, scantrons, pencils, scrap paper,
and scoring keys. Get a timer or a watch with a second hand.
Progress checklists, HSST's & keys, textbooks and curriculum spirals
If any are missing, have them sent from the central office. Make
sure there are a reasonable number of each.
Math office
Find a convenient place to keep testing materials and extra or
shared resources. Remember that tests and valuable things
(e.g. graphing calculators) need to be kept secure. Suggested
places: coordinator's classroom, the math staff's house/dorm, or an
office.
Study hall policy
This is an annual source of confusion. Sometimes the site-wide
studyhall format or location just isn't appropriate for pre-calc,
and the math coordinator has to point this out to the site director
and say "Let's do this differently.". There are several possible
ways to conduct the pre-calc study hall: in dorm rooms, in dorm
lounges, in classrooms, in lecture halls, etc. I'm not going to make
a specific recommendation. Instead, here are pros & cons:
General stuff: Seven hours a day in the same classroom is a long
time, and the students enjoy a change of scenery (as do the
staff!). Unfortunately, holding study hall anywhere but the regular
classroom building means everyone -- staff and students -- has to
carry their stuff back and forth every day. Of course, if you're at
a commuter site, the students are stuck with this scenario
anyhow. Also, few places are as well designed for studying as a
classroom. Dorm-room desks may come close, but lecture hall desks
are often too small and lounges are simply not on: they're generally
poorly lit and not furnished with writing surfaces.
Dorm rooms: This is the only study-hall location which allows the
students to use their computers. However, distractions abound
(including those same computers), and there aren't enough
math-staffers or teacher's editions to go around. It's a nuisance
for the staff to have to trudge from dorm to dorm with a heavy load
of books and folders. Finally, there's no good way to handle
evening testing: if you allow testing during study hall, then you
have to assign a math staffer to proctor the student(s) in an office
or dorm lounge, or else impose on the RA to act as a proctor.
Dorm lounges: The whole class is in one place, so the instructor &
TA don't have to run a marathon each evening. Unfortunately, other
classes have discovered these benefits, so there may be contention
for lounges. There's probably a TV and a soda machine to act as
distractions. Some lounges are so close to student rooms that they
cannot be used if the rooms' residents are present. Also, since the
lounge is by definition a casual place, the students feel less bound
by rules of classroom behavior.
Lecture halls: If the lecture hall is big enough, more than one
class can share it. This is good because the staff members can split
duties & resources and keep an eye on each others' students, but bad
because the large number of students is harder to control (and
lecture halls tend to echo).
Classrooms: Seven hours a day in the same classroom is too much, but
this can be adjusted by holding study hall in a different
classroom. If it's in the same building, then everyone can leave
their stuff in their regular classroom during the afternoon and
overnight. This helps the staff be aware of students who are
spending all their free time studying -- they're the ones who take
their books home.
Post-testing policy
Another annual source of confusion: do we allow the students to take
HSST's and/or finals after classes are officially over? The possible
times include: during the last afternoon (when they're supposed to
be packing), the dance that night, or the morning they leave. There
are pros and cons to every one of these, and they're very site-
dependent because each site schedules its end-of-session activities
differently. Choose for yourself. (Consult with the other
administrative folks, of course.) What's most important is that you
choose early, and see that everyone knows the policy so that
confusion doesn't arise at the end of the session.
Math staff orientation
Take some time during staff orientation to make sure that all the
math folks get to know each other. Go do something fun together.
(Mandatory Fun! ... and it's your last chance to get off campus)
This schedule is straight from the 1992 job description. Alter the
timing as appropriate to your site's orientation schedule.
Thursday evening: Meet, explore each other's experience and areas of
strength. Decide who will work with whom and what courses they will
teach (see below for more on this. It can -- and I think should --be
put off until everyone's had a day or two to get familiarized with
each other and CTY).
Friday afternoon: Discuss the history and philosophy of CTY
pre-calc. Share past experiences about students and their abilities,
instructors and their attitudes toward math and teaching, and the
nature of a CTY class.
Saturday morning: Focus on pragmatic issues: how to administer a
class, where to start students, flexible pacing, appropriate
questioning, appropriate progress, and assessment.
Study skills workshop
Many students have never needed to develop good study skills, and so
have an especially difficult time with a self-paced course. Try to
arrange with the academic counsellor to offer math study skills
workshops. It's useful to have a completely optional one during the
first week and another during the second week which you can require
that specific students attend.
Emphasize to the math staff the importance of paying close attention
to the students' study habits, and taking action right away when a
problem is noticed.
Mattababy
The CTY math staff email network. Okay, most of the school-year
traffic concerns The Simpsons or sumo, but if you want fast answers
from a whole bunch of long-time CTY math staffers, this is the place
to ask. During the course of the summer, a lot of useful information
goes back and forth.
Before (or at the start of) each session
Math questionnaires
These may be available several days in advance if you're at a
Baltimore site. If not, you probably won't have them in your hands
for very long before the kids arrive. In any case, take the time to
sort through these -- get other math folks to help! -- and determine
how many Regents or other Unified-Math students you have, how many
geometry-only requests, and a rough estimate of the counts for each
subject. It's hard to tell who needs what with the trig-plus
courses, but there aren't generally very many students that advanced
so they'll end up in the same classroom anyhow.
If you're really ambitious, generate a list of pre-calc students for
whom you're missing questionnaires (or whose information is
unclear). Then flag their registration packets so that you can have
them fill out questionnaires when they check in. This requires some
coordination with whoever's organizing registration, but it's worth
the effort. If you try to get this information after the parents
have gone home, your success rate will be much lower.
Who teaches what
Once you've looked through the questionnaires, you can make a
tentative decision about how many sections of each pre-calc course
you're going to need. Ask your instructors and TAs what they'd like
to teach and who'd like to work together, then try to match up their
requests with what you need. You'll probably have to do some
shuffling after the placement testing, but with luck most of your
tentative plans will hold. Then you can distribute course materials
and make up class lists, student folders, etc.
It's helpful to pair new staff members with experienced ones. Trying
for gender balance is good too, since we're supposed to be role models
for the students to identify with. Don't put a great deal of effort
into this, though. Pairing people with course content is much more
important.
RAs and dorms
Find out who the math RAs are. Introduce yourself to them, and check
that they know the plans for study hall. Make sure the instructors
(and TA's, if possible) meet at least their own RAs, if not all of
them. Find out which dorms the math kids are in. If you're going to
be holding study hall in dorms, get keys to those dorms.
Some math RAs are quite comfortable with math, and are willing or
even eager to help their students with their work, answer questions
during class visits, etc. This is delightful when it happens, and
worth encouraging. On the other hand, be alert to RAs who are not so
mathematically inclined. Reassure them that this sort of
participation is entirely voluntary, and there will be no negative
consequences if they opt not to.
Course materials and progress records
Make sure that the instructors have progress chart masters, and the
appropriate textbooks, curriculum spirals, progress checklists, and
supplementary materials. Make sure that they know where the rest of
these materials are kept.
Classrooms
See that the instructors know which classrooms they have and get the
keys. Find out which keys open which other classrooms. (The ability to
swap keys can come in very handy, especially if the TAs don't have
their own keys.) If there are multiple classes using the same
resources (e.g., two rooms of Algebra II) try to assign them to
nearby rooms. Also, if there's an extra classroom nearby, try to get
it for use as a testing room.
Go to the classrooms (with the other instructors, if possible) and
make sure that everything is set up and working. Rearrange
furniture, put up posters, try out the overhead projector,
etc. There may be restrictions on what you can do to the rooms, so
check first. (For example, at Dickinson you can't take extra
furniture out of the rooms.)
Parent/student orientation
Be on hand during as much of orientation as possible, because some
parents will be in a hurry and unable to stay until the official
question-&-answer time, and since they don't know who's going to be
their child's instructor they'll all want to talk to YOU. Keep a
notebook handy, since you'll get a lot of placement info from
parents. Don't promise a specific placement or instructor, make
overly glowing assurances about how much work the student will
finish, etc.; if the parents ask these things, explain the placement
testing process and repeat the words "self-paced instruction" as
necessary. If they ask about residential things, answer what you can
but feel free to direct them to the residential dean or someone else
who really knows these things.
At some sites, the math coordinator talks to the pre-calc parents
separately after the all-parents welcome speech. This gives you a
chance to introduce the math staff, give a little history of the
math program, describe day-to-day events and the rigors of the
program, explain what we expect from students and from parents,
etc. This is a good time to talk some more about the meta-learning
that's going on: even if a kid doesn't finish trig, he or she has
learned a good deal about how to learn. Try to keep this speech short,
especially at residential sites, because the parents are anxious to
get back on the road for the many-hour drive home.
In your conversations with parents, and in your speech if you give
one, stress the importance of making plans with schools now, instead
of waiting until the student comes home or worse, until
September. Emphasize the importance of being supportive, but not
overly demanding. Point out that not finishing a year's worth of
work does not mean that the student failed.
Every session, there are a small number of parents who didn't read
the course description and are just now discovering that pre-calc is
not a group-activity or lecture course. Describe the interactive
things we do (extra problems, small-group lectures, students studying
together) and if they're still not happy send them to an
administrator. There's no need to apologize for providing exactly
what was offered.
Placement testing (ADT's)
When, where, and how the testing happens is really
site-dependent. Whether or not there's a Scantron machine to do the
scoring is also unpredictable (but "no" is the safer guess). If not,
making plastic stencils to go over the Scantron forms speeds things
up a lot.
Once you've got the tests scored, it's time to match scantrons with
questionnaires, and assign kids to classes. This is known as "The
Party Game", and usually CTY will spring for pizza and sodas, for
sustenance while you tackle this administrative nightmare. Pull all
the Geometry kids' scantrons right away (this is why you sorted out
their questionnaires earlier!) since their class assignments are
independent of their ADT scores. Make sure none of them have really
atrocious scores. If any do, they're candidates for an algebra
review before beginning Geo. Then split up the rest of the bunch
based on ADT scores, school history & plans, Regents/Unified, and your
innate good judgment. :-)
During each session
Progress records
Make sure everyone is keeping thorough, detailed records of what the
students are doing -- strong areas as well as weak. Checklists can
wait, but it wouldn't hurt to update them weekly.
Math staff meetings
This can be completely informal -- e.g., a chat over lunch -- or you
can schedule a time and place. Just make sure that you're not
discussing sensitive issues where students might overhear. Try to meet
at least twice a week.
Observing the other instructors
Spend an hour or two in each classroom during the first half of the
session. This isn't a real formal thing, but check with the instructor
& TA beforehand to see what's a good time. They may have special
activities planned. This is a good time to peep at their
record-keeping, and to acquire info for staff evaluations. Pay
attention to the interactions of staff with students, and of staff
with staff (i.e., is the instructor using the TA appropriately?).
Afterwards, tell them what you thought, and offer any suggestions or
praise that apply. If there were any serious problems, check up later
to be sure that improvements have been made.
Partner trouble
Unfortunately, not every instructor-TA pair gets along
perfectly. The staff members need to know that it's okay to
disagree, as long as the discussions are held out of earshot of the
students. Also, make sure they're aware that they should bring any
serious problems to the attention of the coordinator or the academic
dean quickly, so that they don't drag on unnecessarily.
RA visits to classes
For self-paced courses, these visits will be quick. Policy says that
each RA is to attend classes 2 hrs/wk, but in self-paced classrooms
there's little to see or do, and the RA's presence may in fact be a
distraction. Also, pre-calc RAs frequently have students in several
classes, and they must split their visitation time accordingly.
Student evaluations
It's Never Too Early to Start Writing Your Evals. Check with an
administrator to make sure you know the little quirks of this year's
evaluation format -- it changes every year, sometimes between
sessions. Encourage new instructors to go to the how-to session that
someone (probably the academic dean) will offer. Distribute sample
math evals. Get your own done early so you can worry about other
things.
Phone calls to families
In the middle of the second week, ask all the instructors to review
their students' progress and identify those kids who are unlikely to
reach whatever goal they've set -- e.g., they've signed up for Algebra
II in the fall and aren't going to finish Algebra I. Each instructor
should call the families of these students and explain the situation,
being very careful to emphasize that the purpose of the call is to
allow the family to start making plans for the fall ASAP, not a
disciplinary action or an indicator of failure.
Anyone who calls a student's family must keep a record of what was
said during the conversation. This is helpful not only if problems
come up later, but also in making your evaluations and
parent-conference conversations more specific.
Extra Problems sessions
There are a large number of interesting math problems (and computer
science, and physics, and chemistry, and ...) which the students will
enjoy tackling in their spare time and discussing in class. To many
students, this is the best part of the day, so it's well worth a
little of the instructors' time to prepare activities. The workload
can be kept to a minimum if the staff take turns writing problems. CTY
has a collection of suggested problems, but everyone on the math staff
is strongly encouraged to bring their own as well.
Usually, the problems are handed out one day and discussed the
next. The logistics of the discussion group vary from site to site,
but the most common set-ups (with pros & cons) are: During the
second hour of study hall -- this will require instructor's
permission, otherwise kids will go to Extra Problems just to get out
of study hall. However, it avoids most of the problems of the other
two plans. During an afternoon activity period -- doesn't interfere
with class time, but not many kids are going to give up Ultimate to
do more math. Even if they're really interested in the problem. On
the other hand, kids from other classes might show up. At the end
of the afternoon class -- it's tricky to do this in a way that
allows kids from different math classrooms to interact. More often,
this is done in each classroom separately. Unfortunately, class
discussions disrupt those kids who would rather keep working.
Tailoring the CTY curriculum
Many students in the upper pre-calc classes (those using the Brown
Advanced Math book) are trying to place out of a class back home
that involves pieces of several CTY courses. If you're lucky,
they've brought curricula and/or textbooks from back home so that
you'll know what their schools expect. More likely, you'll have to
ask them to call home and have information sent (or you may have to
make the calls yourself). The best way to handle the
curriculum-matching problem is to have the student complete one CTY
course (so that he/she will have certified in something), followed
by piece-wise study to complete the home-school curriculum.
HSST's, scantrons, scoring keys, and testing procedure
The tests etc. should be at hand in the coordinator's classroom or
some other convenient place. Make sure the instructors and TAs know
how and where to administer the tests, and how to score them -- red
or green Flair pens only! Also, see that the tests and keys are
returned promptly so that they can remain secure.
The instructions included with the tests pretty much explain what to
do. The two most important things for everyone to remember are: keep
an eye on the clock, and have someone else double-check your scoring.
End of session
Student program evaluations (SPE's)
Allow time for these to be filled out on the last or next-to-last
day. The last study hall might be a good time. Make sure that the
students know this is coming, so that they're not counting on this
class time in order to study for or take a final exam.
Student evaluations
Hassle the other instructors as necessary to get their student evals
finished on time. Yes, it's possible to drag out first session evals
into second session, but this is a bad idea since there's so much
stuff going on for session II. Encourage TA involvement in writing
the evals. This doesn't just mean asking the TAs to type up the
instructors' scribbled notes, although it's okay to ask for this
type of help too. Often the TA gets to know some of the students
better than the instructor does, and can give the instructor
descriptions of these students' strengths, weaknesses, study habits,
etc. This information makes an evaluation more personalized and
informative.
You may be expected to pre-read the other instructors' evals before
they go to an administrator. Don't worry about making them perfect,
since your style is almost guaranteed to be slightly different from
that of the official reader -- but you can filter out the obvious
grammatical, punctuation, and content errors.
Staff evaluations
Write one for your TA. This will be kept on file for him/her in case
of later job-reference requests. You may also be expected to write
evals of the other instructors and of the other TAs, or of your math
staff in general. There may be examples available. The time limits
on writing these are a bit looser, but try to have them done before
you leave the site.
Progress records, checklists, certification forms
Make sure everyone fills out the checklists and cert forms according
to whatever directions Baltimore has sent out this year. Don't
assume it's the same as last year. It rarely is.
Parent conferences
TAs are not required to attend, but encourage them to do so. It's
good practice if they're thinking of being an instructor. Most of
them want to go to the conferences anyhow, so this isn't really an
issue.
Parents will ask you what courses their children should take next,
in regular school or at CTY. Try to have suggestions in
mind. However, recognize that some parents will take what you say as
gospel instead of discussing it with anyone else. Emphasize the
necessity of talking to their home schools, and of considering the
student's interests.
Most likely, the other instructors can handle all their parents'
questions, but let them know that they can send tough ones your
way. The same rules apply here as at the beginning of the session:
answer what you can, don't make unnecessary promises or apologies,
and don't feel compelled to deal with the really far-out cases (send
them to an administrator and move along to the next family).
Between sessions
Departing staff
Make sure that staff members who are leaving or switching jobs after
first session get all their paperwork done and approved before they
go. Find out where they have left classroom keys and teaching
materials. Also, see that they've left an address which is valid for
the remainder of the summer.
Incoming staff members
Try to be on hand to greet math staff members arriving between
sessions. If you know during first session that people already on site
will be joining the math staff during second session, try to meet them
and introduce them to other math staffers before Intersession. They
may want to borrow books to brush up on their math during first
session; if you have books to spare, fire away. It may also be
possible to get in touch with session II staff members who are not
already on site, especially if they're at another CTY site for session
I. This is rarely necessary, but in some cases (e.g., someone won't be
arriving until just before placement testing) it becomes reasonable.
End of summer
Packing up
Make sure all the textbooks, curriculum spirals, Regents books,
etc. make their way back to Baltimore (or wherever they're going to
spend the winter). Baltimore needs an inventory of what's staying on
site, if anything. |
Precalculus with Trigonometry and Analytical Geometry
Description
This text provides a strong foundation for work with functions that culminates with an introduction to the calculus topics of the derivative and the integral. Beginning with a review of basic trignometry, the study progresses to advanced topics including functions, identities, and trigonometric equations. Development of analytical geometry topics include a logical approach to the study of lines, conics, quadric surfaces, polar coordinates, and parametric equations. Colorful graphs in one, two, and three dimensions illustrate the concepts and provide a frame of reference for discussion. Helpful tips and example problems show step-by-step solutions that aid in understanding and problem solving. Balanced exercises in each chapter provide ample opportunity for students to understand both the algebraic solution and practical application of problem solving |
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This Textbook
Overview
Building off the success of Zill and Dewar's popular Essentials of Precalculus with Calculus Previews, the new Fifth Edition continues to include all of the outstanding features and learning tools found in the original text while incorporating additional topics of coverage that some courses may require. With a continued effort to keep the text complete, yet concise, the authors have included four additional chapters making the text a clear choice for many mainstream courses. Additional chapters include a new chapter on Polar Coordinates, as well as Triangle Trigonometry, Systems of Equations and Inequalities, and Sequences and Series.
This student-friendly, full-color text offers numerous exercise sets and examples to aid in students' learning and understanding, and graphs and figures throughout serve to better illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student's successful transition into future calculus courses.
New to the Fifth Edition:
Includes a new Chapter 8, Polar Coordinates.
A new appendix on Complex Numbers has been added.
Available with a new graphing calculator manual, Exploring Mathematics: Solving Problems with the TI-84 Plus Graphing Calculator.
Available with WebAssign |
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Math
Linear algebra
Matrices, vectors, vector spaces, transformations, eigenvectors/values. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
This is one of those tutorials that bring many ideas we've been building together into something applicable. Orthogonal projections (which can sometimes be conceptualized as a "vector's shadow" on a subspace if the light source is above it) can be used in fields varying from computer graphics and statistics!
If you're familiar with orthogonal complements, then you're ready for this tutorial!
Finding a coordinate system boring. Even worse, does it make certain transformations difficult (especially transformations that you have to do over and over and over again)? Well, we have the tool for you: change your coordinate system to one that you like more. Sound strange? Watch this tutorial and it will be less so. Have fun!
As we'll see in this tutorial, it is hard not to love a basis where all the vectors are orthogonal to each other and each have length 1 (hey, this sounds pretty much like some coordinate systems you've known for a long time!). We explore these orthonormal bases in some depth and also give you a great tool for creating them: the Gram-Schmidt Process (which would also be a great name for a band).
Eigenvectors, eigenvalues, eigenspaces! We will not stop with the "eigens"! Seriously though, eigen-everythings have many applications including finding "good" bases for a transformation (yes, "good" is a technical term in this context). |
Calculus Open Textbook
free calculus textbook from Boundless Learning is based off openly available educational resources such as "government resources, open educational repositories, and other openly licensed websites." The textbook contains 5 chapters such as Building Blocks of Calculus, Derivatives and Integrals, and Inverse Functions and Advanced Integration15:25 -0600PhysicsAlgebra Open Textbook
free algebra textbook from Boundless Learning is based off openly available educational resources such as "government resources, open educational repositories, and other openly licensed websites." The textbook contains 8 chapters such as The Building Blocks of Algebra, Graphs, Functions, and Models, and Conic Sections01:31 -0600StatisticsProject Laboratory in Mathematics
it like to do mathematical research? The "Project Laboratory in Mathematics" course from MIT's OpenCourseWare provides some fine insights into this endeavor. The course was originally developed by Professor Haynes Miller and features information about how to help students "explore puzzling and complex mathematical situations." The site includes selected video lectures from the course, instructor insights, and a selection of projects and examples, such as "The Dynamics of Successive Differences Over Z and R." Also, the site includes information on how to customize this course for a variety of settings, along with examples of classroom activities and helpful resources.Thu, 20 Feb 2014 14:22:52 |
Online encyclopedias contain a wealth of information, be it user-generated or professionally vetted. The hyperlinked nature of an online encyclopedia makes reading about related topics as simple as clicking a link.
Courseware is software or organized content that can be used in the preparation or teaching of a course. This section contains links to web-based courseware resources. Downloadable courseware is listed on our Software page.
WikiBooks is a free, collaborative online collection of textbooks, including a set of mathematics texts. As always with online content, these are under construction.
CCNYMath.net is a Flash-based set of instructional web pages written and designed by Stanley Ocken, Professor of Mathematics at City College, and the late Jack Schwartz, a former CCNY math graduate and Professor Emeritus of Mathematics and Computer Science at New York University. You may contact Professor Ocken with any questions or suggestions for the site. You will need to have a Flash plug-in installed in your web browser to use this site.
Baruch College's Student Academic Consulting Center links to sample handouts and exams for some of Baruch's math classes, as well as math tutorial videos in Baruch's Digital Media Library. Video tutorials include college algebra, precalculus, and calculus. You must have a web browser with a plugin capable of playing QuickTime movies to view these videos.
Calculus+ is a series of tutorials in precalculus, calculus, linear algebra, and differential equations, using Maple 8 or higher. These projects were developed by CUNY faculty and tested in CUNY classrooms from 1998-2004.
Wolfram|Alpha, the Wolfram "computational knowledge engine", calculates answers to various questions using Mathematica packages and data from multiple online sources.
Math Overflow is a "place for mathematicians to ask and answer questions." The primary criterion for determining whether a question is appropriate for Math Overflow is, "is this of interest to mathematicians?"
The Tricki, a "a repository of mathematical know-how," is a wiki which seeks to codify methods of mathematical technique and problem-solvingPythagoras, ancient Greek mathematician and religious leader, believed that all existence could be described with whole numbers. |
Eventually, they develop confidence in their own abilities, and they realize that there is nothing to fear.Topics include basic algebraic operations, elementary equations, laws of integral exponents, factoring and radical notation, rational expressions and the introduction to the Cartesian coordi |
Summary: Chapter Zero is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which students construct their own understandings. However, while students are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers ''proof sketches'' and helpful technique tips to help studen...show morets as they develop their proof writing skills. This book is most successful in a small, seminar style class. ...show less
Elementary Axioms The Axiom of Infinity Axioms of Choice and Substitution
B. Constructing R
From Natural Numbers to Integers From Integers to Rational Numbers From Rational Real Numbers to Real Numbers 020143724487.59 +$3.99 s/h
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Introductory Linear Algebra An Applied First Course
9780131437401
ISBN:
0131437402
Edition: 8 Pub Date: 2004 Publisher: Prentice Hall
Summary: This book presents an introduction to linear algebra and to some of its significant applications. It covers the essentials of linear algebra (including Eigenvalues and Eigenvectors) and shows how the computer is used for applications.Emphasizing the computational and geometrical aspects of the subject, this popular book covers the following topics comprehensively but not exhaustively: linear equations and matrices an...d their applications; determinants; vectors and linear transformations; real vector spaces; eigenvalues, eigenvectors, and diagonalization; linear programming; and MATLAB for linear algebra.Its useful and comprehensive appendices make this an excellent desk reference for anyone involved in mathematics and computer applications.
Kolman, Bernard is the author of Introductory Linear Algebra An Applied First Course, published 2004 under ISBN 9780131437401 and 0131437402. Two hundred twenty Introductory Linear Algebra An Applied First Course textbooks are available for sale on ValoreBooks.com, sixty four used from the cheapest price of $19.72, or buy new starting at $14537401-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:9780131437401 |
Intermediate Algebra - With 2 CDs - 10th edition
Summary: This concise and cumulative guide shows students the art of technical writing for a variety of contexts and institutions. Using examples from the business and non-corporate world, the book emphasizes transactional writing through practical explanations, real-world examples, and a variety of ''role-playing'' exercises. Each section builds on the next as readers learn a variety of models of style and format. This edition features a stronger emphasis on electronic commu...show morenication, integrated coverage of ethics, and more explanation of how to create technical documents that produce concrete results. ...show less
3.1 The Rectangular Coordinate System 3.2 The Slope of a Line 3.3 Linear Equations in Two Variables Summary Exercises on Slopes and Equations of Lines 3.4 Linear Inequalities in Two Variables 3.5 Introduction to Functions
Chapter 4: Systems of Linear Equations
4.1 Systems of Linear Equations in Two Variables 4.2 Systems of Linear Equations in Three Variables 4.3 Applications of Systems of Linear Equations 4.4 Solving Systems of Linear Equations by Matrix Methods
9.1 The Square Root Property and Completing the Square 9.2 The Quadratic Formula 9.3 Equations Quadratic in Form Summary Exercises on Solving Quadratic Equations 9.4 Formulas and Further Applications 9.5 Graphs of Quadratic Functions 9.6 More about Parabolas and Their Applications 9.7 Quadratic and Rational Inequalities
11.1 Additional Graphs of Functions 11.2 The Circle and the Ellipse 11.3 The Hyperbola and Functions Defined by Radicals 11.4 Nonlinear Systems of Equations 11.5 Second-Degree Inequalities and Systems of Inequalities4.95 +$3.99 s/h
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Smiths Books MO Florissant, MO
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...Also learning to do proofs is another important lesson for example you see a potential relationship between two things and through induction you prove this is true in all cases instead of just being a coincidental relationship. I like to apply discrete math to real life situations to make it mor |
MATH 101-205: Integral calculus
Description
Basically, we are going to learn how to integrate functions, compute antiderivatives, figure out whether infinite sums add up to something finite or not, and we are going to study some of the applications of integrals to science and engineering problems. |
This site offers several tutorials on algebra, trigonometry, calculus, differentail equations, complex variables, matrix...
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This site offers several tutorials on algebra, trigonometry, calculus, differentail equations, complex variables, matrix algebra, and tables. Cyber Exam which contains quizzes and tests, and Cyber Board which answers FAQs and more are included.
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of...
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
The applet displays the direction field for the differential equation ...
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The applet displays the direction field for the differential equation dy/dx = axm + bxn .You choose the parameters a, b, m, n, by using the sliders or by typing directly in the right-hand control panels. The applet draws the direction field. Source code is available at
Hello world. Here's my design of a PowerPoint presentation similar to the famous Jeopardy quiz game. The topic showed is...
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Hello world. Here's my design of a PowerPoint presentation similar to the famous Jeopardy quiz game. The topic showed is Differential Equations, but can be easily configured to any other. This learning object is designed to work with several interactive whiteboards like polyvision, smartboard or mimio (another great option is the low cost interactive whiteboard based on the Wii remote provided by Johnny Chung Lee).This presentation should run in Microsoft Office 2010 to avoid compatibility issues.Enjoy and bring the excitement to the classroom!
These instructional exercises (modules) are part of a series of quantitative biology courses (Q courses) developed and taught...
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These instructional exercises (modules) are part of a series of quantitative biology courses (Q courses) developed and taught at UC Davis. The main files are written as MathCad 13 documents and require a copy of MathCad 13, or higher, to run. The downloadable MathCad documents are unanswered versions suitable for distribution to students. |
0070592004This supplemental text for the standard calculus course focuses on how the Casio FX 7700G (a graphing calculator) will aid in improving students' understanding of calculus. Since the calculators are capable of rapid production of graphics and calculations,students with access to the machines will not need to spend as much time on hand graphing and calculations as their more traditional counterparts. By letting the calculators handle the details,students can see the big picture by discovering relationships and experimenting. With calculators such as the Casio FX 7700G,students can focus on important calculus concepts rather than on computational details. This book can be used with any standard text or |
Algebra and Trigonometry - 5th edition
Summary: Bob Blitzer has inspired thousands of students with his engaging approach to mathematics, making this beloved series the #1 in the market. Blitzer draws on his unique background in mathematics and behavioral science to present the full scope of mathematics with vivid applications in real-life situations. Students stay engaged because Blitzer often uses pop-culture and up-to-date references to connect math to students' lives, showing that their world is profoundly mathematical...show -used book - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front or back used book - free tracking number with every order. ?book may have some writing or highlighting, or used book stickers on front or back
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Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd
9780077460396
ISBN:
0077460391
Edition: 8 Pub Date: 2011 Publisher: McGraw-Hill Higher Education
Summary: Be guided through every step of the fundamentals of statistics. It is a great introduction to statistics for college students who have a basic grasp of algebra. It covers all the main concepts effectively and provides a lot of opportunity for practical application. Students are taught problem solving using detailed instructions and examples. It also focuses on the different digital applications used in statistics suc...h as Excel, graphing calculators and MINITAB. It also complements an online course so students can receive more from their course and excellent feedback from the online platform. We offer many top quality used statistics textbooks for college students.
Bluman is the author of Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd, published 2011 under ISBN 9780077460396 and 0077460391. Five hundred thirteen Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd textbooks are available for sale on ValoreBooks.com, one hundred thirty seven used from the cheapest price of $73.88, or buy new starting at $173 Comes with CD only. This is an international edition. Brand New 8th Ed. Same Content High Quality Color and Paper as US Edition, International Softcover Edition. Ship within 2 [more]
ALTERNATE EDITION: Comes with CD only. |
Vectors
online exercise lets students practice vector addition. They choose the precision of the test by selecting a target size, then estimate the sum of the two vectors by dragging and dropping a third arrow. Points are awarded; a higher degree of precision scores more points.Wed, 1 Sep 2010 03:00:02 -0500Vectors
web page, authored and curated by David P. Stern, introduces vectors as an extension of numbers having both magnitude and direction. The initial motivation is to describe velocity but the material includes a general discussion of vector algebra and an application to forces for the inclined plane. The page contains links to a related lesson plan and further opportunities to explore vectors. This is part of the extensive web site "From Stargazers to Starships", that uses space exploration and space science to introduce topics in physics and astronomy. Translations in Spanish and French are available.Thu, 16 Apr 2009 03:00:01 -0500Vectors
lesson was created by Larry Friesen and Anne Gillis for Butler Community College. It will help physics and calculus students differentiate between the uses of vectors in mathematics vs. physics. This website provides two PDF documents that give detailed lessons about vectors, including an overview of terminology, sample problems, and an HTML worksheet is also provided. For educators or students, this site offers well laid-out lessons and/or practice with vectors.Fri, 18 Apr 2008 03:00:02 -0500Abstract Linear Spaces
essay covering the beginning of the vector concept and the move away from coordinate methods through the beginning of the 20th century with Peano, Hilbert, Schmidt and Banach, with 13 references (books/articles).Wed, 5 Dec 2007 03:00:01Multivariate Calculus With Maple
experiment in the use of the World Wide Web as a teaching aid for a course in multivariable calculus, using Maple as a symbolic calculator. Topics include Review of Calculus 1; Vector Geometry; Geometric Algebra; Vector Functions; Functions of Several Variables; Integration; Surface Area; and Vector Calculus.Fri, 3 Aug 2007 03:00:01 -0500Maths Help: Working with Vectors
of a wide range of physical properties such as force, velocity, and acceleration, requires a firm understanding of the mathematics of vectors. This comprehensive Web site covers many aspects of vector algebra and trigonometry. The often-used dot product and cross product are defined, as well as vector representations of lines and planes. Illustrations are used to demonstrate vector analysis and its real-world applications. A few extra sections delve into related topics, including transformation between Cartesian and spherical coordinates. The material is mostly suitable for high school or college students who have taken pre-calculus.Tue, 8 Nov 2005 18:24:17 -0600 |
Linear Algebra and Differential Equations, CourseSmart eTextbook
Description
Linear Algebra and Differential Equations has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations. By introducing matrices, determinants, and vector spaces early in the course, the authors are able to fully develop the connections between linear algebra and differential equations. The book is flexible enough to be easily adapted to fit most syllabi, including courses that cover differential equations first. Technology is fully integrated where appropriate, and the text offers fresh and relevant applications to motivate student interest.
Table of Contents
1. Matrices and Determinants.
Systems of Linear Equations.
Matrices and Matrix Operations.
Inverses of Matrices.
Special Matrices and Additional Properties of Matrices.
Determinants.
Further Properties of Determinants.
Proofs of Theorems on Determinants.
2. Vector Spaces.
Vector Spaces.
Subspaces and Spanning Sets.
Linear Independence and Bases.
Dimension; Nullspace, Rowspace, and Column Space.
Wronskians.
3. First Order Ordinary Differential Equations.
Introduction to Differential Equations.
Separable Differential Equations.
Exact Differential Equations.
Linear Differential Equations.
More Techniques for Solving First Order Differential Equations.
Modeling With Differential Equations.
Reduction of Order.
The Theory of First Order Differential Equations.
Numerical Solutions of Ordinary Differential Equations.
4. Linear Differential Equations.
The Theory of Higher Order Linear Differential Equations.
Homogenous Constant Coefficient Linear Differential Equations.
The Method of Undetermined Coefficients.
The Method of Variation of Parameters.
Some Applications of Higher Order Differential Equations.
5. Linear Transformations and Eigenvalues and Eigenvectors.
Linear Transformations.
The Algebra of Linear Transformations; Differential Operators and Differential Equations. |
Algebra for Dummies is a comprehensive book teaching about the basics of algebra while making simple all the concepts about it. However, for anyone to fully learn and understand Algebra, there are certain prerequisites that students have to master first.
For any student or person to excel in algebra, he or she should be adequately knowledgeable about certain concepts. Knowledge about the proper way of converting one unit into another is one of such requirements. Students should know beforehand how to convert liters into gallons and vice versa. Memorizing the metric to English conversions is also crucial.
But that wont be all. Even before one should try to read the Algebra for Dummies book, he should be confident enough to know the right order of operations and the precedence used for mathematical and algebraic expressions. These are where the parentheses, exponents, multiplication, division, addition, and subtraction are involved. Know which numbers you have to evaluate first, given a complicated set of mathematical problem. There is also what is known as the properties of roots, exponents, absolute value, and of the four basic mathematical operations. Everybody getting ready to learn algebra should be familiar with these topics as well.
Learning how to convert between percents, decimals, and fractions is necessary also. The fractional equivalent of a percentage and its decimal form should be second nature to students who want to excel in algebra. This is a pre requisite that you can find in several algebra worksheets. Practice your knowledge on these concepts to make algebra a whole lot easier for you.
With Algebra for Dummies, how to do algebra do become an easier and a more worthwhile experience. Find yourself enjoying algebra despite its complexity. With this book, mathematics becomes a walk in the park.
Algebra is a subject that can be made easy once you learn all the necessary rules and use the right formulas. Some of the concepts of algebra have to be memorized more than understood. Keeping useful algebraic formulas at the back of your mind, ready for access when you need them, would help you speed up the entire process of solving just about any problem. Many algebraic formulas are useful even if you are not solving any word or linear problems at all. As a matter of fact, you can be doing something as ordinary as going on a road trip or planting in your garden and find the need to solve distance problems or area equations. Many of the concepts of algebra can be applied in ones everyday life. And it follows that the many things youll find in Algebra for Dummies will prove to be useful.
Memorizing the formulas about area, circumference, distance traveled, simple interest, compounding interest, temperature, the Pythagorean Theorem, and the solution to quadratic equation are going to help you solve even the most complicated algebraic problems in the easiest possible way. Try to tuck these formulas in your mind and youll definitely find algebra a lot simpler than you thought it is.
Learning all about the divisibility rules will also make your struggle with algebra a whole lot easier. Algebra for dummies will teach you all about these divisibility rules that would make solving algebraic problems so much faster. Simply memorize them and youll see how simple algebra can really be.
Algebra worksheets also come with the book. These worksheets are very useful for practice as it can make a student excel in all the topics explained and illustrated in the book. With Algebra for Dummies, how to do algebra becomes a simple task. Everybody can be a master of it, regardless if youre a student, an employee, or a plain hobbyist.
Algebra is not a very easy subject. As a matter of fact, it is one of the most complex subjects that students will encounter during their stay in school. It is such a great thing that Algebra for Dummies is created, which is a very easy-to-follow manual for students to help them understand algebra in a less complicated way. With the book, they will be able to solve a lot of complex problems and still arrive at an accurate solution each time. The book is also designed to increase ones understanding on how to do algebra and the different processes in which it works.
The book also includes algebra worksheets that will allow students to practice their new-found understanding of the topics as explained in the book. This book is written by Mary Jane Sterling, an educator who teaches in three academic levels: college, high school, and junior high. Sterling has been in the field of education right after graduating from college, thus giving her all the necessary experiences and opportunities to expound on the different mathematical subjects, more particularly Algebra. Sterling has been teaching for 30 years at Bradley University in Peoria, Illinois.
Algebra for Dummies comes in three different versions Algebra for Dummies I, Algebra for Dummies II, and Linear Algebra for Dummies. Each book is divided into different parts or topics so students will be able to understand the different concepts surrounding algebra better. Working on an algebraic equation is a lot easier now, thanks to this book that breaks down the topics into smaller concepts. As such, students need not suffer from information overload. Each book is over 300 pages long, written with the intention of making algebra a very easy subject not just for students but also for professionals, businessmen, hobbyists, and alike.
For all of those who find algebra a very challenging subject, Algebra for Dummies is here to help. Let the book teach you how to do algebra in a way that is much easier and simpler for a regular student like you. After reading the book from cover to cover, you wont be vexed by the variables x, y, and z anymore. The plain-English explanation of algebraic concepts will guide you towards the most accurate solutions all the time.
Learn algebra explained in the words that you will fully understand. Practice your lessons with the included algebra worksheets so you can solve similar or more complicated problems with full confidence. With this book, you will be able to factor out variables, solve quadratic equations, and find your way through linear equations with full ease.
Algebra for Dummies is a pain-free way to learn and ace this subject. First off, students will be taught what numbers are and their different forms. Learn the difference between integers, both positive and negative integers, as well as rational and irrational number. Also, factoring will become a fun method for you with this book. Work yourself through prime numbers and all the concepts of distribution will full ease.
Equations will become an easy subject for anybody who is reading the book. The book is filled with many algebra worksheets involving the most common equations encountered under this subject like age problems, distance problems, work problems, and the likes. Solving these equations will be a walk in the park.
Lastly, and maybe the most important use of the book is that it will teach readers on how to put into practical use all the algebraic concepts that they have learned. With it, youll be more confident of your measurements, story problems, formulas, and graphs. Algebra can definitely improve your life for the better.
Learning algebra might be hard and confusing especially to beginners. But we can be able to remedy this with the use of proper resources that would enable us to learn algebra in easier and faster way. We can refer to these sources as Algebra for Dummies. In this article I will be providing you with some of the best Algebra for Dummies Resources in order for you to find easier ways in learning this subject.
Algebra for Dummies: Algebra Websites
One of the best and easiest resources to come by is Algebra Websites. These are internet sites that offer the basic and a very comprehensive information in Algebra such as equation solving, graphing and number systems. Some of the best website also offers programs, graphing tools, topic outlines, list of reliable resources and interactive lessons that can greatly help you out, these are also all free, so you dont have to worry about the budget. Sites may also contain algebra games and exercises where you can have fun and learn at the same time.
Algebra for Dummies: Online Classes
Another thing you can go for is going on free algebra classes online. There are a lot of class websites that offer materials such as downloadable lesson and exercises. There are also site like mathhops.com and algebra-class.com which allow students and teachers to interact through their community forums and share their ideas and questions pertaining to algebra. There are also streamable video lessons that would make you easily understand the topics being discussed.
Algebra for Dummies: Algebra Video Tutorials
Video tutorials which you can either stream online or download had become a really popular way of learning algebra. Lots of people prefer this type of learning as it makes it very easy to understand and it would feel like you are going to a regular algebra class. The video content is also created in a way to assist the viewers and provide the convenience in making the video lesson easy to grasp and view. Some of the websites you might want to try to get algebra video lessons are mathexpression.com, virtualnerd.com and lots mores.
Algebra for Dummies: Books
Of course you also can take the traditional method of reading books for granted. In fact it is one of the most convenient methods to do. You can bring a book almost anywhere without any hassle; also you dont need anything else when you have this aside from a properly lit room. The only thing you need to consider when purchasing one is that it should be a right fit for you and your level. Choose a book that makes it easy for you to understand the lessons. One of the best ways to help you out regarding is researching online abut algebra book reviews and what people who are expert in these thing can advice on what particular book would be fit for you. You can even order the book online too so that it you need to go to the bookstore.
If you are sitting in your algebra class looking at your book, seeing the numbers, letter and the stuffs you normally find in an equation, you might be asking yourself if it is really necessary to learn algebra. We might typically say that we could avoid jobs dealing with the subject and therefore avoid having to learn it in the first place. However you have to realize that learning algebra can be very important as it has lots of applications in our everyday life though we dont normally notice it.
Regarding learning the subject, it might a bit confusing at first but once you get the fundamental concepts you can actually discover that trying to learn it isnt that hard. There are also different ways on how to learn the subject and make it easier. This article algebra for dummies would provide you with great tips a beginner should learn in order to learn the subject.
Algebra for Dummies Tip One: Learn your Multiplication Tables
One of the most fundamental concepts one should master before delving in the world of algebra is mastering the multiplication table. This is really important as lots of algebraic equations normally use a lot of multiplication than most of the other mathematical operations, thus making it easier for you to understand equations if you are already a master of multiplication.
Algebra for Dummies Tip Two: Understand your Lessons by Heart
This tip is really important, you need to understand that there are no shortcuts in algebra, and the concepts you learn from the beginning can be used and applied even to very complex equations. Thus, you should not take your basic algebra classes for granted, in fact you should take it a lot more seriously and learn it by heart, since this things will be your foundation in learning the more complex lessons on the subject. By learning the basic concepts by heart you wont ever forget the basics and can have an easier time understanding the more complex stuff.
Algebra for Dummies Tip Three: Dont be afraid to ask questions
If you are confused about something then ask other people or your instructors about it. Dont be afraid to ask questions because you are still on the process of learning. Keep in mind that the key in learning algebra is understanding the reasons for the different ways the equations acts, and this might be a bit confusing since there are lots of different ways it could act. Thus, ask questions and clear out your understanding.
Algebra for Dummies Tip Four: Practice
If you want to learn algebra you need to devote time for it. You have to practice and become familiar with how different equations work. You should also take the learning process step by step. Dont be in a hurry; you cant just directly proceed with the complex equations without learning the basic as youd just make your head ache. Start at the easiest until you master it completely before going to the next level.
If you are trying to teach your kids algebra, then you have to find a teaching that would be appropriate for their age and thus make them interested and curious in learning the subject. This article will provide with very suitable way in teaching kids algebra. We can refer to it as algebra for dummies!
The term algebra was derived the Arabic term al-jabr which means the reunion of broken parts. Some algebraic ideas have already been used even an early as the 1650 B.C in Ancient Babylon and Egypt and thus brought to Europe by the Arabs. Now, in our world today thousands and thousands of year later it is considered as one of the major subjects and foundations of every education. Thus learning it a very important task to get the education you want especially for kids.
Here are some great algebra games for kids:
Algebra for Dummies: Algebra Bingo
This game requires working out certain equations and then marking it off in their bingo board. The teacher will provide equations and the students should work out the answer to the equation and mark it on their boards. Kids would be given a minute or more before moving to the next equation. This allows kids just beginning algebra to work with just a pencil and a paper.
Algebra for Dummies: Algebraic Equation Race
This is actually a very simple classroom game, but offers the motivation for the students to learn and practice. Its really easy to do, there would be two teams composed of the same number of people, the teacher would then ask algebraic equations and the two teams would race who could answer first, once they are able to give the correct answer they move closer to the finish line, this process is repeated until one completes and finishes. This actually has the element of competitiveness which provides the kids with the motivation to learn their algebra.
Algebra for Dummies: Slope of Letters Game
This simple activity helps students to recognize the different slopes of common lines found everywhere around them. This game was actually an idea from Jim Wilson from the University of Georgia; the teacher would be explaining the differences between the oblique, negative and positive slope lines. The teacher would then provide a letter and ask the student the lines that make up the letter.
Algebra for Dummies: Guess My Point
This game is actually a graphing guessing game in which players are given turns to ask others about the different properties of a point in a graph. They players can either ask if the point is either positive or negative, which axis is it located or of it is higher than a specific number or spaces from the axis.
These are only one of the many algebra games for dummies that you can try out. This is actually a very good way to motivate kids and other algebra beginners to start learning algebra. This is also a very good way to practice and train the mind to process algebra more quickly.
There are lots of people are really weak when it comes to algebra or mathematics. Lots opt to read books attend algebra classes, research the internet or perhaps do interactive lessons that can be found on some websites. This article will focus on teaching algebra for dummies. We will provide you with the things you need to consider in order to learn algebra.
Algebra for Dummies Tip One
In order to learn algebra you need to start with the basics. Therefore, you need to start with the easiest form and learn and understand by heart. Do all the equations that is related to the fundamental or the most basic of the algebraic equations and master it. once you are done with mastering the basics you can now go ahead and level up to a bit more complicated issue, once again you just to master this again and fully understand its applications after this you can now then repeat the process until you the most advanced and complicated concepts. This can prove to be very effective rather than dipping yourself with a bit of everything without completely immersing your mind and thus having very little understanding of the different algebraic concepts.
Algebra for Dummies Tip Two
Algebra can be mastered with a very simple equation. Algebra = Practice. This is definitely true, in order to fully master and understand very complicated concepts of algebra, one must experience algebra again and again until the understanding of the different algebraic equations become second nature to him and he can then easily respond without forcing the persons brain, as it would naturally once the person sees the equation.
A very effective to learn this is through writing the equations you want to learn on sheets of paper. Youve got to make sure that you write only one equation in one sheet. You the sheets youve written to practice the specific equation you wrote on the paper. Continue doing this and this can have great effects for you.
Algebra for Dummies Tip Three
Dont be in a hurry when trying to learn algebra, because if there are undeniable facts when learning this it would not being able to learn it overnight. Therefore, dont put too much pressure on yourself, and as much as possible relax and be at ease when dealing with the equations. Stressing your brain wont give answers, it would just make it a lot harder to think and understand what is really in front of you.
Algebra for Dummies Tip Four
If you want to be a good soldier, you need to have a good weapon. Therefore arm yourself with the best learning resources you can find. There are thousands of books about algebra, however there are very few that aims to explain it in a manner that is easy to understand, therefore you have to research and find the best book that would your mode thinking and become an effective tool to learn the subject. You may also join community forums where you find tips and ask for help in your struggles.
The concepts of math are seen to be difficult to comprehend; many regards math as a subject to the extremely gifted minds. This is overstated learning math is not as complex as people have made it to be. Algebra happens to be a part of math that is needed in every part of life; decision making and effective reasoning are based on the concepts of algebra. As an algebra tutor, when your students begin to ask about the importance of algebra in life, it is a sign they are not getting the best out of the class. You need to assess the way you take the class either the students are paranoid or they find the class boring. Once you figure out what the problem is, it is your responsibility as a tutor to fix the problem. You can ask them to buy a particular algebra for dummies book, and practice with them to aid their learning.
Math is required in every part of life, to survive in this ever changing society; your knowledge of basic math is extremely useful. Math is required to control expenses and budgets, and to help you with your decisions. Sometimes, algebra problems come as real life problems; students see themselves in such situations and apply their math skills to solve such problems. Basically, as math is essential, so is algebra the aspect of math that comprises of symbols and the basic math rules that manage their operations.
Algebra defines the procedures required to solve complicated math problems, though many find it difficult; it can also be very easy, depending on your knowledge. People exaggerate its complexity because they are not willing to dedicate their time in learning. If you are determined to learn how to do algebra, there are numerous tools algebra worksheets available online you can use to aid your learning. Work with different books (any algebra for dummies book), you will be provided with lots of exercises to work with. This eliminates the fear you have towards algebra and increases your learning curve.
But it is advised to learn basic math skills before learning algebra; lots of pre algebra for dummies textbooks are available that will guide you with the long division, and multiplications, the additions and subtractions. After which you can lay your hands on any algebra for dummies books. You dont have to memorize or cram the steps involved; the book will walk you through any obstacle you might be faced with. All the reasons behind each concept are explained thoroughly and accurately. You will learn different classifications of numbers, fractions and decimals, radicals and exponents and how to solve quadratic and linear equations. You will learn how to use graphs in solving equations, and importantly means of solving word or real life problems.
Learning algebra can be fun once you work with the right book any algebra for dummies book will be extremely valuable. It takes you literarily by the hand to shows you ways of solving algebra problems. You dont need to cram your way to success in class, once you understand the basics of algebra; you will realize how easy it is. Get yourself any college algebra dummies book to understand algebra once and for all.
Algebra seems complex and overbearing on many, but can be fun when done right. Lots of students find its concept difficult to comprehend they hate the algebra class. It is down to their algebra tutor to understand their frustration at the subject and do everything necessary to reaffirm their belief. There are two ways a tutor can do this; allowing the students to use proven algebra books (any algebra for dummies books will do) or increasing their learning by incorporating algebra games into the class. One option that is quite affordable is the use of quality algebra books to aid the students learning. Quadratic and linear equations and graphs are concepts that students find challenging, but are important in their adequate understanding of math. Therefore it is always a good idea for their parents to assist them with any college algebra dummies books so as to help them know how to do algebra.
Learning the basics of algebra requires adequate understanding of the core math concepts long division and multiplication and others are necessary. If you find difficulty with these, you need to learn pre algebra concepts before going on to learn how to do algebra. Pre algebra for dummies is useful, if you are just starting out.
This article is written to talk about a simple and effective way to solve two or more linear algebraic equations involving two variables (x and y variables). The only way to do this is manipulating the equations so as to find a pattern. Substitution method (substituting one value of a variable in one equation into the other) is the simplest means of solving such algebraic equations. Carrying this out requires you to look for the common property shared amongst all the equations. This is achieved after lots of practice; you need to practice different forms of linear algebraic equations to master how to find solutions. Make use of algebra for dummies, or talk to your teacher, he/she will guide you.
For example, when you are given an equation like 6x 3y = 0, and y x = 1. It is easy to find the value of y in the 2nd equation; y = 1+x, to find the other value, all you need is to substitute this value into the 1st equation, 6x 3(1+x) = 0. As you can see, we have eliminated the y terms from the 1st equation. Solving for the value of x gives 6x 3x = 3, which yields x = 1. Plug this value into any equation and the value of y can be found (using the 2nd equation, y = 2). This method gives the accurate means of solving a system of linear algebraic equation, this example is quite simple, for tougher ones, consult your algebra textbooks.
There are other means of solving two or more linear equations; any college algebra dummies book will be helpful. If you hit the brick wall, talk to your algebra tutor, he/she will tell you what to do. Therefore start learning how to do algebra by consulting any college algebra dummies book, you will be provided with a host of means of solving different forms of algebra equations. |
97805212970: The Core Course for A-Level
Designed to meet the Common Core requirements of the University of London Syllabus B, and other similar schemes offered by the major boards, this book incorporates both modern and effective traditional approaches to mathematical understanding. Worked examples and exercises support the text. An ELBS/LPBB edition is available |
This unit consists of two computer programs. The first teaches X,Y plotting; the second is a demonstration of coordinate transformations, matrices, vector equations of lines and perspective and will draw a picture of...
High school or college students taking an introductory trigonometry course may find this site useful. Three modules comprise the site, and each provides an overview of basic concepts. Some of the most common... |
Category:Mathematics study guides
This category contains books that are mathematics study guides: books that prepare students for standardized exams on mathematics, as well as texts that follow a specific curriculum covering mathematics. |
This course will provide you with a recognised GCSE qualification in Mathematics. There are various opportunities for progression once you have completed this course depending on whether you wish to improve your employability or progress onto other courses including Teacher Training.
GCSE in Mathematics will provide you with the essential skills required for success in your chosen field.
What will I study?
- The specification covers the GCSE Mathematics National Curriculum.
- The specification is divided into 3 sections.
- In 'Money and Number' you will learn how to calculate percentages, work with fractions and decimals and manipulate numbers.
- In 'Statistics' you will learn how to draw pie-charts, calculate probability and understand graphs.
- In 'Core' you will learn to understand trigonometry, algebra, geometry and Pythagoras.
By three modular examinations (two with calculator and one non-calculator).
There are exam sittings in November, March and the final module exam in May/June. At each stage of the course your performance is monitored so that the appropriate level of work can be maintained.
How do I get a place on the course?
Places are offered by interview and an initial assessment test. Students will take an assessment to determine if they have a basic level of numeracy which will allow them to be successful in GCSE Mathematics.
We will advise every student of the most suitable pathway for them, both before and during the course, which will lead them to success in their qualification.
What are the entry requirements?
No formal qualifications are required, although an interest in mathematics and/or work experience will greatly enhance your chances of passing the diagnostic test.
What else do I need to know?
GCSE Mathematics is also offered alongside several full-time programmes and 16-18 students in this category are advised to study their GCSE Mathematics qualification alongside their main course.
Details of the full-time GCSE Mathematics provision will be available through your full-time programme tutors.
Solihull College offers full time and part time courses for businesses and residents in Birmingham, Walsall, Wolverhampton, Coventry Warwickshire and the whole of the West Midlands.
If you have a Learning Difficulty or Disability please let us know when you apply. You will be offered support in your interview. If you need help completing your application we can help with this too.
What can I do after this course?
GCSE Mathematics is an essential qualification to achieve. It is recognised by all employers and is a requirement for the majority of University courses (including teacher training) . |
Thinking Mathematically, Fifth Edition
Average rating
3.7 out of 5
Based on 127 Ratings and 105 Reviews
Book Description pr... More provides helpful tools in every chapter to help them master the material. Voice balloons are strategically placed throughout the book, showing what an instructor would say when leading a student through a problem. Study tips, chapter review grids, Chapter Tests, and abundant exercises provide ample review and practice. |
Algebra and Trigonometry-Stud. Solution Manual - 3rd edition
Summary: Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
0840069235 |
365 total
5 944
4 273
3 73
2 45
1 30
Problems Doesn't recognize hyperbolic functions and will not produce indefinite integrals. It would also be nice if the taylor series option would show the expansion instead of giving just the numerical result
Problems Doesn't recognize hyperbolic functions and will not produce indefinite integrals. It would also be nice if the taylor series option would show the expansion instead of giving just the numerical result musicThis app can help update firmware when someone uses this app has been updated.
First device get update. Your device get it with.
In update system feature. This app help get update package file and install by recovery mode. (like OTA or manual update by sideload method) You can be sure that it is safe.
If you find any problems in recovery mode can be viewed by pressing the Volume up button. Followed by the power button. If you not understand you can email inquiries please do not ask for trouble by writing a comment in the app.Basics: -Enter values and view results as you would write them -Swipe up, down, left, or right to quickly switch between keyboard pages. -Long click on keyboard key to bring up dialog about key. -Undo and Redo keys to easily fix mistakes. -Cut, Copy, and Paste. -User defined functions with f, g, h
Graphing: -Graph three equations at once. -View equations on graph or in table format. -Normal functions such as y=x^2 -Inverse functions such as x=y^2 -Circles such as y^2+x^2=1 -Ellipses, Hyperbola, Conic Sections. -Inequalities -Logarithmic scaling -Add markers to graph to view value at given point. -View delta and distance readings between markers on graph. -View roots and intercepts of traces on graph.
Q. Is there are tutorial anywhere explaining how to use the graphing calculator? A. There are three into tutorials in the app for the calculator, graph equations, and graph screens. Additional tutorials can be found on our website
Q. How do I get to the keys for pi, e, solve, etc? A. There are four keyboard pages. Each swipe direction across the keyboard moves you to a different page. The default page is the swipe down page. To get to the page with trig functions, swipe left. To get to the matrix keys, swipe up. To get to the last page, swipe right. No matter what page you are on, the swipe direction to move to a specific page is always the same.
Q. What do you have planned for future releases? A. You can keep up to date on the latest news on our blog at . This news will include what is coming up in future releases. Also feel free to leave comments and let me know what you think!Tips: -sto() function may be used for infinite series/mathematical induction, Newton's Method, etc.
Notes: -When tracing functions with fractional powers, tangent line is reversed for negative x-values. -Odd-numbered roots with real solutions are evaluated as a real number (e.g.: (-8)^(1/3) = -2), unlike other calculators, and computer algebra systems such as Wolfram.
Grapher is useful application for all pupils and students. Ease interface will help you to build any graph or function on Cartesian coordinate system in few seconds. You can drow simple,parametric or polar type of function.
You can build a lot of functions in one time on same screen in different colors.
Description Calculator Plus is an advanced, modern and easy to use scientific calculator #1. Calculator Plus helps you to do basic and advanced calculations on your mobile device. IMPORT * easy to use * home screen widget * no need to press equals button any more - the result is calculated automatically * smart cursor positioning * copy/paste in one button * landscape/portrait orientations * drag buttons up or down to use special functions, operators etc * modern interface with possibility to choose themes * highlighting of expressions * history with all previous calculations and undo/redo buttons * variables and constants support (build-in and user defined) * complex number computations * support for a huge variety of functions * expression simplification: use 'identical to' sign (≡) to simplify current expression (2/3+5/9≡11/9, √(8)≡2√(2)) Why Calculator plus needs INTERNET permission? Currently application needs such permission only for one purpose - to show ads.
How can I use functions written in the top right and bottom right corners of the button? Push the button and slide lightly up or down. Depending on value showed on the button action will occur. How can I toggle between radians and degrees? To Examples: 268° = 4.67748 30.21° = 0.52726 rad(30, 21, 0) = 0.52726 deg(4.67748) = 268 Does Calculator Plus support %? Yes, % function can be found in the top right corner of / button. Examples: 100 + 50% = 150 100 * 50% = 50 100 + 100 * 50% * 50% = 125 100 + (100 * 50% * (25 + 25)% + 100%) = 150 Note: 100 + (20 + 20)% = 140, but 100+ (20% + 20%) = 124.0 100 + 50% ^ 2 = 2600, but 100 + 50 ^ 2% = 101.08 Does Calculator Plus support fractional calculations? Yes, you can type your fractional expression in the editor and use ≡ (in the top right corner of = button). Also you can use ≡ to simplify expression. Examples: 2/3 + 5/9 ≡ 11/9 2/9 + 3/123 ≡ 91/369 (6-t) ^ 3 ≡ 216 - 108t + 18t ^ 2 - t ^ 3 Does C++ support complex calculations? Yes, just enter complex expression (using i or √(-1) as imaginary number). ONLY IN RAD MODE! Examples: (2i + 1) ^ = -3 + 4i e ^ i = 0.5403 + 0.84147i Can C++ plot graph of the function? Yes, type expression which contains 1 undefined variable (e.g. cos(t)) and click on the result. In the context menu choose 'Plot graph'. |
The American Mathematical Association of Two-Year Colleges (AMATYC) has compiled a collection of mathematics resources related to various subjects and disciplines. ?Math Across the Community College Curriculum? is the...
This Office Administration course was created by a team of educators at Florida Community College at Jacksonville to combine business and math. In-depth lessons are provided that address mathematics in consumer finance...
A collection of games and puzzles for math review, this page provides visitors with a number of ways to engage in math topics. There are ten java-based and eleven non-java flashcard collections on concepts including...
Produced by Science Academy Software, this site is a collection of math questions on subjects including basic arithmetic, order of operations, calculating perimeters and distance, exponents, and bar graphs. It is an... |
This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of...
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This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of calculus. Analysis lies at the heart of the trinity of higher mathematics—algebra, analysis, and topology—because it is where the other two fields meet. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 241)
This is a free online course offered by the Saylor Foundation.'Real Analysis II is the sequel to Saylor's Real Analysis I,...
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This is a free online course offered by the Saylor Foundation.'Real Analysis II is the sequel to Saylor's Real Analysis I, and together these two courses constitute the foundations of real analysis in mathematics. In this course, you will build on key concepts presented in Real Analysis I, which focused on the study of the real number system, including real numbers and real-valued functions defined on all or part (usually intervals) of the real number line. In particular, MA241introduced you to differentiation and integration, powerful analysis techniques that enable the solution of many problems at the heart of science, including questions in the fields of physics, economics, chemistry, biology, and engineering. Real Analysis II will help you extend these techniques to the solution of more complex mathematical and scientific problems.As long as a problem can be modeled as a functional relation between two quantities, each of which can be expressed as a single real number, the techniques of single-variable real-valued functions should suffice. However, quite often a problem fundamentally involves information requiring more than one real number to describe, or it depends on more than one variable, or both. For instance, a particle moving in a room requires three coordinate real numbers to determine its location. Or, in another example from physics, the altitude a projectile will reach – a quantity measurable by one real number – depends on the weight of the projectile as well as the initial velocity it acquired from some external force.Sometimes a problem can be modeled as a single-variable or multivariable function depending on the answer desired. For example, a particle in three-dimensional space moving through a force field (think of a dust particle floating in the air as it is blown by strong or minute gusts of wind) can be modeled both as a function of time (a single-variable function) describing the coordinates of the particle at each instance of time; or, if one is interested in the final resting place of the particle as a function of its initial position, the problem can be modeled as a multivariable function requiring three inputs and producing three outputs.In this course, you will learn about some of the intricacies of the geometry of higher-dimensional spaces. You will develop the theory of multivariable functions and apply advanced techniques of differentiation and integration to such functions. Finally, you will explore applications of these advanced techniques in solving scientific problems.'Early users of the differential calculus made use of the concept of an infinitesimal; a quantity so small that although it is...
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Early users of the differential calculus made use of the concept of an infinitesimal; a quantity so small that although it is not zero its square and higher powers are zero. There are no real numbers with this property and its use was discouraged as nonrigorous. It was however a very convenient construct and it did not seem to result in incorrect results.In 1960 Abraham Robinson discovered a way to provide a rigorous basis for infinitesimals. The webpage explains this foundation for infinitesimals. It requires a new concept of number different from the real numbers.AccoI have taught the beginning graduate course in real variables and functional analysis three times in the last five years,...
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AccoI have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. The elements of the topology of metrics spaces are presented (in the nature of a rapid review) in Chapter I. The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem and its applications. In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhaps for the first half of the course) is the Riesz representation theorem. Included is the spectral theorem for compact self-adjoint operators and applications of this theorem to elliptic partial di erential equations. Chapter III is a rapid presentation of the basics about the Fourier transform. Chapter IV is concerned with measure theory.״rding to the author, " |
Geometry
The aim of this course is to familiarize future teachers with the following approaches to geometry: (1) constructions and axioms; (2) coordinates and vectors; (3) perspective and projective planes; and (4) transformations and non-euclidean planes. This knowledge will help the student to see the connections between school geometry and more modern branches of mathematics.
Description
We will discuss these four themes: (1) After a brief review of some classical constructions we will examine the flaws of Euclids axiom system. Next, we will discuss Hilberts solution to this problem. We will see how the perception of the relation between geometry and numbers has changed since Euclids times. (2) We will briefly review coordinates, distances, vector spaces, inner products and matrices. (3) We will motivate projective planes by considering perspective in drawing. Projective planes are then introduced axiomatically. Next we treat some basic topics such as homogeneous coordinates, projections, broken linear transformations, double ratio and some standard theorems (Pappus and Desargues). (4) After studying transformations (isometries) of the Euclidean plane and the sphere we will introduce the peculiar geometry of the hyperbolic plane. (5) Depending on the interests of the participants these themes can be extended or other, related topics will be added, such as finite projective planes and elliptic curves with modern applications.
Organization
3 hours mixture of lecture and exercise class
Examination
A midterm written exam, and a take home assignment plus oral exam at the end.
Literature
John Stillwell, The four pillars of geometry, Springer (2005), ISBN 0-387-25530-3
Prerequisites
Basic linear algebra; familiarity with elementary group theory is not assumed, but can be helpful. |
Math 2001: Geometry for Elementary School Teachers
Note that this class has previously been taught as Math 5002.
This class is intended for students interested in the Early Childhood Education program at the University of Georgia. It covers the basic geometry that elementary school teachers need to know, including:
angles, parallel lines, triangles, quadrilaterals and circles
what it means to 'measure' something
why the standard formulas for area work (for areas of rectangles, triangles and paralellograms)
why the formulas for volume work (for volume of boxes, prisms and pyramids)
It is strongly recommended that future elementary teachers take the sequence 2001/2/3. These classes satisfy your core math requirements and will be much more use to you as a teacher than precalculus.
The focus for this class is to help students explain why standard formulas and methods work so that math is not just viewed as a set of rules without meaning behind them.
Math 2002: Algebra for Elementary School Teachers
Note that this class has previously been taught as Math 5003.
This class is intended for students interested in the Early Childhood Education program at the University of Georgia. It covers the basic algebra that elementary school teachers need to know. Topics include:
Math 2003: Arithmetic for Elementary School Teachers
Note that this class is also taught as Math 5001 for students that transfer into the Early Childhood Program..
This class is intended for students interested in the Early Childhood Education program at the University of Georgia. It covers the basic arithmetic that elementary school teachers need to know. Topics include:
Decimal notation, comparing decimals, rounding
The meaning of fractions, equivalent fractions, common denominators, percent
Addition and subtraction of whole numbers and fractions; why the standard algorithms work
The meaning of multiplication, commutative, associative and distributive properties, why the standard algorithm works
Math 5020: Arithmetic 2003, above, except that some sections are skipped in order to go deeper into certain topics. The textbook is the same as for Math 2003.
Math 5030: Geometry for Middle School Teachers
This class is intended for students in the Middle School Education program at the University of Georgia that have chosen Mathematics as one of their areas of specialization. It covers the basic geometry that middle school teachers need to know. The content for this class is similar to that for Math 2001, above, except that some sections are skipped in order to go deeper into certain topics. The textbook is the same as for Math 2001.
Math 5035: Algebra 2002, above, except that some sections are skipped in order to go deeper into certain topics. The textbook is the same as for Math 2002.
Math 8200: Algebraic Topology
This is a first class in algebraic topology at the graduate level. It is intended to prepare students in the UGA Math Department Ph.D. program for the algebraic topology portion of their written qualifying exam in topology. Topics covered include: |
Multi step equations worksheet
Students will
Students will be able to solve multistep equations, including the concepts of distributive. Test and worksheet generators for math teachers. Examples as they appear on the tiling equations worksheet. Alfgdebyrqaf n worksheet by kuta software. Algebra multistep equations distribution. |
Lie Groups: A Problem-Oriented Introduction via Matrix Groups
By Harriet Pollatsek
The work of Norwegian mathematician Sophus Lie extends ideas of symmetry and leads to many applications in mathematics and physics. Ordinarily, the study of the "objects" in Lie's theory (Lie groups and Lie algebras) requires extensive mathematical prerequisites beyond the reach of the typical undergraduate. By restricting to the special case of matrix Lie groups and relying on ideas from multivariable calculus and linear algebra, this lovely and important material becomes accessible even to college sophomores. Working with Lie's ideas fosters an appreciation of the unity of mathematics and the sometimes surprising ways in which mathematics provides a language to describe and understand the physical world. This is the only book in the undergraduate curriculum to bring this material to students so early in their mathematical careers.
Errata
About the Author
Harriet Pollatsek (Mount Holyoke College, South Hadley, MA) has served as chair of the MAA's Committee on the Undergraduate Program in Mathematics and led the writing team for Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004. She now chairs the MAA's Council on Programs and Students in the Mathematical Sciences. |
Originally started by Professor Dave Rusin of Northern Illinois University, the Mathematical Atlas is now a very large "collection of articles about aspects of mathematics at and above the university level, but...
"In the Classroom" highlights how some schools and organizations use Mathematica extensively in their curricula. The section on "Collaborative Initiatives" illustrates how businesses have teamed up with Wolfram Research...
The Geometry Junkyard website provides a broad introduction to the specifics of geometry. The site, designed by David Eppstein of UC-Irvine, provides all the basics of geometry for students and teachers alike. Topics...
Educational consultant and textbook author Jill Britton is the author of these metasites listing Web resources for grade 5-8 mathematics. Each metasite revolves around a certain topic. The third metasite listed here...
This site departs from the common themes taught in general geometry classes and introduces projective geometry, which has to do with special properties resulting from the intersection of lines, planes, and points. The... |
A Unit Circle Approach
Ratti and McWaters wrote this series with the primary goal of preparing students to be successful in calculus. Having taught both calculus and ...Show synopsisRatti and McWaters wrote this series with the primary goal of preparing students to be successful in calculus. Having taught both calculus and precalculus, the authors saw firsthand where students would struggle, where they needed help making connections, and what material they needed in order to succeed in calculus. Their experience in the classroom shows in each chapter, where they emphasize conceptual development, real-life applications, and extensive exercises to encourage a deeper understanding. Precalculus: A Unit Circle Approach, Second Edition, offers the best of both worlds: rigorous topics and a friendly, "teacherly" tone. Note: This is the standalone book, if you want the book/access card please order the ISBN below: 0321900472 / 9780321900470 Precalculus: a Unit Circle Approach plus MyMathLab with Pearson eText -- Access Card Package Package consists of 0321431308 / 9780321431301 MyMathLab/MyStatLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 032182539X / 9780321825391 Precalculus: A Unit Circle ApproachHide synopsis |
Countdown to Mathematics
Description: Countdown to Mathematics has been written to help self-study students to revise and practise basic skills in arithmetic, algebra, geometry, graphs and trigonometry. The nine teaching modules in Countdown to Mathematics have been split into twoMore...
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This book presents in a very simple and lucid way the terminology and concepts of linear algebra as they would be used by any mathematician, but presents it in such a way that it is extremely accessable to the undergraduate first course in linear algebra. I used this along with the "required" text for my linear algebra course and found this far superior. It doesn't waste any time on useless details i.e. solving systems of equations, "finding" the inverse, determinant or any form of rote calculations or the ridiculous identity "proofs"etc... which about 50% of every other undergrad linear algebra texts I've seen or used do (he does touch on GE a little). If you're planning of studying math seriously, or are interested in math then this book is definitely a keeper. Another thing I liked about this book is that it doesn't act like a textbook, one can easily sit down and just "read" it, owing again to Janich's unique style.
This book covers most of what you need but it is poorly written and a real struggle to learn from. It is more suited to someone who already knows it all and has a "Oh I've forgotten about this or that property of vector fields. I'll just look it up. Oh there it is, how could I have forgotten" moment. If you're an undergraduate and want to learn linear algebra try "linear algebra" by Anton.
The book sets out to be an introduction to linear algebra, starting out on the premise of sets and maps and going up in complexity to vectors spaces, matrices, systems of equations, and eigenvalues. For an introductory text though, I think the book does not cater to a wide enough audience in that it dwells too much on the pure maths aspects and does not give enough numerical explanations or "real world" examples. If you are a not a pure mathematician but would like to learn more about linear algebra because of its potential applications, then this would not be the right book for you. The writing style is inconsistent and somewhat dry in places. Sections are light where more explanations are needed, and verbose where conciseness would do. |
Writing A Calculus I (Math 151)
Project
1. Objective: To learn how Calculus is linked to your
chosen major or field.
2. Guidelines:
a. You may choose up to three classmates to form a group.
b. You need to identify a real-life problem in your fields
that you would like to do. (For example, it could be an
optimization problem.)
c. You need to use technological tools to demonstrate how
you use Calculus to achieve your answer.
3. Writing up your report: You need to prepare a Word
or PowerPoint file
4. Oral presentation: December 10. |
COURSE DESCRIPTION
Calculus is the greatest mathematical breakthrough since the pioneering discoveries of the ancient Greeks. Without it, we wouldn't have spaceflight, skyscrapers, jet planes, economic modeling, accurate weather forecasting, modern medical technologies, or any of the countless
Indeed, calculus is so versatile and its techniques so diverse that it trains you to view problems, no matter how difficult, as solvable until proved otherwise. And the habit of turning a problem over in your mind, choosing an approach, and then working through a solution teaches you to think clearly—which is why the study of calculus is so crucial for improving your cognitive skills and why it is a prerequisite for admission to most top universities.
Understanding Calculus: Problems, Solutions, and Tips immerses you in the unrivaled learning adventure of this mathematical field in 36 half-hour lectures that cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. With crystal-clear explanations of the beautiful ideas of calculus, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce major concepts, this course will be your sure and steady guide to conquering calculus.
Your teacher for this intensively illustrated DVD set is Professor Bruce H. Edwards, an award-winning instructor at the University of Florida and the coauthor of a best-selling series of calculus textbooks.
Accomplish Mathematical Wonders
Calculus is one of the most powerful and astonishing tools ever invented, yet it is a skill that can be learned by anyone with an understanding of high school mathematics.
Among its many uses, calculus teaches you to
analyze a multitude of situations involving change, whether it's an accelerating rocket, the growth of a bacterial colony, or fluctuating stock prices;
calculate optimum values, such as the greatest volume for a box with a given surface area or the highest feasible profit from the sales of an item;
measure complex shapes—for example, the volume of a doughnut-shaped object called a torus or the area of a plot of land bounded by a river.
Learn about Precalculus and Limits . . .
Solving many types of calculus problems usually requires employing precalculus—algebra and trigonometry—to work out a solution. For this reason, Professor Edwards devotes the first few lectures to reviewing key topics in precalculus, then he covers some basic concepts such as limits and continuity before moving on to the two simple, yet brilliant ideas behind calculus—the derivative and the integral.
Despite the apparent differences between the derivative and integral, you discover that they are inextricably linked by the surprising fundamental theorem of calculus. Throughout the course, you will discover that simplicity is one of the hallmarks of the essential ideas of calculus.
. . . the Power of the Derivative . . .
The derivative is the foundation of differential calculus, which you study through Lecture 17, exploring its many applications in science, engineering, business, and other fields.
You start with a classic problem that illustrates one of the core ideas of calculus: Can you find the tangent line to a curve at a given point? This is the same as asking if the rate of change of the curve can be measured at that point—with a host of potential applications in situations where a quantity is changing, such as the speed of an accelerating vehicle. The answer is: Yes, and with amazing simplicity! After learning the steps involved, you have solved your first calculus problem.
You then
study a variety of ways to find derivatives, including the power rule, the constant multiple rule, the quotient rule, the chain rule, and implicit differentiation;
learn how to find extrema—the absolute maximum and minimum values of functions, using derivatives; and
apply derivatives to solve a variety of real-world problems.
. . . and the Importance of the Integral
Next, you are introduced to the integral, using a classic problem in which you are asked to find the area of a plot of land bounded by curves. To solve this problem, calculus provides us with the integral—a powerful tool that allows us to calculate areas, volumes, and other characteristics of complex shapes. The balance of the course is devoted to integral calculus and its applications. You study
arc length and surface area—two applications of calculus that are at the heart of engineering;
integration by substitution—a method that enables you to convert a difficult problem into one that's easier to solve; and
the formulas for continuous compound interest, radioactive decay, and a host of other real-world applications.
A Calculus Course for All
Understanding Calculus is well suited for anyone who wants to take the leap into one of history's greatest intellectual achievements, whether for the first time or for review. Those who will benefit include these learners:
Any student now studying calculus who would like personal coaching from a professor who has spent years honing his explanations for the areas that are most challenging to students. This course is specifically designed to cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college.
Parents of students studying calculus, a subject with which they often give up trying to help their high-school-age children—at a critical turning point in their educational careers.
Those who have already taken calculus and who need a thorough review.
Anyone who didn't understand calculus on the first try and wants a lucid, in-depth presentation, with lots of interesting, well-explained practice problems.
The plentiful graphs, equations, and other visual aids in these lectures are clear and well-designed, allowing you to follow each step of Professor Edwards's presentation in detail. The accompanying workbook includes lecture summaries, sample problems and worked-out solutions, tips, and pitfalls; lists of formulas and theorems; a trigonometry review sheet; a glossary; and a removable study sheet to use for quick and easy reference during the lectures.
The Ideal Calculus Teacher
Professor Edwards is the ideal calculus teacher—friendly, animated, encouraging, and witty, but also focused on presenting the material in an organized and understandable way. For anyone who feels intimidated by calculus, there is a distinct joy in being able to calculate a derivative after just a few lessons. It's easier than one might have supposed, and it opens an amazing new world of insight.
As an educator who has been honored repeatedly, both for his teaching and for his textbooks, Professor Edwards is a fount of valuable advice. He offers frequent tips for success, including guidance for those preparing for the Advanced Placement Calculus AB exam, for which he has served as a grader and for which this course is excellent preparation. Among his suggestions are these:
Graphing calculators: While some calculus teachers prefer that their students not use graphing calculators, the Advanced Placement exam requires them. Professor Edwards points out the strengths of graphing calculators as well as the weaknesses—for example, that in certain situations they can fool you.
Memorization: Always memorize what your teacher assigns. However, no one can memorize all the formulas in calculus. A good approach is to commit to memory the idea behind a technique—for example, that the disk method of computing the volume of a solid involves slicing it into innumerable disks.
Ever since its inception in the 17th century, calculus has spawned a continuing flood of new ideas and techniques for solving problems. It's easy to be overwhelmed by the richness of this subject, which is why many beginning students find themselves struggling.
Through Professor Edwards's exceptional teaching in Understanding Calculus, you will come away with a deep appreciation for the extraordinary power of calculus, a grasp of which methods apply to different types of problems, and, with practice, a facility for unlocking the secrets of the ceaselessly changing world around us.
LECTURES
36Lectures
Calculus is the mathematics of change, a field with many important applications in science, engineering, medicine, business, and other disciplines. Begin by surveying the goals of the course. Then get your feet wet by investigating the classic tangent line problem, which illustrates the concept of limits.
In the first of two review lectures on precalculus, examine graphs of equations and properties such as symmetry and intercepts. Also explore the use of equations to model real life and begin your study of functions, which Professor Edwards calls the most important concept in mathematics.
Continue your review of precalculus by looking at different types of functions and how they can be identified by their distinctive shapes when graphed. Then review trigonometric functions, using both the right triangle definition as well as the unit circle definition, which measures angles in radians rather than degrees.
Jump into real calculus by going deeper into the concept of limits introduced in Lecture 1. Learn the informal, working definition of limits and how to determine a limit in three different ways: numerically, graphically, and analytically. Also discover how to recognize when a given function does not have a limit.
Broadly speaking, a function is continuous if there is no interruption in the curve when its graph is drawn. Explore the three conditions that must be met for continuity—along with applications of associated ideas, such as the greatest integer function and the intermediate value theorem.
Infinite limits describe the behavior of functions that increase or decrease without bound, in which the asymptote is the specific value that the function approaches without ever reaching it. Learn how to analyze these functions, and try some examples from relativity theory and biology.
Building on what you have learned about limits and continuity, investigate derivatives, which are the foundation of differential calculus. Develop the formula for defining a derivative, and survey the history of the concept and its different forms of notation.
Practice several techniques that make finding derivatives relatively easy: the power rule, the constant multiple rule, sum and difference rules, plus a shortcut to use when sine and cosine functions are involved. Then see how derivatives are the key to determining the rate of change in problems involving objects in motion.
Learn the formulas for finding derivatives of products and quotients of functions. Then use the quotient rule to derive formulas for the trigonometric functions not covered in the previous lecture. Also investigate higher-order derivatives, differential equations, and horizontal tangents.
Discover one of the most useful of the differentiation rules, the chain rule, which allows you to find the derivative of a composite of two functions. Explore different examples of this technique, including a problem from physics that involves the motion of a pendulum.
Conquer the final strategy for finding derivatives: implicit differentiation, used when it's difficult to solve a function for y. Apply this rule to problems in related rates—for example, the rate at which a camera must move to track the space shuttle at a specified time after launch.
Having covered the rules for finding derivatives, embark on the first of five lectures dealing with applications of these techniques. Derivatives can be used to find the absolute maximum and minimum values of functions, known as extrema, a vital tool for analyzing many real-life situations.
Use the first derivative to determine where graphs are increasing or decreasing. Next, investigate Rolle's theorem and the mean value theorem, one of whose consequences is that during a car trip, your actual speed must correspond to your average speed during at least one point of your journey.
What does the second derivative reveal about a graph? It describes how the curve bends—whether it is concave upward or downward. You determine concavity much as you found the intervals where a graph was increasing or decreasing, except this time you use the second derivative.
By using calculus, you can be certain that you have discovered all the properties of the graph of a function. After learning how this is done, focus on the tangent line to a graph, which is a convenient approximation for values of the function that lie close to the point of tangency.
Attack real-life problems in optimization, which requires finding the relative extrema of different functions by differentiation. Calculate the optimum size for a box, and the largest area that can be enclosed by a circle and a square made from a given length of wire.
Conclude your investigation of differential calculus with additional problems in optimization. For success with such word problems, Professor Edwards stresses the importance of first framing the problem with precalculus, reducing the equation to one independent variable, and then using calculus to find and verify the answer.
Up until now, you've calculated a derivative based on a given function. Discover how to reverse the procedure and determine the function based on the derivative. This approach is known as obtaining the antiderivative, or integration. Also learn the notation for integration.
One of the classic problems of integral calculus is finding areas bounded by curves. This was solved for simple curves by the ancient Greeks. See how a more powerful method was later developed that produces a number called the definite integral, and learn the relevant notation.
The two essential ideas of this course—derivatives and integrals—are connected by the fundamental theorem of calculus, one of the most important theorems in mathematics. Get an intuitive grasp of this deep relationship by working several problems and surveying a proof.
Try examples using the second fundamental theorem of calculus, which allows you to let the upper limit of integration be a variable. In the process, explore more relationships between differentiation and integration, and discover how they are almost inverses of each other.
Investigate a straightforward technique for finding antiderivatives, called integration by substitution. Based on the chain rule, it enables you to convert a difficult problem into one that's easier to solve by using the variable u to represent a more complicated expression.
When calculating a definite integral, the first step of finding the antiderivative can be difficult or even impossible. Learn the trapezoid rule, one of several techniques that yield a close approximation to the definite integral. Then do a problem involving a plot of land bounded by a river.
Review the properties of logarithms in base 10. Then see how the so-called natural base for logarithms, e, has important uses in calculus and is one of the most significant numbers in mathematics. Learn how such natural logarithms help to simplify derivative calculations.
Continue your investigation of logarithms by looking at some of the consequences of the integral formula developed in the previous lecture. Next, change gears and review inverse functions at the precalculus level, preparing the way for a deeper exploration of the subject in coming lectures.
The inverse of the natural logarithmic function is the exponential function, perhaps the most important function in all of calculus. Discover that this function has an amazing property: It is its own derivative! Also see the connection between the exponential function and the bell-shaped curve in probability.
Extend the use of the logarithmic and exponential functions to bases other than e, exploiting this approach to solve a problem in radioactive decay. Also learn to find the derivatives of such functions, and see how e emerges in other mathematical contexts, including the formula for continuous compound interest.
Turn to the last set of functions you will need in your study of calculus, inverse trigonometric functions. Practice using some of the formulas for differentiating these functions. Then do an entertaining problem involving how fast the rotating light on a police car sweeps across a wall and whether you can evade it.
Revisit the area problem and discover how to find the area of a region bounded by two curves. First imagine that the region is divided into representative rectangles. Then add up an infinite number of these rectangles, which corresponds to a definite integral.
Learn how to calculate the volume of a solid of revolution—an object that is symmetrical around its axis of rotation. As in the area problem in the previous lecture, you imagine adding up an infinite number of slices—in this case, of disks rather than rectangles—which yields a definite integral.
Apply the shell method for measuring volumes, comparing it with the disk method on the same shape. Then find the volume of a doughnut-shaped object called a torus, along with the volume for a figure called Gabriel's Horn, which is infinitely long but has finite volume.
Investigate two applications of calculus that are at the heart of engineering: measuring arc length and surface area. One of your problems is to determine the length of a cable hung between two towers, a shape known as a catenary. Then examine a peculiar paradox of Gabriel's Horn.
Review integration formulas studied so far, and see how to apply them in various examples. Then explore cases in which a calculator gives different answers from the ones obtained by hand calculation, learning why this occurs. Finally, Professor Edwards gives advice on how to succeed in introductory calculus.
Closing your study of integration techniques, explore a powerful method for finding antiderivatives: integration by parts, which is based on the product rule for derivatives. Use this technique to calculate area and volume. Then focus on integrals involving products of trigonometric functions.
Explore slope fields as a method for getting a picture of possible solutions to a differential equation without having to solve it, examining several problems of the type that appear on the Advanced Placement exam. Also look at a solution technique for differential equations called separation of variables.
Use your calculus skills in three applications of differential equations: first, calculate the radioactive decay of a quantity of plutonium; second, determine the initial population of a colony of fruit flies; and third, solve one of Professor Edwards's favorite problems by using Newton's law of cooling to predict the cooling time for a cup of coffee.
Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. After his years at Stanford, he taught mathematics at a university near Bogotá, Colombia, as a Peace Corps volunteer.
Professor Edwards has won many teaching awards at the University of Florida, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year, and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991–1993.
Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of mathematics textbooks with Professor Ron Larson. Their textbooks have been honored with various awards from the Text and Academic Authors Association.
VIDEO OR AUDIO?
This course features visual elements, including graphs of functions, detailed animations, and step-by-step solutions to hundreds of equations. |
Mathematics 90
Mathematics 90
The Mathematics 90 program consists of a review of arithmetic operations with whole numbers, integers, fractions, and decimals, and an introduction to algebra, informal geometry, consumer mathematics, and statistics. Problem solving is an integral part of the mathematics program. The content in Cyber School Mathematics is no different than regular Mathematics 90 except now we have a different delivery model which allows for flexibility in the students' time constraints. It is a student centered program opposed to a teacher centered program. The course is intended to be interactive in that students are also able to interact with the instructor and other students on a daily basis through chat-rooms, bulletin boards and e-mail. |
Invigorate instruction and engage students with this treasure trove of "Great Ideas" compiled by two of the greatest minds in mathematics. From commonly taught topics in algebra, geometry, trigonometry, and statistics, to more advanced explorations into indirect proofs, binomial theorem, irrationality, relativity, and more, this guide outlines concepts and techniques that will i...show morenspire veteran and new educators alike.
This updated second edition offers more proven practices for bringing math concepts to life in the classroom, including:
114 innovative strategies organized by subject area
User-friendly content identifying "objective," "materials," and "procedure" for each technique
A range of teaching models, including hands-on and computer-based methods
Specific and straightforward examples with step-by-step lessons
Written by two distinguished leaders in the field-mathematician, author, professor, university dean, and popular commentator Alfred S. Posamentier, along with mathematical pioneer and Nobel Prize recipient Herbert A. Hauptman-this guide brings a refreshing perspective to secondary math instruction to spark renewed interest and success among students and teachers |
Instructor Class Description
Calculus I: Origins and Early Developments
Develops modern calculus by investigating the questions, problems, and ideas that motivated its discovery and practice. Studies the real number system and functions defined on it, focusing on limits, area and tangent calculations, properties and applications of the derivative, and the notion of continuity. Emphasizes problem-solving and mathematical thinking. Prerequisite: either a minimum grade of 2.5 in B CUSP 123, sufficient score on approved mathematics assessment test, or a minimum score of 2 on either the AB or BC AP Calculus test. Offered: AWSp.
Class description
This course, the first part of a two-quarter sequence, develops the modern calculus by investigating the questions, problems, and ideas that motivated its discovery and practice. We will begin with two questions posed by the philosophers of ancient Greece: What is the area of a planar figure? How can one find the line tangent to a point on a curve? These and related questions occupied the creative attention of mathematicians for two millennia. In one form or another, they will occupy our creative attention for the duration of this course.
In order to answer these questions, we will study the real number system and the properties of functions defined on it. In particular, we will explore the notions of continuity and differentiability, the theory of limits, and the problem of optimization. Each concept will be studied as it first appeared in scientific and mathematical discourse, and as it now appears in contemporary applications. A highlight of the course will be the study and complete solution of the Brachistochrone Problem. Rigorous mathematical thinking and problem-solving skills will be emphasized throughout.
Learning Goals and Objectives
During this course, students will be expected to:
1) Identify the major conceptual and theoretical themes of Calculus;
2) Solve mathematical problems of both contemporary and historical importance by applying the techniques learned in the course;
3) Describe the contributions made be various mathematicians and philosophers to the development of Calculus, including Archimedes, Descartes, Fermat, Pascal, Barrow, Roberval, Newton, and Leibniz.
4) Employ calculator- and computer-based technologies in solving computation-intensive problems;
5) Develop the skills required to write and communicate mathematical ideas.
Student learning goals
General method of instruction
I will strive for a balance between interactive lecturing and small group work.
Recommended preparation
This course will be challenging. As a result, it will be both exciting and rewarding. Calculus rests on a foundation of arithmetic, algebra, and geometry. As such, facility with arithmetic and algebraic manipulations is essential. Also, familiarity with polynomials, rational functions, trigonometric functions, and the conic sections will be helpful. Please contact me if you would like to discuss these topics further.
Class assignments and grading
Course assignments will include written problem sets and worksheets. The assignments will call upon you to think critically, to develop facility with mathematical methods and techniques, and to write clearly and effectively. You can expect an average of 12-15 hours of out-of-class work each week.
Your grade will be based on your performance on quizzes, the midterm, and the final exam, and the quality of your written work Peter J. Littig
Date: 08/10/2006
Office of the Registrar
For problems and questions about this web page contact icd@u.washington.edu,
otherwise contact the instructor or department directly.
Modified:March 8, 2014 |
Algebra and Trigonometry With Analytic Geometry - 13th edition
Summary: Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this book popular among students year after year. This latest edition of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY retains these features. The problems have been consistently praised for being at just the right level for precalculus students. The book also provides calculator examples, including specific keystrokes that...show more show how to use various graphing calculators to solve problems more quickly. Perhaps most important--this book effectively prepares readers for further courses in271.60 +$3.99 s/h
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Singapore Math Level 6 Curriculum Review
Our Experience
Singapore Level 6, like the rest of their curriculum, is divided into semesters – 6A and 6B. I have very mixed feelings about level 6. There are a number of new concepts presented to prepare the student for Pre-Algebra. As with most things Singapore, they are presented in a logical and engaging manner. Unfortunately, there are not enough practice problems on the new concepts to prove useful. There is also a great deal of review of basic math skills and concepts. Okay, now for the good news…..There are 22 pages titled "More Challenging Word Problems." These challenging word problems allow the student to put some of his new skills to use as well as cement previously learned concepts. Most importantly, the Word Problem section takes the student to a much higher level of critical thinking and forces him to address the word problems in layers (multiple steps). I have a child who despises "steps," so for him, this section was priceless! If you are comfortable with the your child's retention at the end of 6A, you can move through 6B fairly quickly. I would highly suggest using the Intensive Practice Books for level 6.
The Facts
In order to use Singapore to its fullest advantage, you will need to purchase the text books and workbooks for both 6A and 6B, as well as the Home Instructor's Guide. Singapore is published in different formats. There is a version of Singapore used by schools simply called Singapore Math. This version of Singapore does not cover as much information and the formatting is not as user friendly – this version is widely available in "School Stores." Most Homeshoolers prefer the Primary Mathematics U.S. Edition – which is what I suggest. The U.S. edition covers both standard and metric measurement and the material is presented in a manner that ensures life long retention. Singapore uses mental math and word problems much earlier than other math curriculum which proves advantageous in later years for upper school math. |
Summary: Math 105 Workbook
Exploring Mathematics
Concordia College Mathematics Department
Spring 2012
Acknowledgment
First we would like to thank all of our former Math 105 students. Their successes,
struggles, and suggestions have shaped how we teach this course in many important
ways.
We also want to thank our departmental colleagues and several Cobber mathematics
majors for many fruitful discussions and resources on the content of this course and
the makeup of this workbook.
Some of the topics, examples, and exercises in this workbook are drawn from other
works. Most significantly, we thank Samantha Briggs, Ellen Kramer, and Dr. Jessie
Lenarz for their work in Exploring Mathematics, as well as Dr. Dan Biebighauser
and Dr. Anders Hendrickson. We have also used:
· Introductory Graph Theory by Gary Chartrand,
· The Heart of Mathematics: An invitation to effective thinking by Edward B.
Burger and Michael Starbird,
· Applied Finite Mathematics by Edmond C. Tomastik.
Finally, we want to thank (in advance) you, our current students. Your suggestions |
Teaching Math Without a Plan? You've Got to be Kidding!
Product Description
This workshop is designed to help parent-educators understand the scope, the sequence, and the logic of mathematics instruction from pre-school through adult. Join Tom Clark, founder of VideoText Interactive and author of Algebra: A Complete Course and Geometry: A Complete Course, as he takes you on a sometimes-humorous journey, describing all levels of arithmetic and all mathematics courses encountered in high school and college. In addition, considerable attention will be given to identifying the "why" of the study of mathematics with an emphasis on the development of concepts instead of rote memorization. (This workshop is especially helpful for beginning home schooling parents.)
Speaker Information:
Tom Clark is a lifelong teacher of mathematics and science, with 46 years' experience in education. In addition to teaching, he has served as the state mathematics supervisor for the Indiana Department of Education, the supervisor of K-12 mathematics for Indianapolis Public Schools, and director of curriculum development. In addition, he has authored several mathematical resources for the Houghton-Mifflin Publishing Co. and for the Addison-Wesley Publishing Co. His unique awareness of the needs of both teachers and students has helped him win the IUPUI Chancellor's Award, the Purdue Chancellor's Award, and the Purdue School of Science Faculty Teaching Award. In the last 18 years he has focused on the development of multimedia programs that challenge traditional methods of instruction and that help with both individualized and group learning. He has written several articles on the subject and has been a featured speaker at many conferences across the country, addressing techniques of interweaving technology and instruction for concept development, especially in the areas of middle school and high school mathematics. Tom is currently president of VideoText Interactive, a company that specializes in bringing the textbook to life through technology. The company's two major programs, "Algebra: A Complete Course" and "Geometry: A Complete Course," have been acclaimed nationwide, as comprehensive college-preparatory mathematics courses. |
Easy Algebra Master Algebra in 24 hours! This Tutorial. intended for mature students, covers the Algebra Topics taught in School and required for College. It makes Algebra easy by carefully explaining the Algebra
commutative algebra in description
SINGULAR SINGULAR is an Algebra software which was designed to help you manage polynomial computations with special emphasis on the needs of commutativealgebra, algebraic geometry, and singularity theory.
Sagemath This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutativealgebra, group theory, combinatorics...
Algebra 1 for 7th Grade Designed as an educational and interactive software, algebra 1 for 7th Grade can be used to improve your mathematics skills. Algebra 1 for 7th Grade is built in Java and comes included with algebra an... |
Course Description: This course focuses on the understanding of mathematical properties of real numbers and problem solving skills. Multiple representations will be used including algebraic. Emphasis is placed on verbal and written communication of mathematical concepts.
Welcome to Dimensions of Mathematical Understanding
This course is designed to develop your understanding of mathematics by providing opportunities for you to experience what it means to problem solve and reason about mathematics. Emphasis is on problem solving (investigating, conjecturing, and justifying), on understanding of concepts, on connections among concepts, and on written and verbal communication of strategies and reasoning. This requires practice and commitment to sense making on the part of the student.
It is important that you realize that you cannot solve, with understanding, mathematical problems by observing and mimicking others doing mathematics. You must participate mentally in the learning process. This participation includes studying the material; working with others; struggling with non-routine problems; using calculators for exploring, reasoning about, and solving problems; symbolically representing mathematical thinking and reasoning; listening to others; reflecting about what you are doing; as well as the more typical tasks of taking examinations and doing homework. The emphasis in this course will be on problem solving and reasoning with understanding rather than memorizing and using equations or algorithms. As a consequence you will be expected to provide complete explanations of the reasoning you used to solve problems.
Too often our previous experiences with mathematics have caused us to focus on memorization and finding correct answers. Consequently our understanding of what mathematics is and what it means to do mathematics is shaped by these experiences and is rather limited and narrow. And yet, mathematical problem solving consists of so much more. In this course we will focus on problem situations as described in different guises: visual, quantitative, graphic, abstract, and concrete. From these we will focus on the various dimensions of mathematical problem solving: investigating and exploring, reasoning and conjecturing, justifying and verifying, connecting, and communicating.
Discussion Problems: You will be required to work on the problems from the handouts outside of class. It is expected and required that you will come to class prepared to present your solutions and explanations to the class. Class discussion will be most meaningful when you have worked on the problems beforehand. You will better understand the solutions presented by your classmates as well as able to participate by asking and answering questions. In addition, you will be preparing for exams by working on your own solutions.
Exams and quizzes: The exams and quizzes in this course consist of short answer, computational, and essay questions. Emphasis of this course is on problem solving, sense making, and reasoning with understanding of concepts, on connections among concepts, and on verbal and written communications of your strategies and ideas. Thus, you will be expected to provide complete explanations of the reasoning you use to solve problems and the explanations should make sense to both you and me.
Attendance: You are expected to attend all classes. Your participation in class activities and discussions is important not only for your own learning, but also for the learning of others. You are expected to attend class and be a collaborative participant in the work of the class. Because much of the learning that will take place during class cannot be effectively transmitted through notes, it is recommended that you attend class regularly.
Class handouts: Handouts are distributed on a regular basis. If you miss class, it is your responsibility to login to blackboard and print your needed handouts.
Participation: This class is built around student participation. You are expected to present solutions to problems, answer questions posed by the instructor and classmates, and ask questions of your classmates. Each student has the potential to earn 40 points participation. The points will be awarded according to the following rubric
35-40 points: You have excellent attendance. You have missed no more than 1 class. You have volunteered to present multiple solutions to the class. You ask questions of others and voluntarily answer questions posed to you or the class in general.
25-35 points: You have good attendance. You have missed no more than 2 classes. You have presented multiple solutions voluntarily or when requested. You ask questions and answer questions when called upon.
15-24 points: You have fair attendance. You have missed no more than 3 classes. You have presented as at least once. You answer questions when class upon, but might not volunteer.
11-14 points: You have attendance problems. You may have missed at least 3 classes. You might not have presented solutions to the class. You do not ask questions or answer questions unless prodded.
0-10 points. You have excessive absences. You have virtually no participation.
Please note that using a cell phone, ipod, laptop, or similar device during class without permission will be recorded as an absence.
Study group: You will find it beneficial to form study groups of 3 students. Your study group can be used to work on problems to be presented in class, devise solutions for graded problem sets and prepare for exams. You will also find that your own understanding is strengthened by "teaching" your classmates during your study sessions.
Retakes of Exams and/or extra credit: I do not allow retakes of any assignment or assign extra credit to individuals to raise grades.
Checkpoints: Checkpoints are given periodically during the semester. These are completed in blackboard and must be completed by the due date to receive a score.
Testing policy: You are expected to take each exam and quiz at the scheduled times. However, if you have an unavoidable absence you may request to take the test at an alternative time provided you contact your professor before the exam/quiz begins and explain your absence. I will decide if and when you take your makeup exam/quiz, which is generally no later than 2 business days. If you request a makeup via email or voice mail, it is your responsibility to check your messages for my response. If you do not receive a response from me within a reasonable amount of time, you MUST follow up with another attempt to contact me. Failure to follow the policy will result in denial of your request.
Exceptions to the above policy will only be given for situations including, but not limited to, jury duty, military orders, serious medical problems (yourself or immediate family member) or a death of an immediate family member. You MUST be able to provide documentation. (Acceptable documentation include such things as an accident report, doctor's note or hospital discharge papers.) Immediate family member is defined to be a spouse, partner, parent, grandparent, child, grandchild, sibling, or your spouse's/partner's immediate family member. These requests will be considered on a individual basis.
Repeated requests for makeup exams WILL REQUIRE that you provide documentation.
Requests to take exams/quizzes early are generally approved.
If for any reason, you do not take an exam or quiz, your midterm exam or final exam score will replace one missed exam/quiz. (Scaled to the appropriate amount) If the missed quiz precedes the midterm, the midterm will be used to replace the score. Otherwise, the final will be used. Any other missed exam/quiz will earn a score of zero.
Cheating: A score of zero will be given on any assignment where cheating occurs. Examples of cheating are copying answers off other students' tests, submitting another person's work as your own, and having crib sheets during a test. Repeated acts of cheating may result in a course withdrawal.
Classroom etiquette: Please be courteous of others' rights in the classroom. Do not disrupt their right to learn by inappropriate talking (talking during presentations or while others are asking or answering questions), whispering, or other immature acts. Please turn cell phones to silent and do not text message or play games during class. If you need your cell phone for emergency purposes (EMT, firefighters, sick family member, etc.) this is certainly allowed. Each student is also held to "Student Code of Conduct" as specified in the student handbook. Violation of this student code may result in withdrawal from the course.
Withdrawals: Withdrawal from this course is not automatic. You will need to initiate a withdrawal from this course by completing the form in the Records Office or through webadvisor. IVCC has the right to rescind a withdrawal in cases of academic dishonesty or at the professor's discretion. If you do not initiate a withdrawal, you may receive a grade for this course, which in most cases, is an F.
Students should be aware of the impact of a withdrawal on full-time status for insurance purposes and for financial aid. It is highly recommended that students meet with their instructor or with a counselor before withdrawing from a class to discuss if a withdrawal is the best course of action for that particular student.
Please see your course schedule for the last day to withdraw.
Financial Aid: Withdrawal from a course can affect financial aid.Students who receive financial aid should see an advisor in the Financial Aid Office before withdrawing from a course.
Cancelled class: Every effort will be made to announce class cancellations in a timely manner. Unexpected cancellations will be posted on the IVCC website. ( You may wish to consider checking this webpage each morning before traveling to the college. In the event that class is cancelled on an exam day, the exam will be moved to the next class day. You may also sign up to receive text messages or emails when the college is closed for weather or emergencies.( )
Inclement weather: In the event of bad weather, please listen to your local radio station for school closings. If school has not been cancelled, use your own judgment as to the feasibility of traveling to school.
Grading process: If you do not understand how I graded your work or you disagree with the number of points earned, you have the right and responsibility to initiate contact with me about the matter within 4 class days of the material being returned to you. These matters will be discussed in my office by appointment.
Graded materials: You are to keep all graded materials for this course until after you receive your final grade. If there is a clerical error, and you do not receive the grade you earned, these materials will be needed to resolve this issue. In the absence of these materials, the professor's record will be assumed to be correct. If you are absent when an assignment is returned, you are responsible to visit my office during office hours to retrieve your assignment.
Special Needs Educational Support Services: If you are a student with a documented cognitive, physical or psychiatric disability you may be eligible for academic support services such as extended test time, texts on disc, notetaking services, etc... If you are interested in learning if you can receive these academic support services, please contact either Tina Hardy (tina_hardy@ivcc.edu, or 224-0284) or Judy Mika (224-0350), or stop by the Disability Services Office in B-204.
This course outline is subject to change to meet the needs of the instructor and/or students. |
Offering
9 subjects
including calculus |
Pre-Algebra Help
In this section you'll find study materials for pre-algebra help. Use the links below to find the area of pre-algebra you're looking for help with. Each study guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn pre-algebra.
The Nature and Causes of Math Anxiety
Many students suffer from what is called "math anxiety." Math anxiety is very real, and it can hinder your progress in learning mathematics. Some of the physical symptoms of math anxiety ...
Study and Test-Taking Techniques
Having an understanding of math anxiety and being able to reduce stress are not enough to be successful in mathematics. You need to learn the basic skills of how to study mathematics. These skills include how ... |
"The Manga Guide to Calculus" teaches calculus in an original and refreshing way, by combining Japanese-style Manga cartoons with serious content. This is real calculus combined with real Manga. The book's story revolves around heroine, Noriko. Noriko takes a job with a local newspaper and quickly befriends the geeky Kakeru, a math whiz who wants to help her understand the practical uses of calculus in journalism. Kakeru begins by teaching Noriko (and the book's readers) the basics of calculus, such as approximating with functions, derivatives, techniques of differentiation, and polynomials. As the book progresses, Noriko and readers learn calculus, including complex concepts like the Fundamental Theorem of Calculus, exponential and logarithmic functions, the Taylor Expansion, and partial differentiation. This charming, easy-to-read guide uses real-world examples like celebrity weight gain, TV commercials, and economics, and includes examples and exercises (with answer keys) to help readers learn.This EduManga book is a translation from a bestselling series in Japan, co-published with Ohmsha, Ltd. of Tokyo, Japan.Paperback. Book Condition: New. 179mm x 16mm x 236mm. Paperback. Noriko is just getting started as a junior reporter for the "Asagake Times." She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the sm.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 238 pages. 0.503. Bookseller Inventory # 97815932719472009. Paperback. Book Condition: New. This brand new copy of The Manga Guide to Calculus by Becom Co Ltd should be with you within 7 or 8 working days for UK deliveries. International delivery varies by country. Simple no nonsense service from Wordery. Bookseller Inventory # 97815932719 |
Geometry and Symmetry
Geometry and Symmetry
Clear concise introduction to the geometry of euclidean, affine and projective spaces with special emphasis on the important groups of symmetries of these spaces. Topics include algebraic and combinatoric preliminaries, isometries and similarities, crystallography, fields and vector spaces, affine spaces, projective space, much more. Advanced undergraduate level. Problems. Bibliography. 1968 edition. |
How to Learn Calculus Theorems
Calculus is founded in 17th century and since then it is used in mathematics to solve many problems. Calculus includes rate of change and if someone understand calculus, he will be able to solve problems in science, economics, statistics etc. If you want to understand calculus, we will give you some instructions for learning.
Learning Calculus theorems
- You have to find right literature from which you will learn. You can find those books in library or you can find online resources on some websites that have different texts about mathematics. Whichever resource you choose, you will find information that are necessary for studying calculus.
- When you find theorems try to remember them. Calculus theorems are very important and if you memorize them, you will make your further learning much more easier. Some theorems are complicated so you will have to repeat them before you memorize it.
- Whenever you have free time, practice calculus problems. When you have memorized calculus theorems you will be able to solve many calculus problems. As much you practice problems as much you will be able to solve more complex calculus tasks.
Tips and warnings
You should plan your studying. Decide which concepts you will work and decide what time will be reserved for it. It will help you to gain a work habits and also, it will make calculus materials easier to master.
If you have problems with some calculus concepts, you should consult your friend or your professor. If you practice orderly you will master calculus material pretty faster. |
With the present development of the computer technology, it is necessary to develop efficient algorithms for solving problems in science, engineering and technology. This course gives a complete procedure for solving different kinds of problems occur in engineering numerically.
OBJECTIVES
At the end of the course, the students would be acquainted with the basic concepts in numerical methods and their uses are summarized as follows:
i. The roots of nonlinear (algebraic or transcendental) equations, solutions of large system of linear equations and eigen value problem of a matrix can be obtained numerically where analytical methods fail to give solution.
ii. When huge amounts of experimental data are involved, the methods discussed on interpolation will be useful in constructing approximate polynomial to represent the data and to find the intermediate values. |
Algebraic Videogame Programming
Bootstrap is a curricular module for students ages 12-16, which teaches algebraic and geometric concepts through computer programming. At the end of the module, students have a completed workbook filled with word problems, notes and math challenges, as well as a videogame of their own design, which they can share with friends and family. Our one-page overview summarizes our approach and its connection to algebra.
We work with schools, districts and tech-educational programs across the country, helping teachers reach thousands of students each year. Bootstrap has been used in both math and technology classes, often by teachers with limited prior experience teaching computing. We believe strongly in high-quality professional development, and our hands-on teacher-training workshops cover both content and pedagogic techniques for delivering Bootstrap effectively.
For Math Teachers
Bootstrap also builds in a pedagogical approach to solving Word Problems called the Design Recipe. Students solve word problems to make a rocket fly (linear equations), respond to keypresses (piecewise functions) or explode when it hits a meteor (distance formula). In fact, this same technique has been successfully used at the university level for decades.
For CS Teachers
Knowing how to write code is good, but it doesn't make you a programmer. In addition to learning a full-strength programming language, Bootstrap teaches solid program design skills, such as stating input and types, writing test cases, and explaining code to others. After Bootstrap, these skills can be put to use in other programming languages, letting students build on what they've learned.
A Note for Parents
Before algebra, your child's math homework was all about computing an answer, by adding, subtracting, solving, etc. Once Algebra introduces functions, however, everything changes. Rather than "solving for x", they'll be asked to think about whether a function f(x) is linear, how many roots it has, etc. The jump from "getting the answer" to "describing a function" is challenging for students, as it requires them to think more abstractly than ever before. Algebra isn't just harder — it's completely different.
Unlike Python, Scratch or Javascript, functions and variables behave exactly the same way in Bootstrap that they do in your child's math book. Bootstrap focuses on order of operations, the Cartesian plane, function composition and definition, solving word problems and more. Instead of using the Pythagorean Theorem to calculate the heights of ladders leaning against walls, students use the same class time to determine the distance between characters in their game and make them collide. By shifting classwork from abstract pencil-and-paper problems to a series of relevant programming problems, Bootstrap demonstrates how algebra applies in the real world, using an exciting, hands-on project.
""
—
Our team
Bootstrap is a joint partnership between Emmanuel Schanzer (a computer scientist and former teacher, now at the Harvard Graduate School of Education), Kathi Fisler (WPI), and Shriram Krishnamurthi (Brown University). Emma Youndtsmith is our regional manager in the Northeast. Together, we build curricula, software, and professional development for teachers across the country. Bootstrap builds on the pioneering work of Program By Design by Matthias Felleisen and his collaborators.
Our Supporters
We would like to thank the following, for their volunteer and financial support over the years: Apple, Cisco, the Entertainment Software Association (ESA), Facebook, Google, as well as the Google Inc. Charitable Giving Fund of Tides Foundation, IBM, Jane Street Capital, LinkedIn, Microsoft, The National Science Foundation, NVIDIA, Thomson/Reuters, TripAdvisor and the generous individuals who have given us private donations.
If you would like to support Bootstrap with a donation, send a check made out to Brown University to our PI, Shriram Krishnamurthi,
at his mailing address. Be sure to include this letter, indicating that you wish for the funds to be put towards Bootstrap. Once your check is received, we'll send you a receipt for your tax records. |
Precalculus - 4th edition
Summary: This edition
Chapter Opener Each chapter begins with the discussion of a real-world situation that uses mathematics from the chapter. Examples and exercises that relate back to the opener are included in the chapter.
Graphing Calculator Discussions Optional graphing calculator discussions have been included in the text. They are clearly marked by graphing calculator icons so that they can be easily skipped if desired. Students who do not use a graphing calculator can still benefit from the technology discussions, as well as from the calculator generated graphs occurring in the text. The graphing calculator is used as a tool to support and enhance algebraic conclusions, not to make conclusions.
For Thought Each exercise set is preceded by a set of ten true/false questions that review the basic concepts in the section, help check student understanding before beginning the exercises, and offer opportunities for writing and/or discussion. The answers to all For Thought exercises are included in the back of the student edition.
Writing/Discussion and Cooperative Learning Exercises These exercises deepen students' understanding by giving them the opportunity to express mathematical ideas both in writing and to their classmates during small group or team discussions.
Linking Concepts Located at the end of nearly every exercise set, these multi-part exercises and explorations can be used for individual or group work. The idea of this feature is to use concepts from the current section along with concepts from preceding sections (or chapters) to solve problems that illustrate the links among various concepts. Some parts of these questions are open-ended and require more thought than standard skill-building exercises. Answers are given in the Instructor's Edition only, and full solutions can be found in the Instructor's Solutions Manual.
Chapter Review Exercises These exercises are designed to give students a comprehensive review of the chapter without reference to individual sections and prepare students for the chapter test.
Chapter Test The problems in the Chapter Test measure students' readiness for a typical one-hour classroom test. Instructors may also use them as a model for their own end-of-chapter tests. Students should be aware that their in-class test could vary from the Chapter Test due to different emphasis placed on the topics by individual instructors.
Tying It All Together Found at the end of most chapters, these exercises help students review selected concepts from the present and prior chapters, and require students to integrate multiple concepts and skills.
Index of Applications The many applications contained within the text are listed in the Index of Applications. The applications are page referenced and grouped by subject matter.
4.1. Exponential Functions and Their Applications 4.2. Logarithmic Functions and Their Applications 4.3. Rules of Logarithms 4.4. More Equations and Applications
Chapter 5. The Trigonometric Functions
5.1. Angles and Their Measurements 5.2. The Sine and Cosine Functions 5.3. The Graphs of the Sine and Cosine Functions 5.4. The Other Trigonometric Functions and Their Graphs 5.5. The Inverse Trigonometric Functions 5.6. Right Triangle Trigonometry |
How useful is mathematical proof as a mechanical engineer?
Specifically I plan on specializing as a Mechatronics engineer. I recently bought the book "Mathematical Proofs: A Transition to Advanced Mathematics" and I plan to study it on my own due to curiosity and interest towards mathematics. I would like to listen on one's opinion on how useful it would be as an engineer to understand the theoretical proofs behind the math.
I'm not an engineer, but I know many of them. I can say with a good level of confidence that knowing proof behind mathematical concepts helps very little. Knowing how to prove the square root of 2 is irrational or the rising sun lemma does nothing for you when it comes to your every day work.
It will most probably not be of any direct use to you. However, knowing and understanding how proofs work in math will lead you to a better understanding of the tools you are using in your work. Secondly, it also makes you get used to thinking clearly and also gets you in the habit of stating everything you do very precisely. As a math and physics major, and spending quite some time on pure math-type stuff, physics textbooks can definitely be a bit frustrating sometimes in that they don't state things precisely enough.My university only teaches Calculus in 3 sections, so I am assuming Calc 3 and 4 are multivariable and vector calculus at your univ. I just finished a second semester in linear algebra and a first semester in complex variables (<--final in two days). Complex variables was the hardest class I have ever taken in my life, much more so than linear algebra or differential equations. However, it is very fascinating and it would have been nicer if the professor would have taught the applications in the class, but you can always study applications on your own.
Not sure about mechanical engineering but I am pretty sure you can't go wrong with linear algebra and differential equations in engineering. I know complex analysis is applicable in some fields but I think the only thing that you will take from it is being able to solve difficult integrals with residues/contours. I would take numerical analysis if I were you.
complex variables is also useful for learning conformal mapping which transforms extremely brutal and crazy geometries into not so brutal and crazy ones. that said, computers do that much better than humans do since often you must "guess" the best transform for the job.So would this be "Euclidean Geometry"? I have a course at my university called that; it is offered for third years and requires "Mathematical Proof" course as a prerequisite.
Regarding knowing how to prove theorems: It will certainly strengthen your understanding of the tools you use as an engineer, however I don't think you will find yourself proving theorems on a day-to-day basis. If you plan on doing research in the field of engineering, I can see it being more important, though. You should speak with some of the faculty in the mechanical engineering department and see what they say.
Quote by theBEASTBoth of the courses you mentioned would be helpful. Here are a couple more courses that might be useful to you:
Depends on what kind of engineering you are doing. There are people who do robotics who try to apply very heavy math, for example. On the other end of the spectrum, there are engineers who don't really use any math at all to speak of.
writing things in a pure math notation makes it harder for scientists and engineers to understand, not easier. sure its more "precise" but it does not offer the all-important physical intuition.
That's too much of a generalization. In some cases, if it makes them harder to "understand", that is only because they are content with plugging and chugging and NOT understanding. In other cases, the extra notation is superfluous, except if you want more generality and so on. For example, if you are working in three dimensions, then the old vector notation does a pretty good job. However, if you are working in high dimensions, differential forms really help. The idea that it doesn't offer the all-important physical intuition is not the fault of notation. That is the fault of mathematicians who refuse to explain the ideas behind things and are only concerned with stating things formally and logically.
Indeed from my own experience, I believe that learning mathematical proofs will be of very little use for physical scientists and engineers.
That's probably because you don't really see the intuition behind the proofs, based on your above statement. I can't blame you. Probably most mathematicians fall into the trap of being too formal and obscuring the intuition, but in my experience, the engineers and physicists were often even worse in that respect, though not always.
One thing I noticed is that many ideas in engineering are essentially mathematical ideas, but whereas the mathematician might try to prove the idea using more formal methods, the engineer may skip through the precise details of the proof and yet arrive at the result using "intuition". By intuition, I refer to a process where the engineer can process the main idea of the mathematical proof in his/her mind and arrive at the result without using the actual terminology of the proof that is entailed should one need to actually write down the formal proof. (Sometimes however this results in mistakes that can have big consequences; to prevent this an engineer might use experiments to verify his result holds, which still often saves more time than a rigorous proof).
Here's a trivial example from EE:
Each push-button/toggle switch can control at most 2 possible states. *Then k switches can control [itex]2^{k}[/itex] possible states.* Thus if you want to control m possible states, you need enough switches to satisfy the inequality
[itex] k > log_{2}(m) [/itex].
*Of course, the engineer, or rather, any sane person who is pressed on time would quickly use intuition to arrive at this result, whereas the "rigorous way" of solving this problem would be to use induction, i.e. by showing that the addition of a switch multiplies the state space by 2, and then using that as the inductive case in conjunction with the base case that having a single switch allows you to control 2 states. Using induction to solve the problem makes the proof more formal, yet it takes longer. For the engineer, the important resource is time, not the added bit of certainty that comes from proving the result using more formal means. Of course this varies depending on the problem.
Even the work that most mathematicians do however is not perfectly rigorous. The perfectly rigorous statements are not even expressed in natural languages. They are usually expressed in the form of mathematical logic, for instance the formal definition of a basis of a vector space:
Even up to this level, the formalism is done only "for the records". Sane people usually default to intuition depending on the nature of the task. For engineering, you will be defaulting to intuition many times to the point that you do not notice your mind is proving results (such as the EE example above) without even knowing they are coming from the perspective of proof-based math.
I have seen this observation in a ton of places, from computing and economics to physical chemistry, where many logical but not totally obvious steps are skipped for the sake of time/convenience. It's all a matter of intuition vs. formalism, just like the debates between Hilbert and Poincare, and the scientist/engineer must decide prudently which is to exercise in a given situation.
It's all a matter of intuition vs. formalism, just like the debates between Hilbert and Poincare, and the scientist/engineer must decide prudently which is to exercise in a given situation.
I don't think it's "all" a matter of that.
First off, as you said, mathematicians themselves aren't always completely rigorous, even by your stereotypical standards. Secondly, there's the question of subject matter. A lot of the subject matter won't be relevant to engineering in most cases. The question then, if you want to use the math is what areas of engineering use the math? Thirdly, there's the question of taking stuff on faith to save time, which I like to minimize and engineers who like to minimize that would find more math to be useful. Fourthly, there's the idea that engineering may often rely more on practical experience than on theory. There's a lot of stuff that you might not calculate. You just get a feel for it through experience.
I think in cases where not much math is used, you can always ask if more math would help. Sometimes, it will, sometimes it won't. The question doesn't always have a straight-forward answer. I'm sure there are a million cases out there in science and engineering where people are being too mathematical and equally many where they are not being mathematical enough. That's my suspicion. It all depends on the specifics of what you are trying to accomplish. There's no ready-made, one-size-fits-all answer to this question. |
For the staff in the Department of Developmental Math at Seton Hall University, a top priority is to ensure that incoming students are set for classes from day one.The staff's challenge, therefore, is to make sure that placement tests are administered and completed well ahead of time.These tests are typically very labor intensive, taking away precious time which could otherwise be spent orienting students to their new environment. The Maplesoft-MAA Placement Test Suite helps institutions place their students in the right courses quickly, easily, and at a fraction of the cost normally associated with traditional placement methods. This test suite automates the entire process, enabling the test to be taken anytime and anywhere. Now administering the placement tests is totally stress-free and hardly involves any staff time at Seton Hall.
The faculty's objective was to ensure that students take responsibility for reviewing material from previous courses before starting new ones. This would save a lot of time and effort on the faculty's part and make new courses more efficient by bringing students up-to-date before the start of the course. When they chose Maple T.A. - a Web-based system for creating tests, assignments, and exercises that automatically assess student responses and performance - little did the faculty realize that the successful outcome would go far beyond the anticipated increase in student responsibility.
Two years ago, the Polytechnical Institute of Noordelijke Hogeschool Leeuwarden in Holland (NHL) introduced a collection of online math exercises using Maple T.A.® Since then, 95% of the engineering students who regularly evaluated their math knowledge with Maple T.A. online exercises passed with significant improvement in their final scores. Many of the students who did not regularly test their skills using these exercises failed the course.
Selcuk Arbor is a Computer Science student at Ryerson University in Toronto, Canada. A serious student, Arbor did well in all courses, except Physics. When he didn't pass the midterm exam, he was determined to try harder. Knowing that his professor was a Maple evangelist, he proposed a challenge to turn the entire exam into a Maplet. Read how Maplets helped Arbor pass the exam.
An applied mathematician, Chartier is passionate about finding relevant, exciting examples of using mathematics. He knows that examples engage students. One of his trusted assistants in this project is Maple, Maplesoft's world-leading computation engine, which offers the breadth and depth to handle every type of mathematics.
When Maplesoft® introduced its smart document environment in Maple™ 10 - now enhanced in the recently announced Maple 11 - the new interface presented a paradigm shift in performing complex mathematical calculations. The company knew that the point and click environment would transform the way engineers, students, and researchers approached and used math.
Jim Herod, Professor Emeritus for Georgia Institute of Technology's School of Mathematics, has taught at Georgia Tech for 35 years and is now retired in Southwest Alabama. In his retirement, Herod still teaches a Partial Differential Equations class remotely to engineers working toward masters and doctorate degrees. Since his students are located around the world, he needed a way to efficiently communicate lectures, distribute assignments, and receive reports.
At the State University of New York (SUNY) at Stony Brook, academic success is as important to the university as it is to the students. They want their students to succeed, and the first step to ensuring they do is making sure they are enrolled in the proper classes. For this reason, Stony Brook's mathematics department administers placement tests every year to assess the student's level of math knowledge and the appropriate courses.
To raise the success level in his algebra course, Professor Peiris, Math Department Chair at Indian River Community College, Florida, made a commitment to himself: improve his students' conceptual understanding and provide tutorial practice of math problems while accommodating different learning styles. His strategy was to increase the use of technology in his classroom, and he turned to Maplesoft™, a leading provider of high-performance software tools for science and mathematics.
For many students studying Mathematics at the University of Queensland, using Maple® software is a daily event. In fact Maple has been an integral part of the math taught in many courses including science and engineering.
Over the last 40 years, Finite Element Analysis (FEA) has become the standard method for analyzing complex problems that involve systems of partial differential equations with arbitrary boundary conditions.
This is the second year I have been using Maple T.A. as a tool to enrich the academic experience of my students. The main reason I like this software is because Maple T.A., unlike other pre-packaged software around, gives one the tools needed to customize his or her questions based on the actual needs of a given Math or Physics class.
Maple is used extensively at Rensselaer Polytechnic Institute (RPI)—a leading technological research university—and is accessible to all undergraduate students through their mobile computing program. The availability of Maple across multiple disciplines, made possible by the laptop program, characterizes the interactive approach to research and teaching at RPI. |
Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. In this textbook, João Hespanha covers the key topics of the field in a unique lecture-style format, making the book easy to use for instructors and students. He looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization, and examines advanced foundational topics such as multivariable poles and zeros, and LQG/LQR.
The textbook presents only the most essential mathematical derivations, and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these important tools. The balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Solutions to the theoretical and computational exercises are also available for instructors |
ALEKS has not replaced face-to-face instruction as the assigned instructors and an instructional assistant work individually with students on topics as needed. Transfer level Mathematics (MTH 111 College Algebra and higher) is still taught in the traditional lecture format. ALEKS includes the use of video/audio, text, an electronic textbook and class workbooks, in addition to the instructor and instructional assistant.
Unlike the traditional lecture format locked to set topic schedules for each week of the term-- topics which some students may have mastered, but are too challenging for others who need more time-- ALEKS helps students to focus on the skills they have not mastered as it builds on what they already know. ALEKS is accessible from any computer with web access so that students can work on skill topics outside of class at time convenient for them.
In Mathematics classes at Oregon Coast, students are encouraged to ask questions and seek assistance at every opportunity. Instructors are here to help and guide students to success. Students also can request additional tutoring assistance. Oregon Coast looks forward to further refinements of the Mathematics placement process and to improvements in mathematics instruction in the terms ahead. |
97802018612Packaging and the Environment: Real-World Mathematics through Science (Washington MESA)
The MESA Series combines essential pre-algebra topics with exciting hands-on science explorations to motivate students in both mathematics and science. Using materials and group collaboration to solve open-ended problems, students make connections between classroom and real-world mathematics and science. These easy-to-use Teacher Resource Books include activity overviews, background information, reproducible activity masters, and assessment strategies. Grades 5-8 |
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