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The fact that the vast majority of the numbers on the real number line are irrational (i.e. cannot be put in the form p/q, where p and q are integers) has an associated consequence that the vast majority of equations involving powers of x (i.e. polynomials) are insoluble by closed analytical techniques.
This coursework's solution implies finding values of x say c1, c2-...c3 where f(c1)=0; f(c2)=0 and so on. Further transcendental equations and non- linear equations require numerical methods for their solution. It is to be noted that in no way are numerical methods inferior to analytical solutions, they are indeed the only practical solutions available, however on the down side no exact solution is possible and error bounds have to be placed on the solution given.
In this coursework three main methods of solution from one-dimensional equations are given, each of the methods could be extended to the multi-dimensional case. The aim of this coursework is to show example of the methods in action, where these are successful and where they are not. A comparison between the methods will also be attempted. |
This course presents a variety of applications of algebra to real-world problems and includes an introduction to set theory, probability and statistics. Topics include linear functions, systems of linear equations and inequalities, matrices, linear programming, basic counting and probability, and the mathematics of finance. Prerequisite: Grade G.E.
Prerequisite(s) / Corequisite(s):
Grade
Course Rotation for Day Program:
Offered Fall and Spring.
Text(s):
Most current editions of the following:
Finite Mathematics
By Rolf, Howard L. (Thompson-Brooks/Cole) Recommended
Finite Mathematics
By Armstrong, Bill & Don Davis (Prentice Hall) Recommended
Course Objectives
To communicate mathematically in both written and verbal forms.
To reason with symbolic and graphical representations.
To use mathematics to solve business and other real-world problems.
To construct and discuss mathematical models.
To use technology, such as graphing calculators and computers, to enhance mathematical understandings and to solve application problems.
Measurable Learning Outcomes:
Graph systems of linear equations and inequalities.
Solve systems of linear equations and inequalities both graphically and algebraically |
I am trying to gather an unofficial guide book for the following book
Title: Understanding Analysis
Author: Stephen Abbott
ISBN-13: 978-0387-95060-0
The following three chapter and sections need to have an approximate two page summary written that summarize the content, mathematician credited with first using/discovering concept, theorems, main idea/concepts, important cases, etc etc..... and all exercises for the sections (ten from 4.6, seven from 5.4, and eight from 6.6, a total of 25 problems andsee attachment
The representing cylinders would be 100 feet long 3 feet wide.
1. On the side of each cylinder there would be a rectangular box. The first box would be labeled weight, and I could put any weight I choose to in the box say 3lbs. The pressure of course would start at one atmosphere. The piston as shown above would fall down the cylinder until it met an equal pressure pushing upwards. So cylinder 1 would show how |
calculus: Mathematics for Calculus
This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling ...Show synopsisThis best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, this book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas. The authors' attention to detail and clarity, the same as found in James Stewart's market-leading Calculus text, is what makes this text the market leader840068867 Brand new book. International Edition. Ship...New. 08400688 Precalculus: Mathematics for Calculus
Book is actually pretty good, I like the fact that its first chapter is a review of stuff from intermediate algebra...if you are using this book...and you have just finished intermediate/college algebra...get this book and do each section of ch. 1...this will set you up for a good foundation for the ...
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A beautiful presentation and treatment of all math required before studying calculus. Comprehensive, and a strong focus on theory. Lots of problems to test yourself. Get through this and then star in your calculus study, as you are now VERY well prepared.
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This book is one of the best out there in the current markets. Dr. Stewart explains this subject with geometrical shapes to better understand the subject. For example he explains and proves the the phytogorean theorem, laws of sines and cosines, and alot more. Highly recommend this book as well as |
This algebra lesson helps students make the connection between functions and their graphs. The model of the level of water in a bathtub is used. Students will watch the graph and a chart of the depth of the water at...
This lesson uses the example of successive discounts at a retail store to demonstrate numeric, algebraic, and graphical representations of compositions of mathematical functions. Students will get the opportunity to...
MathGrapher is a stand-out graphing tool designed for students, scientists and engineers. Visitors can read the Introduction to get started, as it contains information about the various functions that the tool can...
This online course includes elements from an undergraduate seminar on mathematical problem solving. The material will help students develop their mathematical and problem solving skills. A few topics that are covered...
This course, presented by MIT and taught by Professor Alar Toomre, provides an introduction to numerical analysis. The material looks at the basic techniques for the efficient numerical solution of problems in science... |
Linear Algebra
9780817642945
ISBN:
0817642943
Edition: 2 Pub Date: 2004 Publisher: Birkhauser Boston
Summary: From a review of the first edition: "A logical development of the subject . . . all the important theorems and results are discussed in terms of simple worked examples. The student's understanding . . . is tested by problems at the end of each subsection, and every chapter ends with exercises." a?CURRENT SCIENCE A cornerstone of undergraduate mathematics, science, and engineering, this clear and rigorous presentation... of the fundamentals of linear algebra is unique in its emphasis and integration of computational skills and mathematical abstractions. The power and utility of this beautiful subject is demonstrated, in particular, in its focus on linear recurrence, difference and differential equations that affect applications in physics, computer science, and economics. Key topics and features: a? Linear equations, matrices, determinants, vector spaces, complex vector spaces, inner products, Jordan canonical forms, and quadratic forms a? Rich selection of examples and explanations, as well as a wide range of exercises at the end of every section a? Selected answers and hints a? Excellent index This second edition includes substantial revisions, new material on minimal polynomials and diagonalization, as well as a variety of new applications. The text will serve theoretical and applied courses and is ideal for self-study. With its important approach to linear algebra as a coherent part of mathematics and as a vital component of the natural and social sciences, Linear Algebra, Second Edition will challenge and benefit a broad audience.
Kwak, Jin Ho is the author of Linear Algebra, published 2004 under ISBN 9780817642945 and 0817642943. Seven hundred twenty eight Linear Algebra textbooks are available for sale on ValoreBooks.com, two hundred six used from the cheapest price of $11.07, or buy new starting at $3.99, Unused, Soft-cover Book with cover and/or page damage (cut, tear or bend/crease typically). Book may have remainder mark on it. Does NOT affect book content! Items ship w [more]
New, Unused, Soft-cover Book with cover and/or page damage (cut, tear or bend/crease typically). Book may have remainder mark on it. Does NOT affect book content! Items ship within 24 hours with FREE tracking |
What jobs use college algebra and what concepts of college algebra do they use?
I have to write a paper for my college algebra class on jobs that use college algebra and the concepts that the jobs use. I've researched and found jobs, just not the concepts. Someone please help me out!
Asked By: - 6/29/2010
Best Answer - Chosen by Asker
All engineering jobs use college algebra either directly or indirectly. If the engineers don't use the algebra in their designs, maintenance or repairs, they will use meters or computers and programs that do. Engineers need to use vectors, scalar products, vector products and linear equations. In stress analysis, the...
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Answered By: Pisces ♥ Math - 7/2/2010
Additional Answers (1)
Great answer. Also in business college algebra principles will be used to calculate prices, break even points, and advertising budgets versus costs and expenses. Another is to calculate the advertisement to editorial ratio of a newspaper or website |
books.google.com - This to Smooth Manifolds
Introduction to Smooth Manifolds Along the way, the book introduces students to some of the most important examples of geometric structures that manifolds can carry, such as Riemannian metrics, symplectic structures, and foliations. The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. John M. Lee is Professor of Mathematics at the University of Washington in Seattle, where he regularly teaches graduate courses on the topology and geometry of manifolds. He was the recipient of the American Mathematical Society's Centennial Research Fellowship and he is the author of two previous Springer books, Introduction to Topological Manifolds (2000) and Riemannian Manifolds: An Introduction to Curvature (1997).
This book is an antidote to the more common style of math text. So many math books feel like they were written by mathematicians, which is to say their authors prize being terse over being ...Read full review
Corrections to Introduction to Smooth Manifolds Introduction to Smooth Manifolds. by John M. Lee. January 14, 2008. Changes or additions made in the past twelve months are dated. ... ~lee/ Books/ Smooth/ errata.pdf
Newtonian limit of GR Text - Physics Forums Library See for example John M. Lee, Introduction to Smooth Manifolds, Springer, for some good discussion of levels of structure in the theory of smooth manifolds. ... archive/ index.php/ t-202783.html |
Overview
Editorial Reviews
Booknews
This text provides a blend of traditional and reform instructional approaches needed to read, write, speak, and think mathematically using the language of algebra. Tussy (Citrus College) and Gustafson (Rock Valley College) provide 11 chapters that expand the students' mathematical reasoning abilities and give them a set of survival skills that will help them to succeed in a world that increasingly requires analytic thinking. They include worked examples followed by self-checks, problem-solving strategies, applications and connections to other disciplines, in-depth coverage of geometry and graphing, study sets and reviews, and one-page summaries of key concepts. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Product Details
ISBN-13: 9780538734035
Publisher: Cengage Learning
Publication date: 1/6/2010
Edition description: Student
Edition number: 4
Pages: 512
Product dimensions: 8.50 (w) x 10.80 (h) x 1.10 (d)
Meet the Author
: Alan Tussy teaches all levels of developmental mathematics at Citrus College in Glendora, CA. He has written nine math books-a paperback series and a hard-cover series. An extraordinary author, he is dedicated to his students' success, relentlessly meticulous, creative, and a visionary who maintains a keen focus on his students' greatest challenges. Alan received his Bachelor of Science degree in Mathematics from the University of Redlands and his Master of Science degree in Applied Mathematics from California State University, Los Angeles. He has taught up and down the curriculum from prealgebra to differential equations. He is currently focusing on the developmental math courses. Professor Tussy is a member of the American Mathematical Association of Two-Year Colleges.
R. David Gustafson is Professor Emeritus of Mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. He is coauthor of several best-selling mathematics textbooks, including Gustafson/Frisk/Hughes' COLLEGE ALGEBRA, Gustafson/Karr/Massey's BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, and the Tussy/Gustafson and Tussy/Gustafson/Koenig developmental mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in AMATYC as a Midwest Vice-president and has been President of IMACC, AMATYC's Illinois affiliate. He earned a Master of Arts from Rockford College in Illinois, as well as a Master of Science from Northern Illinois University.
Diane Koenig received a Bachelor of Science degree in Secondary Math Education from Illinois State University in 1980. She began her career at Rock Valley College in 1981, when she became the Math Supervisor for the newly formed Personalized Learning Center. Earning her Master's Degree in Applied Mathematics from Northern Illinois University, Ms. Koenig in 1984 had the distinction of becoming the first full-time woman mathematics faculty at Rock Valley College. In addition to being nominated for AMATYC's Excellence in Teaching Award, Diane Koenig was chosen as the Rock Valley College Faculty of the Year by her peers in 2005, and, in 2006, she was awarded the NISOD Teaching Excellence Award as well as the Illinois Mathematics Association of Community Colleges Award for Teaching Excellence. In addition to her teaching, Ms. Koenig has been an active member of the Illinois Mathematics Association of Community Colleges (IMACC). As a member, she has served on the board of directors, on a state-level task force rewriting the course outlines for the developmental mathematics courses, and as the association's newsletter |
This isn't really a math textbook, but math is an extremely important
part of physics. Physics textbooks usually at least attempt to include
math support for key ideas, reviewing e.g. how to do a cross product.
The problem with this is that this topical review tends to be scattered
throughout the text or collected in an appendix that students rarely
find when they most need it (either way).
I don't really like either of these solutions. My own solution is
eventually going to be to write a short lecture-note style math
textbook that contains just precisely what is needed in order to really
get going with physics at least through the undergraduate level, including stuff needed in the introductory classes one takes as a
freshman. Most mathematical physics or physical mathematics books
concentrate on differential equations or really abstract stuff like
group theory. Most intro physics students struggle, on the other hand,
with simple things like decomposing vectors into components and
adding them componentwise, with the quadratic formula, with complex
numbers, with simple calculus techniques. Until these things are
mastered, differential equations are just a cruel joke.
Math texts tend to be useless for this kind of thing, alas. One would
need three or four of them - one for vectors, one for calculus, one for
algebra, one for complex numbers. It is rare to find a single book that
treats all of this and does so simply and without giving the
student a dozen examples or exercises per equation or relation covered
in the book. What is needed is a comprehensive review of material
that is shallow and fast enough to let a student quickly recall it if
they've seen it before well enough to use, yet deep and complete enough
that they can get to where they can work with the math even if
they have not had a full course in it, or if they can't remember
three words about e.g. complex variables from the two weeks three years
ago when they covered them.
In the meantime (until I complete this fairly monumental process of
splitting off a whole other book on intro math for physics) I'm putting
a math review chapter first in the book, right here where you are
reading these words. I recommend skimming it to learn what it
contains, then making a slightly slower pass to review it, then go ahead
and move on the the physics and come back anytime you are stumped
by not remembering how to integrate something like (for example):
(1)
Here are some of the things you should be able to find help for in this
chapter:
Numbers
Integers, real numbers, complex numbers, prime numbers, important
numbers, the algebraic representation of numbers. Physics is all about
numbers.
Algebra
Algebra is the symbolic manipulation of numbers according to certain
rules to (for example) solve for a particular desired physical quantity
in terms of others. We also review various well-known functions and
certain expansions.
There is a beautiful relationship between the complex numbers and trig
functions such as sine, cosine and tangent. This relationship is
encoded in the ``complex exponential''
, which turns out to
be a very important and useful relationship. We review this in a
way that hopefully will make working with these complex numbers and trig
functions both easy.
Differentiation
We quickly review what differentiation is, and then present,
sometimes with a quick proof, a table of derivatives of functions
that you should know to make learning physics at this level
straightforward.
Integration
Integration is basically antidifferentiation or summation. Since many
physical relations involve summing, or integrating, over extended
distributions of mass, of charge, of current, of fields, we present a
table of integrals (some of them worked out for you in detail so you can
see how it goes). |
Which brings up the question of how do you get students to actually DO
mathematics? If you have to hide the answer from the student one has to
wonder if they are doing mathematics rather than repeating what they have
memorized or applying a technique they learned to a problem guaranteed to be
adapted to the technique.
Can Mathematica be used to broaden the domain of students who can start
doing some real mathematics? It seems intuitive that Mathematica can play an
important role here just because of the ease of doing the drudge work and
exploring various cases. (Could one be a good mathematician without being an
accurate paper and pencil calculator?) Just using Mathematica to automate
old techniques is not going to achieve this aim. So some suggestions:
How about giving students packages that have hierarchical depth so they can
calculate everything, at all levels, while doing derivations, proofs or
calculations? How about providing convenience routines that are adapted to
the area of interest? WRI is not great at this, and they don't have the time
for it, but they have provided the underlying capabilities for it. There is
plenty of room for people to add capability here. A requirement is that
students must be reasonably capable with Mathematica when they come to it.
How about getting away from standardized tests and having students write
mathematical essays on topics small or large? Mathematica is great at this
kind of thing. There may be no fixed answer and students may go in different
directions and even run into insurmountable problems.
How about letting students rediscover existing mathematics? Of course, they
may rediscover it on the internet so there is a different option. How about
letting students clarify existing proofs or topics? Perhaps they could
expand on difficult steps in a proof. Perhaps they could correlate a visual
proof with a formal proof. Given Mathematica's graphics, active calculation,
dynamics and control structures they might find whole new ways to present
and clarify established mathematical ideas. They can't do this without
understanding the mathematics. It requires innovation and it is definitely
value added.
How about letting students pick their own subject related topic? How about
letting groups of students work on a notebook together?
Maybe all this does not fit in with modern automated mass produced
education. I'm not an expert on it, having never taught anyone anything in
my whole life. I just comment from the perspective of a poor student.
David Park
djmpark at comcast.net
From: Murray Eisenberg [mailto:murray at math.umass.edu]
Back when I was doing such things with student projects in Mathematica,
I sure wish I had had use of David Park's HiddenNotebookData function
from his Presentations application: it would have simplified doing a lot
of things.
(But not all, probably: if you want to test a students definition of a
function on-the-fly against randomized input data, you need to hide a
"correct" definition of that function as well as generation of the test
data. At that point it may be just simpler to use a separate encoded
package of the sort I described in another post on this topic. Doing
this with a whole suite of student functions, each tested against a
series of test data, would likely create so many strings from
HiddenNotebokData that one would want to keep all that separate from the
student's own notebook where she was developing and testing the functions.) |
Synopses & Reviews
Publisher Comments:
This updated third edition addresses the mathematical skills that a programmer needs to develop a 3D game engine and computer graphics for professional-level games. MATHEMATICS FOR 3D GAME PROGRAMMING & COMPUTER GRAPHICS, THIRD EDITION is suitable for advanced programmers who are experienced with C++, DirectX, or OpenGL. The book begins at a fairly basic level, covering areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination and visibility determination. It discusses the math first; then it presents how to translate the math into programs. By providing the math behind the effect, screenshots of the results, and samples of code that translate the math so that the effect is achieved, readers get the full story rather than only a mathematical explanation or a set of code samples that are not clearly drawn from mathematical expressions. With this revised edition, almost every chapter will provide a programming example taken directly from a real-world game programming context, and based on programs that have been written and used in game engine development.
Synopsis:
Synopsis:
About the Author
Eric Lengyel is the author of the first two editions of the book, "Mathematics for 3D Game Programming and Computer Graphics." He is the Chief Technology Officer for the game engine development studio Terathon Software. Eric holds an M.S. in Mathematics from Virginia Tech and has written several articles for gamasutra.com and the "Game Programming Gems" series.
"Synopsis"
by Netread,"Synopsis"
by Netread, |
For anyone who needs to learn calculus, the best place to start is by gaining a solid foundation in precalculus concepts. This new book provides that foundation. It includes only the topics that they'll need to succeed in calculus. Axler explores the necessary topics in greater detail. Readers will benefit from the straightforward definitions and examples of complex concepts. Step-by-step solutions for odd-numbered exercises are also included so they can model their own applications of what they've learned. In addition, chapter openers and end-of-chapter summaries highlight the material to be learned. Any reader who needs to learn precalculus will benefit from this book.
{"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":151.69,"ASIN":"0470416742","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":185.81,"ASIN":"0321558235","isPreorder":0}],"shippingId":"0470416742::hlHjFFnfgP06SNwWtWFs5REMq5JATrFU3J5s0iFhLrueiuvSh58UclMsq1BUdF8yrb07Z41XjlFQgaebNRzl1S8IxIpU9uQp3vCRz%2BrLThI%3D,0321558235::h%2Bp8NT8nlbdBc%2FBeHAhWBw%2Fr8uYE8iTCHgCmpiaV3lQk61uz2tFgXCpCyZn6YpKYZvtdyDbDIIUa755GOTGriB9fsHnG%2FbIPJm9sg8hjGpzE%2BwUkkji5 working through the author's linear algebra done right book I came across this precalculus book. There is no better book. It has complete - and I mean complete - worked out solutions for all the odd problems. I know many students who have suffered through incredibly badly written books dealing with this subject and most, if not all, of them are. This book is a rigorous introduction to calculus - by this I mean that this book develops all ideas logically that a high school student can understand without an instructor - yes, without an instructor. All the usual topics of precalculus are covered in this book - only much better. Buy this for yourself, for your high schooler child and if you are a math teacher in a high school, at the very least, pilot this book!
This is the perfect book to prepare for Calculus. It is NOT one of those 1000-page tombs with every topic under the sun and tons of exercises. This author clearly knows the material and moreover presents it in a way that one can learn on one's own. There was really attention to detail on topics that are pertinent and important to understand and master in order to move on to the next level. I truly enjoyed the fact that the material in pervious chapters (e.g. functions and their inverse) came up again to understand and master other topics (e.g. logarithms). The best thing There was a mix of example exercises with thoughtful problem-type exercises. I must admit to spending several days mulling over thought problems that involved "proving or showing" that something was true. It made me feel more like Sherlock Holmes and less like some robot doing tons of problems to prove I understood something. For the readers that provided a low review (which I went over before writing my own) I must say it probably derives from being unprepared for this level of mathematics. I know from friends who don't really read the book for understanding they just find the closest example in the text when they are doing the exercises and move on. This book really starts to move you in the direction where you should read the text slowly and carefully, do some exercises and sit back and enjoy the "thought" problems - this is where the action is and you truly start to understand why mathematicians exist. I am not planning on being a mathematician and consider myself average but I do enjoy solving problems and this author has written a great math book - maybe I would have chosen math as a major if earlier books were so thoughtful in presentation, discussion and exercises.
This book is short, sweet, and to the point. You will not be disappointed.
I bought this book for my precalculus class and I love it. I don't have much time to talk to my professor after class so when I don't understand my professor's lectures, I can always rely on this book. It explains everything well. It keeps it short and sweet which I like. Also, in the back of the book, it gives answers to odd problems and it tells you have to solve the questions which I like as well.
This textbook is designed to help prepare students for calculus... and it does a great job. Every chapter starts by identifying the topic of the chapter and then breaks down the entirety of the subject matter into individuals parts for a step by step learning of the material with examples, practice problems, and comprehensive solutions (for all the odd problems). Major benefits of this textbook include the analysis of each topic and the provided examples, which aid the learning process, and especially the provision of worked-out solutions that the student can use to check their work |
Description
An easy-to-understand primer on advanced calculus topics
Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams.
It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, with introductions to multivariable calculus, differential equations, and numerical analysis. Best of all, it includes practical exercises designed to simplify and enhance understanding of this complex subject.
Introduction to integration
Indefinite integrals
Intermediate Integration topics
Infinite series
Advanced topics
Practice exercises
Confounded by curves? Perplexed by polynomials? This plain-English guide to Calculus II will set you straightplaws595User reviews
plaws595 plaws595
LibraryThingAbout the author
Mark Zegarelli, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear — and fun — for average readers. He is the author of Logic For Dummies and Basic Math & Pre-Algebra For Dummies.
Similar
Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school 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 a subject. is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores. |
Math 312--Our Book: Table of the integers 1 through 400 with
their prime factorizations, the sum of their divisors, expressed as sums of
squares, and as sums of primes. Chapter 1. Elementary
facts about positive integers. Chapter 2. The
beginnings of divisibility (Other than "indivisibility," can you
think of a word with more i's than this?) theory and some random interesting
facts about triangular numbers, Pythagorean triangles, and perfect numbers. Chapter 3. Mersenne and Fermat primes,
nailing down the square triangles, counting primes, and considering polynomials
that generate them. Chapter 3.5 A characterization of
all abundant numbers with fewer than four factors. Chapter 4. Pythagorean triples,
introduction to congruence, solving linear congruences and systems of them. Chapter 5. The
distribution of primes, Fermat's Little Theorem, and sundry other good stuff. Chapter 6. The proof
of the Chinese Remainder Theorem, Wilson's Theorem, multiplicative functions. Chapter 7. Euler's
phi function and Bertrand's Postulate. Chapter 8. Some notes on the exam and primitive roots. Chapter 9. Some
elementary group theory, stuff about primitive roots, quadratic residues, and
final exam topics. Chapter 10. The Law
of Quadratic Reciprocity and sums of two squares. |
More About
This Textbook
Overview
Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's requirements of accuracy in detail, both in the text and in the illustrations, but involving no changes in the structure and style of the lectures as originally delivered. This book is an enticing introduction to Minkowski's great work. It also reveals the workings of a remarkable mind, such as Siegel's with its precision and power and aesthetic charm. It is of interest to the aspiring as well as the established mathematician, with its unique blend of arithmetic, algebra, geometry, and analysis, and its easy readability.
Editorial Reviews
Booknews
Makes available to the generality of mature mathematical readers the carefully checked, corrected and rewritten text of fifteen lectures presented by Carl Siegel at NYU during 1945/46. The editorial work was done with the explicit permission of Siegel (who died in 1981). Will be valued by experts as a work of art from the hands of a master. (NW) |
Advanced Engineering Mathematics - 6th edition
Summary: Through previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Advanced Engineering Mathematics features a greater number of examples and problems and is fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and probl...show moreem sets, incorporating the use of leading software packages. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Partial Differential Equations, Complex Analysis, and Probability and Statistics.
4.1 Power Series Solutions of Initial Value Problems 4.2 Power Series Solutions Using Recurrence Relations 4.3 Singular Points and the Method of Frobenius 4.4 Second Solutions and Logarithm Factors 4.5 Appendix on Power Series 4.5.1 Convergence of Power Series 4.5.2 Algebra and Calculus of Power Series 4.5.3 Taylor and Maclaurin Expansions 4.5.4 Shifting Indices
13.1 Line Integrals 13.1.1 Line Integral With Respect to Arc Length 13.2 Green's Theorem 13.2.1 An Extension of Green's Theorem 13.3 Independence of Path and Potential Theory In the Plane 13.3.1 A More Critical Look at Theorem 13.5 13.4 Surfaces In 3- Space and Surface Integrals 13.4.1 Normal Vector to a Surface 13.4.2 The Tangent Plane to a Surface 13.4.3 Smooth and Piecewise Smooth Surfaces 13.4.4 Surface Integrals 13.5 Applications of Surface Integrals 13.5.1 Surface Area 13.5.2 Mass and Center of Mass of a Shell 13.5.3 Flux of a Vector Field Across a Surface 13.6 Preparation for the Integral Theorems of Gauss and Stokes 13.7 The Divergence Theorem of Gauss 13.7.1 Archimedes's Principle 13.7.2 The Heat Equation 13.7.3 The Divergence Theorem As A Conservation of Mass Principle 13.7.4 Green's Identities 13.8 The Integral Theorem of Stokes 13.8.1 An Interpretation of Curl 13.8.2 Potential Theory in 3- Space
Part V - Fourier Analysis, Orthogonal Expansions and Wavelets
Chapter 14 - Fourier Series
14.1 Why Fourier Series? 14.2 The Fourier Series of a Function 14.2.1 Even and Odd Functions 14.3 Convergence of Fourier Series 14.3.1 Convergence at the End Points 14.3.2 A Second Convergence Theorem 14.3.3 Partial Sums of Fourier Series 14.3.4 The Gibbs Phenomenon 14.4 Fourier Cosine and Sine Series 14.4.1 The Fourier Cosine Series of a Function 14.4.2 The Fourier Sine Series of a Function 14.5 Integration and Differentiation of Fourier Series 14.6 The Phase Angle Form of a Fourier Series 14.7 Complex Fourier Series and the Frequency Spectrum 14.7.1 Review of Complex Numbers 14.7.2 Complex Fourier Series
Chapter 15 - The Fourier Integral and Fourier Transforms
15.1 The Fourier Integral 15.2 Fourier Cosine and Sine Integrals 15.3 The Complex Fourier Integral and the Fourier Transform 15.4 Additional Properties and Applications of the Fourier Transform 15.4.1 The Fourier Transform of a Derivative 15.4.2 Frequency Differentiation 15.4.3 The Fourier Transform of an Integral 15.4.4 Convolution 15.4.5 Filtering and the Dirac Delta Function 15.4.6 The Windowed Fourier Transform 15.4.7 The Shannon Sampling Theorem 15.4.8 Lowpass and Bandpass Filters 15.5 The Fourier Cosine and Sine Transforms 15.6 The Finite Fourier Cosine and Sine Transforms 15.7 The Discrete Fourier Transform 15.7.1 Linearity and Periodicity 15.7.2 The Inverse N- Point DFT 15.7.3 DFT Approximation of Fourier Coefficients 15.8 Sampled Fourier Series 15.8.1 Approximation of a Fourier Transform by an N- Point DFT 15.8.2 Filtering 15.9 The Fast Fourier Transform 15.9.1 Computational Efficiency of the FFT 15.9.2 Use of the FFT in Analyzing Power Spectral Densities of Signals 15.9.3 Filtering Noise From a Signal 15.9.4 Analysis of the Tides in Morro Bay
18.1 The Heat Equation and Initial and Boundary Conditions 18.2 Fourier Series Solutions of the Heat Equation 18.2.1 Ends of the Bar Kept at Temperature Zero 18.2.2 Temperature in a Bar With Insulated Ends 18.2.3 Temperature Distribution in a Bar With Radiating End 18.2.4 Transformations of Boundary Value Problems Involving the Heat Equation 18.2.5 A Nonhomogeneous Heat Equation 18.2.6 Effects of Boundary Conditions and Constants on Heat Conduction 18.2.7 Numerical Approximation of Solutions 18.3 Heat Conduction in Infinite Media 18.3.1 Heat Conduction in an Infinite Bar 18.3.2 Heat Conduction in a Semi-Infinite Bar 18.3.3 Integral Transform Methods for the Heat Equation in an Infinite Medium 18.4 Heat Conduction in an Infinite Cylinder 18.5 Heat Conduction in a Rectangular Plate
Chapter 19 - The Potential Equation
19.1 Harmonic Functions and the Dirichlet Problem 19.2 Dirichlet Problem for a Rectangle 19.3 Dirichlet Problem for a Disk 19.4 Poisson's Integral Formula for the Disk 19.5 Dirichlet Problems in Unbounded Regions 19.5.1 Dirichlet Problem for the Upper Half Plane 19.5.2 Dirichlet Problem for the Right Quarter Plane 19.5.3 An Electrostatic Potential Problem 19.6 A Dirichlet Problem for a Cube 19.7 The Steady-State Heat Equation for a Solid Sphere 19.8 The Neumann Problem 19.8.1 A Neumann Problem for a Rectangle 19.8.2 A Neumann Problem for a Disk 19.8.3 A Neumann Problem for the Upper Half Plane57.21 +$3.99 s/h
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This activity builds on the previous activity, Limits with Tables. Students investigate limits using tools for controlling delta and epsilon, giving them a concrete, hands-on understanding of the formal definition of a limit. Students start by investigating the limit at a point discontinuity, then use the same techniques to investigate other types of discontinuities. This activity is part of a series of Sketchpad activities introducing the main topics of calculus |
Mr. Andi note is student absent in last three year, that is January, February and March to 3 student that is Arlan, Bronto, and cery like at the table .
On the table can be written : Arlan Bronto Cery January February March 3 4 1 6 2 3 1 2 4
is a rectangular array of numbers, consists of rows and columns and is written using brackets or parentheses. The entries of a matrix are called elements of matrix . An element of a matrix is addressed by listing the row number and then column number M A T R I X
Matrix is generally notated using capital latter
2. The order of the matrix A matrix of A has m rows and n column is called as matrix of dimension on order m x n, and so notated of "A(mxn)". To more understand the definition of the element of a matrix.
The first column The second column The third column The column n-th The second row The first row The third row The row n-th
Example: Matrix A = The first row The second row The first column The second column The third column
The order matrix A is 2 x 3
4 is the second row and the first column
a row matrix Is a matrix that only has a row A = ( 1 3 5), and B = ( -1 0 4 7) The order matrix is and
a column matrix Is a matrix that only has a column
A matrix square A square matrix a matrix has the number of row of a matrix equals the number of its column
Example : rows 4, columns 4 A is matrix the order 4 A = Main diagonal
A = Upper Triangle Matrix is square matrix which all of the element under the diagonal is zero Upper Triangle Matrix
B = B is a lower triangle matrix is square matrix which all of the element upper the diagonal is zero Lower Triangle Matrix
C = Diagonal Matrix is square matrix that all of element is zero, except the element on the diagonal not all of them Diagonal Matrix:
I = I is matrix Identity that is diagonal matrix that elements at main diagonal value one Pay attention the following matrix
Transpose and Similarity of a Matrix
Transpose of a Matrix
Let A is a matrix whit dimension of (m x n). From the matrix of A we can formed a new matrix that obtained by following method:
a. Change the line of i th of matrix A to the row of
ith of new matrix
b. Change the row of j th of matrix A to the line of
jth of new matrix
The new matrix that resulted is called transpose from matrix of A symbolized with A' or From the above changess, the dimension of A' is (n x m)
Transpose matrix A A = IS A t =
Example :
let A = (aij) ang B = (bij) are two matrices with the same dimension. Matrix of A is callled equal with matrix of B id the element that located on the two matrices has the same value. 2. Similarity of two matrix
One located element with the same value One located element with the same value One located element with the same value One located element with the same value
Taking example A = and B = if A t = B, then determine the value x? Example 2:
Answer : A = = A t = B A t =
x + y = 1 x – y = 3 2x = 4 so x = 4 : 2 = 2
Algebraic Operation on Matrix
Addition and Subtraction of Matrix
Scale Multiplication with a Matrix
Matrix Multiplication with Matrix
Addition/Subtraction Two matrix can be summed/reduced if the order of the matrix are same and its statement in one position
Example 1: and B = A = A + B = + =
If A = , B = and C = hence(A + C) – (A + B) =…. Example 2:
(A + C) – (A + B) = A + C – A – B = C – B = = = Answer
Scale Multiplication With a Matrix Let k Є R and A is a matrix with dimension of m x n . Multiplication of real number k by matrix of A is a new matrix which is also has dimension of m x n that obtained by multiplying each element A by real number of k and notates kA
Matrix A = Determine matrix represented by 3A 3A = Example :1
Given Matrix of A = , B = and C = if A – 2B = 3C, So determine a + b ? Example 2 :
Matrix Multiplication with Matrix The Product Of Two Matrices A and B can be got when satisfies the relation A m x n = B p x q = AB m x q Equal
The number of column of matrix A should equal the number of rows of matrix B, the product, that is AB has order of m x q. when m is the number of rows of matrix A and q is the number of column of matrix B |
In this lesson you will learn how Algebra is used in everyday life and how to solve basic problems using multiplication and division along with addition and subtraction from Algebra 101. This application includes a detailed description of basic algebra functions, an unlimited number of practice problems and a step by step solution to each |
Kittredge Precalculus ...For example: If they have a decent grasp on how to differentiate, but have skills that are lacking on integration, I would focus more time on the integration techniques. I also believe that the best way to learn is to learn from our mistakes. So while going over problems I will not give the answer directly, but rather point in the general direction to find the answer. |
Modern Geometries - 5th edition
Summary: This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. The Fifth Edition reflects the re...show morecommendations of the COMAP proceedings on "Geometry's Future," the NCTM standards, and the Professional Standards for Teaching Mathematics. ...show less
Introduction to Geometry. Development of Modern Geometries. Introduction to Finite Geometries. Four-Line and Four-Point Geometries. Finite Geometries of Fano and Young. Finite Geometries of Pappus and Desargues. Other Finite Geometries.
2. GEOMETRIC TRANSFORMATIONS.
Introduction to Transformations. Groups of Transformations. Euclidean Motions of the Plane. Sets of Equations for Motions of the Plane. Applications of Transformations in Computer Graphics. Properties of the Group of Euclidean Motions. Motions and Graphics of Three-Space. Similarity Transformations. Introduction to the Geometry of Fractals and Fractal Dimension. Examples and Applications of Fractals.
The Philosophy of Constructions. Constructible Numbers. Constructions in Advanced Euclidean Geometry. Constructions and Impossibility Proofs. Constructions by Paper Folding and by Use of Computer Software. Constructions with Only One Instrument.
6. THE TRANSFORMATION OF INVERSION.
Basic Concepts. Additional Properties and Invariants under Inversion. The Analytic Geometry of Inversion. Some Applications of Inversion.
Foundations of Euclidean and Non-Euclidean Geometries. Introduction to Hyperbolic Geometry. Ideal Points and Omega Triangles. Quadrilaterals and Triangles. Pairs of Lines and Area of Triangular Regions. Curves. Elliptic Geometry. Consistency; Other Modern Geometries164 |
More About
This Textbook
Overview
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization.
This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces.
Jiri Matousek is Professor of Computer Science at Charles University in Prague. His research has contributed to several of the considered areas and to their algorithmic applications. This is his third book.
Editorial Reviews
From the Publisher
From the reviews:
"Discrete geometry is not quite a newcomer on the stage of mathematics. … The book under review covers … a gap in the pedagogical literature, providing an expository treatment of a wide range of topics in discrete geometry, without assuming too many prerequisites from the reader. … it will be ideal to be used both as a textbook and for self-study. … In fact … this book can be used as a 'mathematical companion' to a textbook on computational geometry … ." (Paul A. Blaga, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLVIII (1), March, 2004)
"Matoušek's excellent new book concerns discrete geometry. … The style is clear and pleasant; things are streamlined and collected in one place, and are explained on simple, concrete examples. … a final chapter on 'What was it about? An informal summary' was an innovation that I found to be an excellent idea. Lectures on discrete geometry is a splendid book. I recommend it both to students and researchers in the field, as well as to those who like mathematics for its own inherent beauty." (Imre Bárány, Bulletin of the London Mathematical Society, Issue 35, 2003)
"This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections, and thus, it can serve as a collection of surveys in several narrower subfields." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 48 (3-4), 2002)
"This is an introduction to the field of discrete geometry understood as the investigation of combinatorial properties of configurations of (usually finitely many) geometric objects … . The book is written in a lively and stimulating but very precise style and contains many figures. It gives a good impression of the richness and the relevance of the field." (Johann Linhart, Zentralblatt Math, Vol. 999 (24), 2002 |
This
dictionary is intended to help you to understand basic concepts
in Math with the help of illustrations as well as examples.
It also provides you with information on how to use rules, properties
and theorems in solving the related problems.
How
to use this dictionary
To
find a mathematical word click on the appropriate letter on
the top menu bar. All words listed on the same letter page are
in alphabetical order. Click table
of content for related topics such as completing the square,
equation with absolute values, equation with radicals, evaluating
expressions, exponential equations, factoring polynomial, fraction,
functions, geometric formulas, inequalities with absolute values,
LCD or LCM, linear equation, linear inequality, log or exponent,
metric in English system, non-linear inequalities, quadratic
equations, removing parenthesis, system of linear equations,
system of linear inequalities, word problems, distributive laws,
etc. in algebra; and limit, continuity, derivative and application
in calculus.
Authors
Dr.
Amy Wang and Dr. Oscar Schiappacasse at NVCC, Alexandria Campus
Acknowledge
We
give special thanks to Mr. Eddy Revollo for his assistance on
the technology side of putting together this web site. |
All the Math You Need to Get Rich: Thinking with Numbers for Financial Success
Book Description: All the Math You Need to Get Rich provides readers with all the necessary tools to make informed decisions about their personal finances. Written in a lighthearted style, the book moves step by step through several sample problems that will help readers make their own day-to-day decisions. Subjects cover the full range of concerns: mortgage payments, compound interest, stocks and mutual funds, cash flow, percentages, probabilities, installment plans, rates of return, gambling and risk-taking, and insurance. Organized and indexed for easy reference, this guide explains these difficult concepts so that even the math-phobic reader will be able to understand without a struggle |
In this factoring worksheet, learners find the common term, use special products or use the diamond method to factor polynomials. Explanations and examples are provided. This three-page worksheet contains 45 problems. Answers are provided at the end of the document.
In this math study guide, students solve problems previously studied throughout the school year. Problems include, but are not limited to, volume, area, perimeter, square roots, binomials, trinomials, graphing, and consumer math. This eight-page worksheet contains 32 problems. Answers are provided on the last page of the worksheet.
Here's a fun way to explore and practice the concepts of multiplying monomials, multiplying binomials, and factoring polynomials. Included is the puzzle worksheet containing nine different sets. Don't worry, there's an answer key also.
Students factor numbers using Algebra Lab Gear. In this factoring quadratic equations instructional activity, students determine a number of different ways to factor a list of numbers. Students create a rectangle out of the pieces with no gaps and figure out what binomials could create such a rectangle for each problem. Students also create a chart in their groups that displays the attachments of each variable.
In this introduction to polynomial function worksheet, students classify, state the degree, find the intercepts, and evaluate polynomial functions. Six of the problems are true/false problems and thirty-eight and free-response problem solving problems.
In this perfect square worksheet, students factor perfect square trinomials and polynomials. They identify trinomials and polynomials that are perfect squares. This one-page worksheet contains 21 problems.
In this polynomial functions worksheet, students solve eight-six various problems concerned with the degree, graph, intercepts, end behavior, and transformations of polynomial functions. Some of the problems are algebraic work and some are graphical.
In this algebra worksheet, pupils solve a variety of problems. They find the greatest common factor of polynomials, factor polynomials and trinomials, and solve algebraic equations and real life story problems. Nine of the hundred problems require the interpretation of a story.
In this expressions and operations activity, 9th graders solve and complete 5 different multiple choice problems. First, they determine the complete factorization of various trinomials. Then, students find the equivalent equation to a completely factored trinomial.
In this perfect squares and factoring instructional activity, students solve and complete 26 different problems that include a number of polynomials. First, they determine whether each trinomial is a perfect square trinomial and factor if possible. Then, students factor each polynomial and write prime for those that are not.
In this completing the square activity, 11th graders solve and complete 24 different problems. First, they solve each equation by using the square root property. Then, students find the value of the variable that makes each trinomial a perfect square and write the trinomial as a perfect square.
A teacher guided lesson on perfect squares and factoring. They discuss perfect squares, observe the expansion steps for finding the product, and practice solving problems. They complete a worksheet on perfect squares and factoring.
In this expressions and operations worksheet, 9th graders solve and complete 10 different multiple choice problems that include various types of expressions. First, they determine the complete factorization of a given trinomial. Then, students find the solution for various equations shown. They also determine the solution set for a given equation.
Learners examine factoring polynomials. They observe a PowerPoint presentation as an introduction to factoring. Students factor binomials, trinomials and the difference of two perfect squares. Learners calculate problems after factoring them.
Students identify and describe polynomials and their elements, discuss simple parts that make up equations, inequalities, and exponents, take notes on definitions of terms and their types, including monomials, binomials, and trinomials, practice independently, and play flash card quiz game. |
Shows steps I accidentally reduced my B matrix too far, and it erased a row in A, mostly: having to clear wrong data from each segment before entering correct #'s is a pain. Besides not preserving the column data and this extra step it's a gem for checking work includingFormulae Helper – A handbook of mathematical formulas in geometry, algebra, trigonometry, calculus and more from the creators of Math Helper Algebra.
Formulae Helper is the best and easiest-to-use mathematics formula reference application for both math teachers and students, featuring hundreds of math formulas at your fingertips.
This math formula app is useful for homework, quizzes, tests, studying, or reference, and can be used for studying pre-calculus, calculus, algebra, trigonometry, geometry, functions, sequences, and more. Also can be used as picture homework helper.
For total access to math formulas without carrying around bulky textbooks, get Formulae Helper today!
In this app you will find such indispensable formulas as rumus, maths trigonometry formulaes, basic trigonometry, math identities, algebra basics, calculus formulae, geometry, also will be good if you look for graphing helper. Better than any algebra textbook or calculus book – all formulae of maths at your fingertips. Algebra, trig, calculus quick help and more! Good to prepare for SSC, SAT I, SAT II, ACT or GCSE Look for help in algebra? started learning calculus formulas? Need help solving algebraic equations? Do not know how to divide polynomials? Formulae Helper – is just what you are looking for. See no further! Download now!
DragonBox Algebra 5+ Is perfect for giving young children a head start in mathematics and algebra. Children as young as five can easily begin to grasp the basic processes involved in solving linear equations without even realising that they are learning. The game is intuitive, engaging and fun, allowing anyone to learn the basics of algebra at his or her own pace.
DragonBox Algebra 5+ covers the following algebraic concepts:
* Addition * Division * Multiplication
Suitable from age five and up, DragonBox Algebra 5+ gives young learners the opportunity to get familiar with the basics of equation solving.
DragonBox uses a novel pedagogical method based on discovery and experimentation. Players learn how to solve equations in a playful and colorfull game environment where they are encouraged to experiment and be creative. By manipulating cards and trying to isolate the DragonBox on one side of the game board, the player gradually learns the operations required to isolate X on one side of an equation. Little by little, the cards are replaced with numbers and variables, revealing the addition, division and multiplication operators the player has been learning throughout the game.
Playing does not require supervision, although parents can assist them in transferring learned skills into pen and paper equation solving. It is a great game for parents to play with their kids and can even give them an opportunity to freshen up their own math skills.
DragonBox was developed by former math teacher Jean-Baptiste Huynh and has been heralded as a perfect example of game-based learning. As a result, it is currently forming the basis of an extensive research project by the Center For Game Science at the University of Washington |
It obviously requires single- and multi-variable calculus and linear algebra, but what else? And where do you suggest to get that background from?this isn't a duplicate because I'm for the math needed ... |
Instructor Class Description
Functions, Models, and Quantitative Reasoning
Explores the concept of a mathematical function and its applications. Explores real world examples and problems to enable students to create mathematical models that help them understand the world in which they live. Each idea will be represented symbolically, numerically, graphically, and verbally. Prerequisite: minimum grade of 2.5 in B CUSP 122, a score of 145-153 on the MPT-AS assessment test, or a score of 151 or higher on the MPT-GS assessment test. Offered: AWSp.
Class description
This course is designed to prepare students for Calculus I (BCUSP124). Upon successful completion of this course, students will be expected to have a solid understanding of functions, their manipulation and their use in mathematical models. Students will also develop and refine their skills in algebra and trigonometry.
Functions are the key to how mathematical models are built. Various mathematical models will be created and studied through the use of real world examples.
Understand how to evaluate mathematical expressions, and solve equations.
General method of instruction
We will aim to have a good balance between lectures and group work. Lectures will rely on student participation, presentations and active discussion.
Recommended preparation
Appropriate score on the UWB math placement test (MPT).
Review of previous work in algebra, geometry and trigonometry.
Attendance of Algebra /or Trigonometry Review Sessions at the Quantitative Skills Center (contact the QSC for more information)
Class assignments and grading
We will have weekly homework, weekly activities (or quizzes), two midterms and a final.
Homework will use the WileyPlus system which includes a printable soft copy of the textbook. You do not need to purchase a hard copy of the textbook. Further details about the textbook and homework will be discussed during the first class.
Weights are as follows: 20% total for homeworks; 20% total for activities/participation; and 60% total for Fabiana Ferracina
Date: 12/16/2013
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:April 18, 2014 |
@book {IOPORT.00046698,
author = {Althoen, Steven C. and Bumcrot, Robert J.},
title = {Introduction to discrete mathematics.},
year = {1988},
isbn = {0-534-91504-3},
pages = {xii, 346 p.},
publisher = {Boston, MA: PWS-Kent Publishing Company},
abstract = {This very readable book ``is designed as an introduction to those mathematical topics necessary for the future computer scientist. It was written on the freshman/sophomore level to introduce a discrete mathematics course currently being offered at most colleges and universities and at an increasing number of two-year schools. The text assumes a familiarity with mathematics consistent with a standard high- school level education. No knowledge of programming languages is assumed, and therefore the text is not tight to any specific language. $\dots$ This text is unified by the use of algorithms. $\dots$ Examples are presented with the use of a powerful and friendly IMarginary COMputer (IMCOM)'' (from the preface). From the contents: 1. Algorithms and data structures, 2. Combinatorics, 3. Logic and circuits, 4. Graphs, 5. Graph algorithms, 6. Relations, algebraic systems, and machines. Answers to odd-numbered exercises.},
reviewer = {B.Richter (Berlin)},
identifier = {00046698},
} |
Pre-Algebra—Semester A
The number one place for all things number.
Course Description
Are you one of the many students out there that shivers at the thought of having to work with equations and graphs? What about rational and irrational numbers? Okay, enough with the scary words. Sometimes we think Stephen King doesn't have anything on the tales from middle and high school math classes.
What we're about to tell you might come as a surprise: Pre-Algebra isn't really that scary. Sure, there's something creepy about walking into a dark basement. But once the lights get flicked on, you just might find a surprise party waiting at the bottom of the stairs. (We wish!) Our goal is to turn on that light bulb and shed some insight—and hilarity—onto the darkness that is hiding the Pre-Algebra party.
In this course, we'll give you all the examples, practice problems, and projects you need to
learn all about the nuts and bolts of equations;
understand and use equations themselves;
and tackle graphs of lines, which happen to come from equations.
See how it all comes full circle?
P.S. Pre-Algebra is a two-semester course. You're
looking at Semester A, but you can check out Semester B here.
Technology Requirements
Microsoft Office, Google Docs, or another word processing program
A scanner (or access to one)
A camera (a camera phone is sufficient)
All other work can be done via the Shmoop website
Supported browsers:
IE 7+
Firefox 4+
Chrome 10+
Safari 4+
Opera 11+
Required Skills
This course is an accelerated course meant to be taken after 6th grade math and before algebra I. If you are looking for pre-algebra to be split into two years, check out our 7th and 8th grade math courses (coming soon).
No special technological skills are necessary for this course other than very basic computer literacy.
Course Breakdown
Unit 1. Expressions and Basic Operations
To be sure our math skills are in tiptop shape, we are going to start you out with some basic review. You may see some new and crazy things, like powers and roots, but other concepts will be old friends of yours, like addition and subtraction. Did we hear a sigh of relief or were those the baked beans you had earlier?
$14.92add to cartremove
Unit 2. Solving Equations
This unit is mainly about learning the rules that come along with expressions and equations, like the commutative and distributive properties. We'll also practice translating verbal sentences into written numeric and variable equations. No, that doesn't mean you can go around telling everyone you're bilingual.
$14.92add to cartremove
Unit 3. Multi-Step Equations and Inequalities in One Variable
This unit is all about solving multi-step equations and inequalities. It might feel a little shaky at first, but as long as you remember the basics of like terms and one-variable equations, you'll find yourself on solid ground again. And as long as you pay a little bit of attention, we'll make sure you don't get there face first.
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Unit 4. Radicals and Exponents
Here's where powers and roots will come back to haunt us. More like Casper the Friendly Ghost than the Exorcist, though. We'll go from prime numbers, GCFs, and factor trees to full-on radicals, exponents, and even negative powers (which—trust us—aren't nearly as evil as they sound).
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Unit 5. Rational and Irrational Numbers
Rational and irrational numbers are just types of numbers, like whole numbers and integers. Not only will we get to know these puppies, we'll learn how to use them in the real world. They might sound intimidating, but don't be fooled; they're all bark and no bite.
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Unit 6. Ratios and Proportions
In this unit, we'll get a really good flavor for how algebra and numbers mix together. Using fractions, units, and one-variable equations, we'll discuss ratios, proportions, rates, and we'll even do a fair amount of graphing on the coordinate plane. Who needs those dinky number lines, anyway?
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Unit 7. Equations in Two Variables
We'll learn all about how two-variable equations and inequalities can describe all sorts of different relationships—except your love-hate relationship with Lost. Those feelings are sort of inexplicable.
$14.92add to cartremove
Unit 8. Linear Equations and Functions
We start out this unit by learning about relations and functions, plotting ordered pairs, and graphing linear equations. Once we've got graphing down pat, we'll delve deep into the linear equations and their slope-intercept form. To top it all off, we'll tie these concepts together with a bit of modeling. Not that kind of modeling, so put that sequin dress away. |
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...
How will various institutions respond to global warming? It's a multifaceted question, and one that forms the basis of this thoughtful course offered by MIT's Sloan School of Management. Materials for the course are...
Created by Tony R. Kuphaldt, this web site from the Open Book Project provides educational resources for learning and teaching electronics. It is promotes student discussion and individual research. The web site...
This course, created by Wen Xiao-Geng of the Massachusetts Institute of Technology, is the second in the series of undergraduate Statistical Physics courses and features comprehensive lecture notes and assignments....
Created by Richard Dudley of the Massachusetts Institute of Technology, this lesson, Mathematical Statistics, is a graduate-level course featuring book chapters and sections presented as lecture notes, problem sets,... |
Two-Dimensional Calculus (Dover Books on Mathematics)
by Robert Osserman Publisher Comments
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids... (read more)
Precalculus : Graphing Approach (5TH 08 - Old Edition)
by Ron Larson Publisher Comments
As part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, Precalculus: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality... (read more)
Handbook of Networks in Power Systems II (Energy Systems)
by Panos M. Pardalos Publisher Comments
Energy has been an inevitable component of human lives for decades. Recent rapid developments in the area require analyzing energy systems not as independent components but rather as connected interdependent networks. The Handbook of Networks in Power... (read more)
Functional Calculus Pseudodifferenti 2ND Edition
by Gerd Grubb Publisher Comments
Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." A replacement of compositions of operators in n-space by simpler product rules for thier symbols. The main purpose of this... (read more)
Numerical Mathematics and Computing (7TH 13 Edition)
by E. Ward Cheney Publisher Comments
Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. NUMERICAL MATHEMATICS... (read more)
Calculus I With Precalculus : a One-year Course (3RD 12 Edition)
by Ron Larson Publisher Comments
Carefully developed for one-year courses that combine and integrate material from Precalculus through Calculus I, this text is ideal for instructors who wish to successfully bring students up to speed algebraically within precalculus and transition them... (read more)
Super Reviews Calculus (Super Reviews; All You Need to Know)
by Rea Publisher Comments
CALCULUS SUPER REVIEW Need help with calculus? Want a quick review or refresher for class? This is the book for you! CONCISE SUBJECT REVIEW Covers the material students typically learn in an introductory calculus course. Clear, easy-to-understand format... (read more)
Advanced Calculus: An Introduction to Linear Analysis
by Leonard F. Richardson Publisher Comments
Advanced Calculushighlights the connections between calculus and linear algebra and provides a mathematically sophisticated introduction to functional analytic concepts. The book stresses that proofs must be written down, scrutinized step-by-step |
Algebraic and Stochastic Coding Theory
Description: Written for advanced readers, this book examines recent theoretical developments in coding theory. It covers technical topics and includes numerous examples to explain the underlying principles in coding theory. The text proves and illustrates theMore...
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Written for advanced readers, this book examines recent theoretical developments in coding theory. It covers technical topics and includes numerous examples to explain the underlying principles in coding theory. The text proves and illustrates the results with examples that detail that construction of the codes. The authors provide a clear, detailed description of each code and discuss its applications as well as advantages and disadvantages. In addition, they present historical developments and simplify mathematical theory, including exercises in most chapters of the text. Topics covered include belief propagation, distributions, finite fields, bounds, and Golay codes |
Calculus II: Modeling With Differential Equations
An infectious disease spreads through a community: What is the most effective action to stop an epidemic? Populations of fish swell and decline periodically: Should we change the level of fishing allowed this year to have a better fish population next year? Foxes snack on rabbits: In the long term, will we end up with too many foxes or too many rabbits? Calculus can help us answer these questions. We can make a mathematical model of each situation, composed of equations involving derivatives (called differential equations). These models can tell us what happens to a system over time which, in turn, gives us predictive power. Additionally, we can alter models to reflect different scenarios (e.g., instituting a quarantine, changing hunting quotas) and then see how these scenarios play out. The topics of study in Calculus II include power series, integration, and numerical approximation, all of which can be applied to solve differential equations. Our work will be done both by hand and by computer. Conveniently, learning the basics of constructing and solving differential equations (our first topic of the semester) includes a review of Calculus I concepts. Conference work will explore additional mathematical topics. This seminar is intended for students planning further study in mathematics or science, medicine, engineering, economics, or any technical field, as well as students who seek to enhance their logical thinking and problem-solving skills. Prerequisite: Calculus I (differential calculus in either a high-school or college setting). |
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A college-level study of Calculus. This course emphasizes computational techniques, geometry and theoretical structure, creative problem solving, and proofs. Upon successful completion of the course, the student will receive 4 credit hours from the Central Virginia Community College.
Course Materials:
Textbook: Larson, Hostetler, and Edwards, Calculus of a Single Variable, 4th ed. We will also use graphing calculators and various web-sites, including interactive applets.
Semester Grading:
Homework 5 %
3 Midterm Tests 18 % each
Projects 16%
Semester Exam 25 %
Grading will be on a 10-point scale as described in the student handbook.
Nine-week grades are cumulative progress reports for the semester.
You will incur poor participation penalties for inattentiveness or not working during independent study time.
Class Methodology and Expectations:
A typical class will consist of lecture (including discussion and question answering) and a period of independent work during which the students should solidify their understanding of the concepts, identify remaining questions about the concepts, work examples, and start homework assignments. Some specific expectations follow.
I expect you to learn the material thoroughly. Through the brief lectures and individual meetings, I will try to facilitate your learning, but ultimately, you must actively take responsibility for your learning. Please work with the other members of the class.
I expect you to participate in each class meeting. During the lecture portion, be attentive, ask questions, and provide answers to questions posed by your classmates and myself. Work cooperatively with your classmates during the independent portion.
I expect you to work diligently on each homework assignment. Working on these problems is the most important part of the course. Please see the attached sheet for the assignments and homework rules.
I expect you to carefully read the textbook. During lecture, I will address major ideas and some examples, but there will be topics and examples you should learn from the textbook. You will often have to creatively solve problems based on your knowledge of the concepts. This expectation of creative problem solving is typical of a challenging college mathematics course.
I expect you to take the midterm tests as scheduled. If you need to miss a test, you must make arrangements in advance. For policies concerning the final exam, please refer to the CVGS Student Handbook. Many test and exam questions will be quite similar to homework questions and/or examples from class; however, you will also be asked a few questions (including essay questions and proofs) based on your understanding of the concepts.
Course objectives:
You should learn the computational techniques of Calculus and their geometric meanings. This interplay between computations and geometry is extremely important and will be emphasized throughout the course.
You should learn how to use these computational techniques to solve applied problems (often guided by geometric insight).
You should develop an understanding of the theory of Calculus, including the techniques of writing proofs. The more you understand this structure, the clearer the overall picture of Calculus will be.
Absences/Tardiness:
If a student is absent (excused) for only one class meeting, then upon return, the student is expected to submit any work that was due during the absence. If a test was missed, the student is expected to take the test on the day of return. If a student misses two or more consecutive class meetings, then the student should talk to the instructor on the day of return to devise a plan to catch up. For planned absences (e.g., college visits, conference attendance, etc.), the student should discuss the plan with the instructor in advance. Failure to do so will result in an unexcused absence. For any unexcused absence, homework will not be accepted late and test grades will be lowered by 10 points per day (counted from the scheduled test date until the day the test is taken).
You are expected to be in class on time. During each semester, your first tardy will be excused; for each additional tardy, 1/2 point will be deducted from your overall semester average.
Honor Code:
Students are required to pledge all work that they turn in for a grade. Please refer to the CVGS Student Handbook for complete requirements
Typical Hours for Students Session I (7:30-10:10)Session II (8:25-11:05)
Period 1: 7:30-8:20 Period 2: 8:25-9:15
Period 2: 8:25-9:15 Period 3: 9:20-10:10
Period 3: 9:20-10:10 Period 4: 10:15-11:05 |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
Math Basics SparkChart - 02 edition
ISBN13:978-1586636180 ISBN10: 1586636189 This edition has also been released as: ISBN13: 978-0593361894 ISBN10: 059336189X
Summary: Imagine if the top student in your course organized the most important points from your textbook or lecture into an easy-to-read, laminated chart that could fit directly into your notebook or binder.
SparkCharts-created by Harvard students for students everywhere-serve as study companions and reference tools that cover a wide range of subjects, including Business, Math, Science, History, Humanities, Foreign Language, and Writing. Titles like Presentations a...show morend Public Speaking, Essays and Term Papers, Resumes and Cover Letters, and Test Prep give you what it takes to find success in college and beyond. Outlines and summaries cover key points, while diagrams and tables make difficult concepts easier to digest.
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Data and Probability Connections - 07 edition
Summary: Part of a project funded by the National Science Foundation to improve the quality of mathematics and science teaching in grades K-12, this new text helps future teachers connect their college-level statistics to topics in standards-based middle school mathematics curricula. Designed to promote active learning, Data Analysis and Probability Connections models the student-centered approach recommended by the National Council of Teachers of Mathematics. Feat...show moreures
Connections to standards-based middle school curricula - Provides future middle grade mathematics teachers with a strong mathematical foundation, connecting the mathematics they are learning with the mathematics they will be teaching.
Visual or geometric approach to formulas and procedures - Gives enhanced meaning to formulas often presented as simply definitions to be memorized.
Numerous illustrations and problems drawn from middle school mathematics curricula - Assist students in making explicit connections between a typical college elementary statistics course and the statistical concepts taught by middle school teachers.
Exploration problems at the start of each chapter - Lay the foundation for developing key concepts and ideas throughout the chapter and provide a more active way to engage students.
''Focus on Understanding'' activities - Provide opportunities for students, working either in groups or individually, to apply and extend chapter concepts under discussion.
Integrated technology throughout - In keeping with the NCTM principles, explicit directions for using the TI-83 Plus calculator is integrated throughout the text, as well as additional computer software projects in the appendices.
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Product Description
Algebra 1/2 Home Study Kit includes the hardcover student text, softcover answer key and softcover test booklet. Containing 123 lessons, this text is the culmination of prealgebra mathematics, a full pre-algebra course and an introduction to geometry and discrete mathematics. Some topics covered include Prime and Composite numbers; fractions & decimals; order of operations, coordinates, exponents, square roots, ratios, algebraic phrases, probability, the Pythagorean Theorem and more. Utilizing an incremental approach to math, your students will learn in small doses at their own pace, increasing retention of knowledge and satisfaction!
Product Reviews
Algebra 1/2 Home School Kit, 3rd Edition
5
5
24
24
Great math product!!!
This math system is so easy to follow and teach. My son has learned so much while using this product..
November 11, 2013
Perfect for my 8th grader!
We recently switched from abeka math to Saxon and it was a great fit for us! My daughter was struggling with the fast pace of Abeka and not enough explanation and with Saxon she has been completely independent. We got the teaching DVD and the teacher explains the lesson so well! My daughter said that the teacher breaks it down in a way that she can really understand. We are very happy!
August 20, 2013
working well for my 8th grader.
We were looking for a program that my 8th grader could basically on his own. He picks up things slow, and when we just had the book he tended to skip the instructions. He also loves to do anything on the computer. This is working very well for him. The instruction portion of each lesson takes usually 30 minutes, an goes through everything from the book, for him he needs that. It may be too drawn out for some kids (get bored), but works well for us. He is able to do math completely on his own (so far after 6 weeks of school).
September 21, 2012
Very good product.
Very good product. I recommend buying Saxon teacher.
September 7, 2012 |
Elementary and Intermediate Algebra for College Students
About this title: The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight |
Course Description
MA 1000
Foundations of College Mathematics
Topics include computation with integers and rational numbers using correct order of operations, ratios, and proportions. The student also learns percent concepts and solving equations involving percentages. Other topics covered include exponents, simplifying and solving equations, and inequalities with one variable. Using linear equation problem solving strategies to solve application problems is emphasized. Graphing lines using slope and y-intercept is also taught. Problem solving is integrated throughout and appropriate use of calculators is expected. |
OVERVIEW
As you will have seen in MTH5103 "Complex Variables", when we do calculus with complex
numbers in place of real numbers we find a whole new world of mathematics.
Some results become simpler: for example
Taylor's Theorem, which for real functions is about approximating differentiable functions
by power series, now tells us that complex differentiable functions are equal to power
series. But the complex world brings completely new results, for example Cauchy's Theorem, and
the Calculus of Residues, which are not just beautiful mathematics, but have consequences and
applications to many different problems which at first sight have nothing to do with complex numbers.
In this course we are going to take the subject much further than did "Complex Variables". This will
involve us first covering some of the same ground again (for example Cauchy's Theorem), but with
more precise statements and detailed proofs. This part of the course will apply the mathematical
rigour of "Convergence and Continuity" and "Differential and Integral Analysis" to the main results
of "Complex Variables". We shall then explore a number of applications - some will be developments
of themes already introduced in "Complex Variables" (for example the geometry
of conformal maps, and harmonic maps, and the application of the calculus of residues to the summation of
power series), and others will be new to most students (for example analytic continuation and Riemann surfaces).
We shall encounter many famous results (Picard's Theorem, the Riemann Mapping Theorem, the Prime Number
Theorem,...) most of which we shall only state, but some of which we may prove, or at least sketch
prove. And I hope that we shall have time in the final couple of weeks to look at how complex analysis
is involved in two very different areas of very active current research:
(i) Iteration of complex functions (the theory behind the beautiful pictures of Julia sets and the Mandelbrot set..)
(ii) The Riemann Hypothesis (the most important unresolved question in mathematics today...)
A detailed syllabus will appear bit by bit as the course progresses. The official course description on
is quite flexible as regards the contents
of the second half of the course, and I would like to take your interests into account in deciding exactly what we cover.
Learning Outcomes
A rigorous understanding of classical complex analysis. (A more detailed version of this
objective is available on the School of Mathematical Sciences learning outcomes
webpage.)
Lecture Notes
These will appear here chapter by chapter in downloadable pdf form, one to two
weeks after the relevant lecture. The list of headings below is from the 2009-2010
course, and may change a little in 2010-11.
Apologies that the downloadable pdf notes below have no examples or pictures, and
for any misprints (please bring these to my attention).
Exercise sheet 9
to be handed in by 12 noon on Fri 25 March 2011.
This is a corrected version. Apologies that the version that originally appeared here and was handed out in class had several lines in question 1 repeated due to a "cut and paste" error.
EXAMINATION
The examination will last 2 hours. The paper will contain SIX questions and
the rubric will state:
"You may attempt as many questions as you wish and all questions carry equal marks. Except
for the award of a bare pass, only the best FOUR questions answered will be counted."
Here is the 2010 Examination Paper. If anyone who tries the 2010 paper would like me to mark their solutions, I would be happy to do so.
You are reminded that examinations are designed to test "Learning Outcomes", and
that the Learning Outcome of MTH6111 is:
"A rigorous understanding of classical complex analyis".
(A more detailed version of this
objective is available on the School of Mathematical Sciences learning outcomes
webpage.)
BOOKS
The following books are good references introducing 'Complex Analysis' from
a pure mathematical point of view and covering much of the course except for
some advanced topics. There are advantages and disadvantages to each textbook,
and I have not chosen any particular textbook
to follow as regards notation and terminology this year:
There are also many more advanced texts on complex function theory you might find it interesting to
dip into, for example Lars Ahlfors, 'Complex Analysis' (McGraw-Hill, 3rd edition 1979),
or Serge Lang, 'Complex Analysis' (Springer Graduate Texts in Mathematics No. 103, 4th edition 2003).
And there are specialist texts on individual topics which also cover much more than we shall:
some of these will be mentioned in the course as we go along.
I shall also try to sort out some interesting web references, for example relevant articles
in Plus Magazine (such as
Marcus du Sautoy's article
and Bob Devaney's article).
For biographies of some of the
celebrated mathematicians responsible for the development of the subject, Cardano, Bombelli, Wessel, Argand, Gauss, Cauchy, Riemann, Liouville, Weierstrass, Picard, Jordan, Poincare, ...
see the University of St Andrews mathematical biographies website.
I recommend a video made a couple of years ago
by Etienne Ghys, of the Ecole Normale Superieure de Lyon. Chapters 5 and 6 have material on complex numbers and complex iteration, but you should find the other Chapters interesting too. The video can be watched on the web,
downloaded for free, or bought as a DVD.
The website address is
Watch this space,
and let me know of anything interesting you find too.
Finally, for bed-time reading on the Riemann Hypothesis (and for much more
about the properties and uses of prime numbers): |
TRIANGLE: A TRI-MODAL ACCESS PROGRAM FOR READING, WRITING,
AND DOING MATH
1. Introduction
TRIANGLE is a DOS and Windows 95 computer program intended for
print-impaired students and professionals in math, science, and
engineering. It includes:
a math/science word processor
a graphing calculator
a viewer for y versus x plots
a table viewer
the Touch-and-Tell Program for audio and/or braille-assisted
reading of tactile figures on an external digitizing pad.
The keyboard or any assistive device/software that emulates a
keyboard may be used for input. TRIANGLE output may be viewed
visually, audibly, and/or by braille.
DOS TRIANGLE[1] has an on-line help file describing all
editing, calculating, graph-viewing, table-browsing, and
figure-reading commands. Several tutorials are also included with
the distribution files. DOS TRIANGLE is available to anyone
interested in trying it.[2] The expanded symbol set used with the
mathematical word processor can be accessed with DOS screen
readers only if the appropriate character tables are installed.
Support is included for Vocal-Eyes speech screen reader and TSI
braille displays. Instructions are included for use with other
screen readers, but some expertise and effort on the part of the
user is required. TRIANGLE menus and help files are in English,
but the program should work with most languages using the roman
alphabet. The new Windows 95 TRIANGLE (beta release expected in
summer 1998) has all the features of DOS TRIANGLE but is
self-voicing through any MS SAPI-compliant speech engine and will
also be accessible in braille through any on-line screen display
that supports the new MS Braille API. This version of the
TRIANGLE program will be demonstrated during the
presentation.
2. Windows TRIANGLE mathematical word processor
The Windows TRIANGLE word processor is an RTF (rich text
format) word processor whose character set includes typographic
and foreign characters and the math symbol fonts of math editors
bundled with MS Word or Word Perfect. TRIANGLE also utilizes
special math and markup symbols to permit all scientific
expressions (including fractions, superscripts, subscripts, and
tabular arrays) to be written in a linear form. These characters
may be entered through a Windows menu, with several of the most
common characters having single-stroke short cuts. This is a
particularly convenient format for blind users.
Expressions may be entered and manipulated with the usual
kinds of editing capabilities found in any text processor, such
as the Windows clipboard for cutting and pasting. In addition
TRIANGLE has a number of special editing and browsing
capabilities that make it particularly convenient for reading and
writing math and scientific expressions. For example, there are
ten specially-addressable clipboards that allow a user to cut and
paste several text selections without losing the last one every
time a new item is saved. This facility provides significantly
increased flexibility that is handy when manipulating math,
solving algebraic equations, etc.
There are several browsing features designed for ease of
reading equations. These include "read enclosed expression"
commands that jump to the beginning of the next or previous
enclosure and read aloud either the entire expression or the
portion of that expression to the next enclosure. Enclosures
include standard items such as parentheses, brackets, and braces,
as well as markup characters defining numerator and denominator
of fractions, complex superscripts, subscripts, or radicals. The
user has a number of audio templates for representing math
symbols and can custom- design them to personal preferences.
Braille access poses a difficult problem, since there is no
"accepted" braille representation for anything except letters. We
have adopted the GS braille representation used in DOS
TRIANGLE[2]. Although DOS TRIANGLE is restricted to 8-dot GS,
Windows TRIANGLE can use either 8-dot or 6-dot GS codes.
GS is a dual 6/8-dot braille representation developed by John
Gardner and Norberto Salinas (Prof. of Mathematics, Univ. of
Kansas). GS was inspired by the current on-going unified braille
code (UBC) development effort by the International Committee on
English Braille[3]. GS adopts the UBC philosophy of retaining as
much as possible of current literary braille. TRIANGLE includes a
GS tutorial for braille users.
Users have a number of options for printing from the TRIANGLE
editor. An ink copy for sighted people can be printed on any
standard printer. The sighted reader must learn the GS markup
symbols for such things as subscript, superscript, fractions, and
arrays, but the representations are straightforward and the
authors believe that such copy should be acceptable for almost
any academic purpose.
There are a number of options for making tactile hard copies.
A GS6 braille copy may be made on any braille embosser. A GS8
copy may be made on any braille embosser that has the ability to
load the GS8 font set. Copies printed in DotsPlus[4], GS6, or GS8
may also be printed using the new TIGER printer[5]. Another
output option is to make a font change to an on-screen braille
dot pattern and print using swell paper[6] or with the Tektronix
Phasor wax jet printer[7].
3. The Windows TRIANGLE graphing calculator
TRIANGLE includes the equivalent of a scientific graphing
calculator. The calculator allows the user to input or define
constants and expressions for convenience and accepts several
types of notation for operations - e.g. one can use a GS multiply
symbol or the * which is commonly used to indicate multiplication
on computers. The result of the computation is displayed in a
calculator window. Results may then be copied and pasted into an
editor window.
TRIANGLE also has a graphing calculator that computes and
displays a y vs. x function (or several functions simultaneously)
on the screen. A number of screen display choices are available.
The graph may be printed for sighted people on any standard
printer. TIGER[5] can print a tactile copy directly, or
indirectly with swell paper[6] or the Phasor[7]. A graphics
braille embosser can be used to make a low resolution copy of the
graph (without any text or labels of course). However the graph
may also be viewed on-line with the x-y graph viewer.
4. The DOS and WINDOWS TRIANGLE x-y graph viewer
A graphed function is scaled so that it can be displayed as a
convenient size picture on the screen. It is "viewed" audibly by
a blind user through the use of a tone plot. The user may move a
pointer along the independent variable axis, and the value of the
function is indi-cated by the pitch of a tone. The function is
scaled so that the full range from the minimum and maximum of the
function corresponds to a pitch well within the normal range of
human hearing. The function is also displayed with a moving icon
on the bottom line of the screen. As the pointer is moved along
the independ-ent-variable axis, the icon moves to the right as
the function becomes larger and to the left as it becomes
smaller. This icon is primarily intended for deaf blind users who
would view it with an on-line braille display.
The graph's pointer may be moved one point at a time or
allowed to scan automatically from left to right, or from right
to left. In addition to the tone indicating the function, the
values of the independent variable and the function are displayed
on the screen, and may be read aloud if desired. The viewer
functions include the ability to find both relative and absolute
maxima and minima, zeros, etc. The simple tone reader gives a
reasonable qualitative overview, and a user may look individually
at various points for quantitative information.
5. The DOS and Windows TRIANGLE table viewer
Tables may be included as part of a text file or saved as
table files with a defined file extension. In either case, they
should be marked up with the GS markup indicators that tell where
the table begins and ends and where each element and line
ends.
The table view has two modes. A formatted mode is intended
primarily for small tables being read using an on-line braille
display. In this mode, tables are displayed on the screen much as
they would be if formatted for sighted readers.
The formatted table mode is clumsy if the table is large or if
the user (of DOS TRIANGLE) is reading with a speech synthesizer.
The cell-by-cell mode is intended for such cases. The reader
views one cell at a time and can navigate right and left, up and
down from cell to cell in the table. The screen also shows the
title and the cell row and column number. Optional information
such as the row or column labels may also be displayed. This mode
permits blind readers to read extremely large or complex
tables.
The table viewer may be entered at will, and a table remains
in the viewer until it is replaced by another one. Tables
appearing in the text may be captured into the reader by placing
the cursor anywhere within the table and pressing a "capture
table" short cut key.
6. The DOS and Windows TRIANGLE Touch-and-Tell figure
viewer
This feature requires use of an external digitizing tablet on
which a tactile figure is mounted. A computer "map" file is
required, so that whenever a user identifies an object on the
figure, the computer can display information about that object.
The information is read by speech and/or braille and may be
arbitrarily large. The map files are produced by a sighted user
to create the annotated pictures. Once the files are created,
they can be read by the TRIANGLE program and printed to a
graphics embosser.
The figure viewer can be entered at will, and once a map file
is read in, the figure is scaled by indicating marks at the top
right and bottom left of the figure. This information remains
until a new figure is mounted and a new map file read into the
table viewer.
7. Preparing materials for TRIANGLE
Both sighted and blind users can create scientific documents
in the word processor, save expressions to be computed and
graphed, and create tables in the table viewer. It is possible in
principle to translate TRIANGLE files to and from other formats
that typeset information in standard two-dimensional notation for
sighted people. The authors expect to support the new XML world
wide web language for this purpose.
A sighted person can create tactile figures and the
accompanying computer map files with our Objectif[2] program.
Objectif runs under Microsoft Windows and permits a sighted
person easily to edit and simplify a bit mapped image file to be
printed on a braille graphics embosser or one of the new direct
technologies.[5-7]
The map file is created by selecting objects on the computer
screen and entering labels or any desired text information to be
displayed when the blind user selects that object. At present
there is no way for a blind user to create TRIANGLE figures and
map files.
8. Acknowledgments
This research was supported by National Science Foundation
grant HRD-9452881.
[5] The TIGER (TactIle Graphics EmbosseR) is a Windows 95
tactile printer capable of printing from standard Windows 95
applications. Text can be printed in 6- or 8-dot DotsPlus or any
braille font including American, DIN, or British computer braille
or either GS6 or GS8. TIGER was invented and developed in this
research group and has been licensed to ViewPlus Technologies,
Inc. That company has a booth at this conference. TIGER will be
available commercially in summer 1998 at $6,000. For more
information, see
[6] Swell paper is the currently most common technique for
making tactile printouts of arbitrary line and block graphics.
See
[7] Tektronix Inc. is marketing a version of their Phasor wax
jetcolor printer that allows extra wax to be deposited in order
to make a tactile image. Cost for the lowest priced model is
$14,000. |
Huntingtown CalculusMATLAB is used in the course to some extent. MATLAB stands for Matrix Laboratory and involves the formulation of a problem in matrix terms. Matlab can handle vast amounts of input data and manipulate the data in accordance with the instructions that the user provides |
combined differential equations and linear algebra courses teaching students who have successfully completed three semesters of calculus.
This complete introduction to both differential equations and linear algebra presents a carefully balanced and sound integration of the two topics. It promotes in-depth understanding rather than rote memorization, enabling students to fully comprehend abstract concepts and leave the course with a solid foundation in linear algebra. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. A vast array of problems supports the material, with varying levels from which students/instructors can choose.
Features
• A better integration of DE and Linear Algebra than other texts on the market.
• One of the most lucid and clearly written narratives on the subject, with material that is accessible to the average student yet challenging to all students.
• Several application problems introduced in the first section of the text – Subsequently uses them throughout the following chapters to help motivate students.
New To This Edition
• Enhanced visual appeal – Includes a 2-color design as well as a more natural, attractive, and consistent presentation of mathematics.
• Enlargement of most exercise sets – Now features over 2600 problems.
• Enhanced end-of-section pedagogy:
– Includes a list of key terms, skills students should acquire from the section, a true-false review section, and problems.
– Encourages students to take an active role in mastering each section's concepts.
• End-of-chapter summary and some additional exercises for chapter:
– Give students a broad perspective on the chapter and encourage them to review topics on a larger scale.
– Some chapters also contain project ideas for students interested in deeper applications of the material.
• New problems in many sections – Provide additional practice and exposure to the ideas, methods, theoretical foundation, and applications presented.
• Reorganized material:
– The material on second-order linear differential equations has been moved into Chapter 6, which covers general nth order differential equations.
– Matrix functions are now introduced in Chapter 2.
– The matrix exponential function is now introduced in Chapter 5, which covers linear transformations.
• New sections added to the Third Edition:
– Sections 2.8 and 4.10 keep track of the many characteristics of the invertibility of an n x n matrix.
– Section 4.7 – Change of Basis – introduces the idea of the change of basis matrix, and how components of vectors relative to different bases are related.
– Section 5.5 – The Matrix of a Linear Transformation – illustrates how an arbitrary linear transformation between finite-dimensional vector spaces can be represented by a matrix, once a basis for each vector space has been specified, and shows how linear transformation concepts can be described in terms of matrix algebra |
A number of online textbooks have been created in the past several years, and this course in linear algebra is a nice addition to the existing repertoire of such educational materials. Professor Rob Beezer of the...
Under the motto, "Show me how, now!" algebasics is a fine online mathematics instructional resource that takes young and old alike through the basics of algebra. The breadth of the material is divided into sixteen...
Practice solving algebraic equations with this interactive quiz brought to you by Interactivate and the Computational Science Education Reference Desk. The quiz allows you to select the difficulty level, time limit and...
A course designed to familiarize high school and beginning college mathematics teachers with advanced algebra content and teaching strategies. The approach stresses modeling and solving real world problems and develops...
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9780471089759
ISBN:
0471089753
Publisher: Wiley & Sons, Incorporated, John
Summary: Combining standard Volumes I & II into one soft cover edition, this helpful book explains how to solve mathematical problems in a clear, step-by-step progression. It shows how to think about a problem, how to look at special cases, & how to devise an effective strategy to attack & solve the problem. Covers arithmetic, algebra, geometry, & some elementary combinatorics. Includes an updated bibliography & newly expande...d index.
Pólya, George is the author of Mathematical Discovery On Understanding, Learning, and Teaching Problem Solving, published under ISBN 9780471089759 and 0471089753. Two hundred ninety eight Mathematical Discovery On Understanding, Learning, and Teaching Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred twenty one used from the cheapest price of $4.12, or buy new starting at $22.50.[read more |
Tucson SAT MathNow the student must learn to see it from the perspective of functions: polynomial, rational, radical, exponential and trigonometric functions. Calculus, as Algebra, is an art; the artist needs a pallet. In this case the pallet is the coordinate plane and the student must learn to draw the faces (graphs) of all the functions and recognize them from their faces |
Synopses & Reviews
Publisher Comments:
— and its relevance to many applications, particularly computer-related functions. Assuming only a knowledge of calculus and some statistics, it concentrates on linear signal processing, with some consideration of roundoff effects and Kalman filters. Numerous examples and exercises.
Synopsis:
Introductory text examines role of digital filtering in many applications, particularly computers. Focus on linear signal processing; some consideration of roundoff effects, Kalman filters. Only calculus, some statistics required.
About the Author
Richard W. Hamming: The Computer Icon
Richard W. Hamming (1915-1998) was first a programmer of one of the earliest digital computers while assigned to the Manhattan Project in 1945, then for many years he worked at Bell Labs, and later at the Naval Postgraduate School in Monterey, California. He was a witty and iconoclastic mathematician and computer scientist whose work and influence still reverberates through the areas he was interested in and passionate about. Three of his long-lived books have been reprinted by Dover: Numerical Methods for Scientists and Engineers, 1987; Digital Filters, 1997; and Methods of Mathematics Applied to Calculus, Probability and Statistics, 2004.
In the Author's Own Words:
"The purpose of computing is insight, not numbers."
"There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think."
"Whereas Newton could say, 'If I have seen a little farther than others, it is because I have stood on the shoulders of giants, I am forced to say, 'Today we stand on each other's feet.' Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way."
"If you don't work on important problems, it's not likely that you'll do important work." — Richard W. Hamming
What Our Readers Are Saying
Average customer rating based on 1 comment:
nimali, October 9, 2006 (view all comments by nimali)
This is an excellent book for who is studing about digital filters.It provides a nice guidence to the student. it explains lot of theories with simple mathematics.thats why i like this book very much |
I'll be teaching an undergraduate level course in elementary numerical
methods next semester. I would seriously consider using Python/SciPy
as the computing environment for the course but I have not been able
to find a textbook that is Python based. The appropriate level for
the text would be similar to Kincaid and Cheney, as you can preview
here:
That book is more expensive than I'd like, however, and is not Python
based.
Any suggestions?
Thanks,
Mark McClure |
Additional product details
Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Intermediate Algebra, Fourth Edition was written to help students effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. |
Greenwich, CT Prealgebra Black Scholes equation is really a partial differential equations which is "one step higher" as compared to the Ordinary Differential Equations. In addition, I've taken classes have expertise in the following types of ODE's:
--- ODE's with "separable variables"
--- first-order linear O... candidates |
Course Information
Overview
In MCS 118, we will study polynomial and power functions. In particular, we will learn how to find limits, calculate instantaneous rates of change, and compute the area bounded by graphs of these functions. We will use these ideas to model various real world problems. At the same time, we will review the algebra and pre-calculus skills that are useful in understanding this material.
In MCS 119, we will continue our study of calculus by extending the ideas from MCS 118 to exponential, logarithmic, and trigonometric functions. Students who complete both MCS118 and MCS119 may use MCS119 to substitute for MCS121.
Prerequisites
Two years of high school mathematics beyond plane geometry, including trigonometry.
Text:
We will use Calculus I with Precalculus, 2nd Edition by Larson, Hostetler, and Edwards. Be sure you have the second edition, not the third. (The third edition is considerably more expensive.)
Calculators
You should have a graphing calculator available for use in class and on exams. If you are buying a new one, the MCS department encourages the use of Texas Instruments calculators, in particular the TI86, or the TI89 (though the use of some of the TI89 features may be restricted, so that I will want you to use another calculator on quizzes and tests). If you have the standard version of any of these calculators there is no need to purchase a new calculator. If you have another brand of calculator please see me before purchasing a new one as you may be able to continue using it. A limited number of calculators are available in the Diversity Center for students who have financial difficulties buying one.
Class Web Site
Classes
Classes will be used for lectures, problem solving, discussions, and other fun activities. You should prepare for
classes by doing the reading beforehand (reading assignments are posted on the Web), thinking about
the problems in the text, and formulating questions of your own. You should also participate as much as possible in
class. Class meetings are not intended to be a complete encapsulation of the course material. You will be responsible
for learning some of the material on your own.
Attendance, both physical and mental, is required.
Should you need to miss a class for any reason, you are
still responsible for the material covered in that class. This means that you will need to make sure that you
understand the reading for that day, that you should ask a friend for the notes from that day, and make sure that
you understand what was covered. You may not make up any in-class work, unless you have accommodations for a disability (see below). If there is a homework assignment due that day, you should be sure to have a friend hand
it in or put it in my departmental mailbox (in Olin 324). You do not need to tell me why you missed a class unless
there is a compelling reason for me to know.
Should you miss more than four classes, no matter what the reason, I reserve the right to make your class participation grade a 0.
Texting (reading or sending messages) in class is prohibited.
If you are expecting an urgent call or text message, you should notify me before class. When you get the call, you should quietly leave class and deal with it in the hall. If you are not expecting an urgent call, your cell phone should be turned off and stored in your backpack.
Homework
You will need to read a section of the book and do problems for each day that we have class.
Homework problems are designed to help you learn the material we cover in class and in the reading. You should read the material and attempt the problems before coming to class. You should finish the problems after class. You may work with other students on these problems; but be sure to give credit. Once or twice a week, you will hand in your solutions to the problems you did. These should be neatly written on standard sized paper, and with all of the pages stapled together. The sections and problem numbers should be clearly labeled. Once you've completed the homework, fill out a homework reflection sheet and then staple all of your solutions together with the homework reflection sheet on top. The grader will only grade a few sample problems.
On the day that homework problems are due, you will be asked to place your work in a homework folder. After class, I place the folder outside my office door for the grader. Any homework that is not in this folder when the grader gets it is considered late. Late homework will be accepted as long as I get it before my grader hands back the graded assignments. (Alternatively, you can put it in the folder for late homework that is outside my office door.) In that case, the homework will be graded but you will lose 30% of the points on that assignment.
Quizzes and Exams
We will have four quizzes, one mid-semester exam, and and a final exam. The mid-semester exam will be given in the evening, on Tuesday, Oct. 15, from 5:00 -7:00 or from 7:00 - 9:00. The final is scheduled for . Be sure to make appropriate travel plans.
Course grade
Your grade is a measure of your learning and growth in the course, rather than a set of points to be "earned" or "lost." Viewed this way, a grade shows the extent to which you have mastered and can communicate important concepts and ideas. Not all work is graded – you do many things in a course that contribute to your learning: reading, writing, revising, thinking, talking, and listening. It is useful to think of work, then, as the set of activities that contribute to learning. Graded work is that subset of activities where you show how well you have learned to reason mathematically and how well you can communicate your reasoning to others.
The graded course components will contribute to your grade in the following proportion:
Class participation
5%
Homework problems
15%
Quizzes
30%
Mid-term exam
20%
Final exam
30%
Letter grades are assigned using the following table.
A 93-100
A- 90-92.9
mastery of the material with developed insight
B+ 87 -89.9
B 83-86.9
B- 80 -82.9
mastery with limited insight
C+ 77-79.9
C 73 -76.9
C- 70-72.9
basic knowledge with limited mastery
D+ 67-69.9
D 60- 66.9
F 0-59.9
minimal to unacceptable performance
Disability Services
Gustavus Adolphus College is committed to ensuring the full participation of all students in its programs. If you
have a documented disability (or you think you may have a disability of any nature) and, as a result, need reasonable
academic accommodation to participate in class, take tests or benefit from the College's services, then you should
speak with the Disability Services Coordinator, for a confidential discussion of your needs and appropriate plans.
Course requirements cannot be waived, but reasonable accommodations may be provided based on disability documentation
and course outcomes. Accommodations cannot be made retroactively; therefore, to maximize your academic success at Gustavus,
please contact Disability Services as early as possible. Disability Services
is located in the Advising and Counseling Center.
Academic Integrity
You are expected to to adhere to the highest standards of academic honesty, to uphold the Gustavus Honor Code and
to abide by the Academic Honesty Policy. A copy of the honor code can be found in the
Academic Bulletin and a copy of the academic
honesty policy can be found in the Academic
Polices section of the Gustavus Guide.
On homework problems, I encourage you to discuss problems and their solutions with each other.
However, each of you should first make a real effort to solve each problem by yourself.
On quizzes and tests, you are expected to work completely by yourself, and to sign the honor pledge on each of
these assignments. The first violation of this policy will result in a 0 on that assignment and notification of the
Dean of Faculty. Further violations will result in failing the course.
Help for Students Whose First Language is not English
Support for English Language Learners and Multilingual students is available through the Academic Support Center and the Multilingual/English Language Learner Academic Support Specialist, Laura Lindell (x7197). She can meet individually with students for tutoring in writing, consulting about academic tasks and helping students connect with the College's support systems. When requested, she can consult with faculty regarding effective classroom strategies for ELL and multilingual students. Laura can provide students with a letter to a professor that explains and supports appropriate academic arrangements (e.g. additional time on tests, additional revisions for papers). Professors make decisions based on those recommendations at their own discretion. In addition, ELL and multilingual students can seek help from peer tutors in the Writing Center. |
Based on Saxon's proven methods of incremental development and continual review strategies, the Saxon Advanced Math program builds on intermediate algebraic concepts and trigonometry concepts introduced in Algebra 2 and prepares students for future success in calculus, chemistry, physics and social sciences.
This set of tests is ideal for the homeschool family that already has the Advanced Math curriculum and needs resources for an additional student completing the program.
Product:
Saxon Advanced Math: Homeschool Test Forms Only
Manufactured by:
Saxon Publishers
Author:
John Saxon Jr
Edition Number:
2
Binding Type:
Paperback
Media Type:
Book
Minimum Grade:
9th Grade
Maximum Grade:
12th Grade
Weight:
0.16 pounds
Length:
11 inches
Width:
8.18 inches
Height:
0.05 inches
Publisher:
Saxon Publishers
Publication Date:
January 2005 Saxon Advanced Math: Homeschool Test Forms Only.
Average Rating
Parent Rating
Comments
My son has used Saxon for most of his school years and scored high in math on his ACT test after 8th and 9th grade.
Our daughter had difficulty with math when we started using Saxon math curriculum. The spiral organization of the curriculum never gave her the opportunity to 'forget' previously learned concepts, but challenged her to continually progress in each concept. Math is now her top subject. |
MATHEMATICS
A scientific calculator is recommended for each student. It is important that students retain their instruction manual for reference.
Due to the complexity of the pathways in Mathematics, we have included this flowchart for
clarification.
While the bolded pathways MCV4U
Grade 12
illustrated are the most likely to The NEW Advance Functions course
Vectors & Calculus
occur, other pathways are possible. can be taken concurrently with or
can precede Calculus and Vectors.
Consult your guidance counsellor
and mathematics teacher for more
information.
To qualify for the Ontario MHF4U
Secondary School Diploma, a MCR3U Grade 12
Grade 11 Advanced Functions
student must have 3 compulsory
credits in mathematics. Functions
University Prep.
MDM4U
Grade 12
Mathematics of
Data Management
MPM1D MPM2D
Grade 9 Grade 10
Academic Academic MCF3M
Math Math Grade 11 MCT4C
Functions & Grade 12
Applications Mathematics for College
Univ./College Technology
MBF3C MAP4C
Grade 11 Grade 12
MFM1P MFM2P Foundations for Foundations for College
Grade 9 Grade 10 College Math Math
Applied Applied
Math Math
MEL3E MEL4E
Grade 11 Grade 12
Mathematics for Mathematics for
Everyday Life Everyday Life
Indicates completion of a supplementary course is required
Principles of Mathematics, Grade 9, Academic MPM1D1
This course enables students to develop understanding of mathematical concepts related to algebra, analytic geometry,
and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students
will investigate relationships, which they will then generalize as equations of lines, and will determine the connections
between different representations of a relationship. They will also explore relationships that emerge from the
measurement of three-dimensional objects and two-dimensional shapes. Students will reason mathematically and
communicate their thinking as they solve multi-step problems. Successful completion of this course prepares students for
Principles of Mathematics, Grade 10, Academic (MPM2D) or Foundations of Mathematics, Grade 10, Applied (MFM2P).
Learning through abstract reasoning is an important aspect of this course.
Foundations of Mathematics, Grade 9, Applied MFM1P1
This course enables students to develop understanding of mathematical concepts related to introductory algebra,
proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and
hands-on activities. Students will investigate real-life examples to develop various representations of linear relationships,
and will determine the connections between the representations. They will also explore certain relationships that emerge
from the measurement of three-dimensional objects and two-dimensional shapes. Students will consolidate their
mathematical skills as they solve problems and communicate their thinking.
Successful completion of this course prepares students for Foundations of Mathematics, Grade 10, Applied (MFM2P).
Learning through hands-on activities and the use of concrete examples is an important aspect of this course.
Principles of Mathematics, Grade 10, Academic MPM2D1
PREREQUISTE: Principles of Mathematics, Grade 9, Academic
This course enables students to broaden their understanding of relationships and extend their problem-solving and
algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore
quadratic relationships and their applications; solve and apply linear systems; verify properties of geometric figures using
analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically as
they solve multi-step problems and communicate their thinking.
Foundations of Mathematics, Grade 10, Applied MFM2P1
PREREQUISTE: Principles of Mathematics, Grade 9 Academic or Applied
This course enables students to consolidate their understanding of relationships and extend their problem-solving and
algebraic skills through investigation, the effective use of technology, and hands-on activities. Students will develop and
graph equations in analytic geometry; solve and apply linear systems, using real-life examples; and explore and interpret
graphs of quadratic relationships. Students will investigate similar triangles, the trigonometry of right-angled triangles, and
the measurement of three-dimensional objects. Students will consolidate their mathematical skills as they solve problems
and communicate their thinking.
Functions, Grade 11, University MCR3U1
PREREQUISTE: Principles of Mathematics, Grade 10, Academic
This course introduces the mathematical concept of the function by extending students' experiences with linear and
quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and
exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving
applications of functions; and develop facility in simplifying polynomial and rational expressions. Students will reason
mathematically and communicate their thinking as they solve multi-step problems. A mark of at least 70% from Grade
10 Academic is strongly recommended.
Functions and Applications, Grade 11, University/College MCF3M1
PREREQUISTE: Principles of Mathematics, Grade 10, Academic, or Foundations of Mathematics, Grade 10, Applied
Note: This is the required Prerequisite for Mathematics for College Technology, MCT 4C1.
This course introduces basic features of the function by extending students' experiences with quadratic relations. It
focuses on quadratic, trigonometric, and exponential functions and their use in modeling real-world situations. Students
will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve
problems relating to financial and trigonometric applications. Students will reason mathematically and communicate their
thinking as they solve multi-step problems.
Foundations for College Mathematics, Grade 11, College MBF3C1
PREREQUISTE: Foundations of Mathematics, Grade 10, Applied
This course enables students to broaden their understanding of mathematics as a problem-solving tool in the real world.
Students will extend their understanding of quadratic relations, as well as of measurement and geometry; investigate
situations involving exponential growth; solve problems involving compound interest; solve financial problems connected
with vehicle ownership; and develop their ability to reason by collecting, analysing, and evaluating data involving one and
two variables. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Mathematics for Work and Everyday Life, Grade 11, Workplace MEL3E1
PREREQUISTE: Principles of Mathematics, Grade 9, Academic, or Foundations of Mathematics, Grade 9, Applied, or a
ministry-approved locally developed Grade 10 mathematics course
This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily
life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations
of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel
in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their
thinking.
Calculus and Vectors, Grade 12, University Preparation MCV4U1
Note: The new Advanced Functions can be taken concurrently with or can precede Calculus and Vectors.
This course builds on students' previous experience with functions and their developing understanding of rates of change.
Students will solve problems involving geometric and algebraic representations of vectors, and representations of lines
and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of
polynomial, rational, exponential, and sinusoidal functions; and apply these concepts and skills to the modelling of real-
world relationships. Students will also refine their use of the mathematical processes necessary for success in senior
mathematics. This course is intended for students who plan to study mathematics in university and who may choose to
pursue careers in fields such as physics and engineering.
Advanced Functions, Grade 12, University Preparation MHF4U1
PREREQUISITE: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12,
College Preparation
This course extends students' experience with functions. Students will investigate the properties of polynomial, rational,
logarithmic, and trigonometric functions; broaden their understanding of rates of change; and develop facility in applying
these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in
senior mathematics. This course is intended both for students who plan to study mathematics in university and for those
wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university
programs.
Mathematics of Data Management, Grade 12, University Preparation MDM4U1
PREREQUISITE: Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11,
University Preparation
This course broadens students' understanding of mathematics as it relates to managing data. Students will apply methods
for organizing large amounts of information; solve problems involving probability and statistics; and carry out a culminating
project that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes
necessary for success in senior mathematics. Students planning to enter university programs in business, the social
sciences, and the humanities will find this course of particular interest.
Mathematics for College Technology, Grade 12, College Preparation MCT4C1
PREREQUISITE: Functions and Applications, Grade 11, University/College Preparation
This course enables students to extend their knowledge of functions. Students will investigate and apply properties of
polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and
algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address
applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their
thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs.
Foundations for College Mathematics, Grade 12, College Preparation MAP4C1
PREREQUISITE: Foundations for College Mathematics, Grade 11, College Preparation
This course enables students to broaden their understanding of real-world applications of mathematics. Students will
analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; simplify
expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve
multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and
human services, and for certain skilled trades.
Mathematics for Work and Everyday Life, Grade 12, Workplace Preparation MEL4E1
PREREQUISITE: Mathematics for Work and Everyday Life, Grade 11, Workplace Preparation
This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily
life. Students will investigate questions involving the use of statistics; apply the concept of probability to solve problems
involving familiar situations; investigate accommodation costs and create household budgets; use proportional reasoning;
estimate and measure; and apply geometric concepts to create designs. Students will consolidate their mathematical
skills as they solve problems and communicate their thinking |
A is for Algebra-and that's the grade you'll pull when you use Bob Miller's simple guide to the math course every college-bound kid must take
With eight books and more than 30 years of hard-core classroom experience, Bob Miller is the frustrated student's best friend. He breaks down the complexities of every problem into easy-to-understand... more...
Confusing TextbooksFrom the author of the highly successful The Complete Idiot's Guide to Calculus comes the perfect book for high school and college students. Following a standard algebra curriculum, it will teach students the basics so that they can make sense of their textbooks and get through algebra class with flying colors. more...
Whether you're a science major, an engineer, or a business graduate, calculus can be one of the most intimidating subjects around. Fortunately, Calculus for the Utterly Confused is your formula for success. Written by two experienced teachers who have taken the complexity out of calculus for thousands of students, this book breaks down tough concepts... more...
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,... more...
Master algebra from the comfort of home!
Want to ?know it all? when it comes to algebra? Algebra Know-It-ALL gives you the expert, one-on-one instruction you need, whether you're new to algebra or you're looking to ramp up your skills.
Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves... more...
We want to help you succeed on the GMAT math section If math is the hardest part of the GMAT for you, we're here to help. McGraw-Hill's Conquering GMAT Math is packed with strategies for answering every kind of GMAT math question. You'll also get intensive practice with every question type to help you build your test-taking confidence. With... more...
Get ready to master basic arithmetic subjects, principles, and formulas! Master Math: Basic Math and Pre-Algebra is a comprehensive reference guide that explains and clarifies mathematic principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced, Master Math:... more... |
a mathematical modeling course in a civil/environmental engineering program
This book has a dual objective: first, to introduce the reader to some of the most important and widespread environmental issues of the day; and second, to illustrate the vital role played by mathematical models in investigating these issues. The environmental issues addressed include: ground-water contamination, air pollution, and hazardous material emergencies. These issues are presented in their full real-world context, not as scientific or mathematical abstractions; and for background readers are invited to investigate their presence in their own communities.
The first part of the book leads the reader through relatively elementary modeling of these phenomena, including simple algebraic equations for ground water, slightly more complex algebraic equations (preferably implemented on a spreadsheet or other computerized framework) for air pollution, and a fully computerized modeling package for hazardous materials incident analysis. The interplay between physical intuition and mathematical analysis is emphasized.
The second part of the book returns to the same three subjects but with a higher level of mathematical sophistication (adjustable to the preparation of the reader by selection of subsections.) Many important classical mathematical themes are developed through this context, examples coming from single and multivariable calculus, differential equations, numerical analysis, linear algebra, and probability. The material is presented in such a way as to minimize the required background and to encourage the subsequent study of some of these fields.
An elementary course for a general audience could be based entirely on Part I, and a higher level mathematics, science, or engineering course could move quickly to Part 2. The exercises in both parts tend to be quite thought-provoking and considerable course time might be well devoted to discussing their solutions, perhaps even in a seminar format. The emphasis throughout is on fundamental principles and concepts, not on achieving technical mastery of state-of-the-art-models.
Excerpt: 2.4 Darcy's Law (p. 19)
In developing any kind of mathematical model, you need to figure out what the key physical variables are that control the situation of interest. We are interested here in the flow of ground water through some kind of porous geologic medium. In about 1850 a French engineer named Henri Darcy was interested in essentially the same question because he was trying to set up a system for filtering water in the city of Dijon, France, by passing it through beds of clean sand (such sand filters are still commonly used today.) The question he faced was really how much water could move at what rate through what size sand filter. To answer this question, he set up some simple experiements.
About the Author
Charles Hadlock received his Ph.D. from the University of Illinois in 1970, specializing in applied mathematics. He taught at Amherst and Bowdoin Colleges before joining the firm of Arthur D. Little in Cambridge, Massachusetts in 1977, where he developed and led an international consulting practice in environmental management and risk analysis. His central focus was the investigation and follow-up to the unfolding environmental calamities of the day, including Love Canal, Bhopal, Three Mile Island, and other well known cases, and the use of mathematical models to enhance the understanding of and response to these situations. In 1990 he moved to Bentley College as Chair of Mathematical Sciences, and is currently Dean of the Undergraduate College and Associate Dean of Faculty. Dr. Hadlock has written an award-winning book on Galois theory, as well as numerous research reports and publications, and he has chaired several major government panels reviewing environmental policies.
MAA Review
The author of this book is particularly well suited to writing about the subject. Starting off as a mathematics professor, he spent 13 years as an environmental consultant before returning to the classroom. Thus, many of the examples, experiences, and insights in the book are realistic and convincing. Continued.... |
Explore higher-level math concepts – Explore symbolic algebra and symbolic calculus, in addition to standard numeric calculations. View exact values – in the form of variables such as x and y, radicals and pi – when doing step-by-step arithmetic, algebraic and calculus calculations.
Visualize in full color – Color-code equations, objects, points and lines on the full-color, backlit display. Make faster, stronger connections between equations, graphs and geometric representations on screen.
Real-world images** – Use digital images or your own photos. Overlay and color-code math and science concepts. Discover real-world connections.
Recharge with ease – The installed TI-Nspire Rechargeable Battery is expected to last up to two weeks of normal use on a single charge. No alkaline batteries needed.
Calculate in style – The slee...
Features: Electronically upgradeable graphing calculator allows you to have the most up-to-date functionality and software applications.
16 preloaded graphing calculator software applications suitable for college math and engineering coursework.
Memory management to create folders for specific applications or subjects.
Icon desktop for easier access to applications and editors.
Pretty Print shows equations and results with radical notation, stacked fractions and superscript exponents.
Permitted for use on many state and standardized tests.
I/O port for communication with other TI products.
Features: Negative sign: Appears to the left of the number displayed
ANYLITE solar power: Operates in low light; never needs batteries
Plastic keys: Tamper proof, and cannot be removed
Large keys: Grouped and color coded by related functions
Extra-large equal key
Percent square root keys
Negative sign appears immediately to the left of the number displayed
Addition subtraction multiplication division
Automatic constant for all four operations
Change sign (+/-) key
Capability to clear last entry and/or all entries
3-key memory
Available in convenient Teacher Kit with 10 calculators
Teacher's Guide in English and Spanish included
Permanent storage cadd...
Features: If you have a Windows computer, the TI-Connectivity Kit cable for Windows/Mac and TI Connect software are compatible with the TI-73, TI-83, TI-83 Plus, TI-83 Plus Silver Edition, TI-89, TI-92, TI-92 Plus and Voyage 200. (Note: will not work with TI-82, TI-85, or TI-86 at this time); If you have a Mac computer, the TI-Connectivity Kit USB cable for Windows/Mac and TI Connect software are compatible with all TI Graphing Products (TI-73, TI-82, TI-83, TI-83 Plus, TI-83 Plus Silver Edition, TI-85, TI-86, TI-89, TI-92, TI-92 Plus and Voyage 200).
Features: Mode menu
The menu is structured for easy, intuitive access to commands. Select degrees/radians, floating/fix, Classic/MathPrint or number format.
Memory variables
Store real numbers and expressions that result in real numbers as one of seven available memory variables.
Data list editor
Enter statistical data in up to three lists, with a maximum of 42 items per list. Any list formulas that are entered can accept all calculator functions. Readily perform one- and two-variable analysis, and display six different regression models.
Solvers
Choose from three solvers to use: numeric equation, polynomial and system of linear equations.
Function Table
Display a defined function in a tabular form.
Derivative & Integral
Determine the numeric derivative and integral for real functions.
Vectors & Matrices
Perform vectors...
Features: Ideal for the algebra classroom.
Lets students graph and compare functions, as well as perform data plotting and analysis.
Horizontal and vertical split screen options.
Advanced functions accessed through pull-down display menus.
Includes tools for finance.
I/O port for communication with other TI products.
Features: Dynamic full-color display with backlit capability.
Thin and lightweight with easy touchpad navigation.
Use digital images or your own photos and overlay with graphical elements on the screen.
Student Software allows students to continue and/or complete assigned work outside of the classroom.
Rechargeable battery included; lasts up to two weeks on a single charge.
Features: TI84Plus Silver Edition ViewScreen Calculator ViewScreen calculators are compatible with the same ViewScreen panel.
ViewScreen handhelds, or "teacher units", have all the functionality of student calculators.
Plus, they can be plugged into a ViewScreen panel or TI-Presenter video interface for projection to the entire class. |
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Many issues of contemporary importance in climate science can be explored using techniques from mathematics and statistics. This timely textbook introduces students and researchers to the conceptual models that capture important aspects of the Earth's climate system and the mathematical and statistical techniques that can be applied to their analysis. |
Welcome to calculus. It will be my great pleasure to guide you on a journey through a world of calculus during these 24 lectures. The tour begins at our doorsteps and takes us to the stars. Calculus is all around us every day of our lives. When we're driving down the road and we see where we are at every moment and we figure out how fast we're going, that's calculus. When we throw a baseball and see where it lands, that's calculus.
But, calculus is not restricted only to physical issues. When we lament the decline in the population of the spotted owl, that's calculus. When we analyze the stock market and we look at economic trends, that's calculus. Calculus comprises a collection of ideas that have had tremendous historical impact. And the reason is that calculus is enormously effective in allowing people to bend nature to human purpose. Much of the scientific description of our world is based on calculus; descriptions of motion, certainly; of electricity and magnetism; of sound waves or waterways—all of these involve calculus. But in addition to that, calculus is an essential tool for understanding social and biological sciences. It occurs every day when we describe economic trends, when we talk about population growth or decline, or medical treatments; all of the description are couched in terms of calculus. That is, its vocabulary, its notation, but most important, more important than any of those, are its ideas, its perspectives.
Well, in this course we're going to emphasize the ideas of calculus, the concepts of calculus, more than the mechanical side of calculus. I'd like to take the remaining part of this lecture to just tell you the structure of the upcoming lectures, the structure of the course.
So, we'll begin in Lectures Two, Three, and Four comprise a collection of lectures that really present the fundamental ideas of calculus. In Lecture Two we introduce the idea of the derivative and say what the definition is and what it means. Then, in Lecture Three, we do the same thing to the integral and say what the definition of the integral is, how it comes about. And, then, in Lecture Four, we introduce the fundamental theorem of calculus, which connects the two.
Well, after we get through Lecture Four, then we proceed to investigate each of these fundamental ideas in more detail. we're going to take the derivative and look at it from the point of view of its algebraic manifestations. One of the properties that makes the derivative so potent, and the integral, is that you can do it algebraically, and that's this mechanical side that students view as—the most common part that they deal with most is learning how to manipulate the algebra. So, we'll see the derivative then physically, that is, with the car moving; and then graphically; and then algebraically; and, then, we'll see it applied to different application areas such as volume, formulas for the volumes of objects—all of these things have manifestations about the derivative.
After that, we turn to the integral and we have a similar sequence of lectures that present the integral in these terms. That is to say, graphically, algebraically, and in terms of their applications to many different areas. So by taking these fundamental ideas and viewing them in different ways, that will show the richness of these themes. Then, the last half of this course will demonstrate the richness of these two ideas by showing lots of examples of their extensions, their variations, and their applications.
Well the purpose of these lectures is to explain clearly the concepts of calculus and to convince you that calculus can be understood from simple scenarios. Calculus is so effective because it deals with change and motion, and it allows us to view our world as a dynamic rather than just a static place. Calculus provides a tool for measuring change, whether it's a change in position, change in temperature, change in demand, or change in population. But, in addition to that, I like to think that calculus is intrinsically intriguing and beautiful, as well as just being merely important. So, calculus is a crowning intellectual achievement of humanity that all intelligent people can appreciate, enjoy, and understand. I look forward to exploring calculus with you during the next 23 lectures. Bye for now. |
Elements of Algebra: Geometry, Numbers, Equations - 1 edition
Summary: This text presents a concise, self-contained introduction to abstract algebra which stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation - both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old problems.
2010 |
* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (see Withdrawal dates explained for more information).
This unit introduces students to the curriculum and pedagogy associated with teaching secondary mathematics (Grades 7 to 10). It is intended that students will be challenged about their ideas of the nature of mathematics. In addition, students will take part in activities that show that mathematics can be taught in more enriching ways than traditional "chalk and talk" methods. This unit will also explore and consider ways in which technology can enhance student learning of mathematics. Students will be encouraged to reflect on their own experience of learning mathematics at secondary school. The responsibility of teachers to foster positive attitudes towards mathematics in the classroom, school and wider community will also be considered |
introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.
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It will not only tell you what rule is applied, but also how & why it is applied in your particular problem. Not only will your homework assignment be done in minutes, but you will learn the important math concepts while observing Algebrator at work
What does Algebrator cover? Algebrator covers every important math concept starting with pre - algebra, all the way to college algebra.
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Design Trees, Charts & Reports! Create colorful trees, heirloom-quality charts, reports and family books that will be cherished by your family members now and in future years, with Family Tree Heritage's genealogy design tools.
Exciting new features to help you easily research your ancestors and share your family story.
No two schools have the exact same spelling lessons, and Spelling Accelerator is the first program to take that variety into account. Each grade level from first to fifth has more than 1,000 words.
If the teacher has provided a weekly spelling list, you can start with a blank list & create your own customized spelling list. With six entertaining, animated games & a weekly spelling test, learning how to spell has never been easier or more fun! |
COMAP Mathematical Contest in Modeling This national contest offers students the opportunity to compete in a team setting using applied mathematics in the solving of real-world problems. The contest is conducted on campus the first weekend in February. Student teams of up to three members have a choice of two problems on which to work. The problems are open-ended, so there is no one right answer. Teams may consult books, write programs etc., as long as they do not get help from live humans. |
Push the power of your computer to its limits with this guide to the extraordinary capabilities of 'Mathematica.' To demonstrate the potential and breadth of the program, Mathematica in Action includes many detailed programs with line-by-line explanations, valuable shortcuts, and alternative methods to generate--three dimensional graphics, iterative graphics, and animations.
Editorial Reviews
Booknews
An example-based introduction to techniques, both elementary and advanced, of using Mathematica, a programmatic tool for mathematical computation and exploration. By integrating the basic functions of mathematics with a powerful programming language, Mathematica allows users to carry out projects that would be extremely laborious in traditional programming environments |
Introductory Algebra - 2nd edition
ISBN13:978-0077281120 ISBN10: 0077281128 This edition has also been released as: ISBN13: 978-0073406091 ISBN10: 0073406090
Summary: Introductory Algebraoffers a refreshing approach to the traditional content of the course. Presented in worktext format,Introductory Algebrafocuses on solving equations and inequalities, graphing, polynomials, factoring, rational expressions, and radicals. Other topics include quadratic equations and an introduction to functions and complex numbers. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of dev...show moreelopmental level students. ...show less
Good condition All pages and cover are intact. Worn edges and cover has creases. Some problem numbers circled in pencil but not worked. Online access code may or may not be used. Satisfaction guaran...show moreteed. ...show less
$32 |
books.google.com - An... Number Theory
Elementary Number Theory
An study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.
User ratings
Good book; covers most of the interesting topics in number theory. Full of good examples and exercises wish solutions in the back. One notation had me a little puzzled - the use of a decimal point for multiplication. But this is easy to get used to since all numbers of concern are integers. 5 stars!
Problems in Elementary Number Theory a collection of interesting problems in elementary Number Theory. Many of the problems. are mathematical competition problems from all over the world like ... pen/ index.php?f=30 |
495829485
/ 049582948X
Basic Geometry for College Students: An Overview of the Fundamental Concepts of Geometry
by:Alan S. Tussy, R. David Gustafson
Intended to address the need for a concise overview of fundamental geometry topics. Sections 1-7 introduce such topics as angles, polygons, perimeter, area, and circles. In the second part of the text, Sections 8-11 cover congruent and similar triangles, special triangles, volume, and surface |
This textbook provides an introduction to the basis of matrix theory. It has been re-written and revised to take account of developments in statistical practice. The more difficult topics have been expanded and the mathematical explanations have been simplified. Vectorising, matrix calculus and complex numbers are also covered.
This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. This new edition has been updated to R 2.6.2 and features new and expanded coverage
Millions of students take algebra every year - and many of them struggle to pass. This book contains explanations, helpful examples, and practice sets. It offers instruction on topics, including: Algebraic expressions; Real and imaginary numbers; Functions and graphs; Exponents and exponential functions; and, Matrices.
Calculus is the fundamental basis of advanced science and math, but it can also be extremely intimidating. This book covers the key concepts of calculus, including: limits of a function; derivatives of a function; monomials and polynomials; calculating maxima and minima; logarithmic differentials; integrals; and, fundamental theorem of calculus. |
NCERT MATHEMATICS SOLUTION BOOK 12MATH
This book is sold subject to the condition that it shall not, by way of trade, be lent, re- ...solutions. We see this as crucial for liberating school mathematics from the .....Mathematics anxiety and 'math phobia' are terms that are used in popular ... even at an early age in a small number of children12. ...
Personal Reflections on Mathematics. Book Review and Resources. F. In the Classroom. C. 8 12... emotions that surface at the very mention of Math: ..... this is the only holistic solution to the problems discussed so ....Mathematics Curriculum in the National Curriculum Framework 2005, NCERT New Delhi |
More About
This Textbook
Overview
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables.
While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...).
From a review of the first editionEditorial Reviews
From the Publisher
From a reviewsFrom the reviews of the second edition:
"The author … has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. … Classical Fourier Analysis also comes equipped with a wealth of exercise … and each chapter is capped off by a wonderful 'Historical Notes' … . I think it's nigh-on indispensable for the aspiring Fourier analyst." (Michael Berg, MAA Online, January, 2009)
"Intended for graduate students who wish to study Fourier analysis. … also suitable for self-study. Proofs are provided in great detail. Each chapter is followed by historical notes with references, often including a discussion of further results. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. … certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises." (Andreas Seeger, Mathematical Reviews, Issue 2011 c)
"This book is intended to present the selected topics in depth and to stimulate further study in Fourier analysis. … proofs are provided in great detail and a large amount of exercises of varying difficulty were carefully prepared by the author … . This book is very interesting and useful. It is not only a good textbook, but also an indispensable and valuable reference for researchers … . The readers will certainly benefit a lot from the detailed proofs and the numerous exercises." (Yang Dachun, Zentralblatt MATH, Vol. 1220, |
The aim of these investigations is not to provide drill (although links to other resources on the web that do have been...
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The aim of these investigations is not to provide drill (although links to other resources on the web that do have been included in places), but to encourage students to think about why things happen the way they do in calculus. Such an understanding can be greatly useful both when rote memorization fails and when studying a new concept. Indeed, many concepts from the single variable calculus studied in APSC 171 form the foundations of later courses. The investigations have been designed to be quick and self-contained and should take at most ten or fifteen minutes each to complete.
From the author: "The SMILE program is designed to enhance the elementary and high school learning of Science and Mathematics...
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From the author: "The SMILE program is designed to enhance the elementary and high school learning of Science and Mathematics through the use of the phenomenological approach. Since 1986 each summer session participant has been asked to create and publish a single concept lesson plan. These lesson plans include the materials needed, a suggested strategy and expected outcomes. There are currently over 800 lesson plans available. The following is a collection of almost 200 single concept lessons. These lessons may be freely copied and used in a classroom but they remain the copyright property of the author. The Biology lessons are divided into the following categories: Anatomy & Physiology, Zoology, Botany, Microbiology, Genetics, Environmental Studies and Ecology, Biochemistry, General Biology and Miscellaneous. "
״A System of Linear Equations" graphs the equations of a 2 x 2 system of linear equations, illustrates the geometric...
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״A System of Linear Equations" graphs the equations of a 2 x 2 system of linear equations, illustrates the geometric interpretation of the system, identifies the type of solution, and finds the solution when applicable
The following applet allows users to plot three 2x1 vectors in 2-Space and gain insight about their linear independence and...
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The following applet allows users to plot three 2x1 vectors in 2-Space and gain insight about their linear independence and linear span. Two vectors are denoted as v1 and v2. The third is b. When possible the applet shows the linear combination of v1 and v2 necessary to form b.
This site provides collections of applets categorized as lessons and references, plotters and calculators, interactive...
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This site provides collections of applets categorized as lessons and references, plotters and calculators, interactive exercises, mathematical recreations, virtual classes and miscellaneous. Several applets from this site have been reviewed separately.
The Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science,...
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The Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a remarkable range of other fields. Its daily-growing collection of interactive illustrations is created by Mathematica users from around the world, who participate by contributing innovative Demonstrations. The free Mathematica Player is required to view the demmonstrations.
The Wolfram Demonstrations Project--Calculus is an open-code resource that uses dynamic computation to illuminate concepts in...
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The Wolfram Demonstrations Project--Calculus is an open-code resource that uses dynamic computation to illuminate concepts in calculus. Its daily-growing collection of interactive illustrations is created by Mathematica users from around the world, who participate by contributing innovative Demonstrations. The free Mathematica Player is required to view the demonstrations; there are 166 at present.
Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra,...
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Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra, Trigonometry, PreCalculus, Calculus or Statistics and enter a problem. The computer solves the problem and shows the steps for the solution. It also has a worksheet generator.
The focus of this website is to help in the transition from a paper oriented environment to one using OER materials with an...
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The focus of this website is to help in the transition from a paper oriented environment to one using OER materials with an emphasis in elementary and secondary school mathematics. The website's material is divided into five major topics: 1. Why OER materials? 2. The learner's environment - a world in change. 3. Mathematics past and present. 4. Exploring OER materials and 5. International mathematics education developments. An emphasis has been placed on linking to other OER materials to cover and expand on each topic. |
math problem demonstrates the concept of geometric progression, through an example of a million dollar contract between an employee and an employer. Application of the concept of geometric progression to social cause activism is addressed. This...(View More) resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
Using the simple example of calculating the probability of reaching a traffic light while green, students are shown how to build a mathematical model using a very commonly-taught formula (sum of first n integers) to solve a rather practical problem....(View More) This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
In the state of Maryland, a local politician once claimed that sea level is rising because there are too many people putting boats on the open ocean. Could that result in a significant sea level rise, perhaps even destroy low-lying nations such as...(View More) Bangladesh? This resource explores the principle of buoyancy, and is part of PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
This exercise shows a practical application of trigonometry in the aviation environment, where student pilots consider the relationship between altitude and distance to complete a landing. It requires a scientific calculator. This resource is from...(View More) PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
This simple example shows how algebra can be useful in the real world by exploring the question: Should Grandpa start receiving his Social Security benefits at age 62 or should he wait until age 65? This resource is from PUMAS - Practical Uses of...(View More) Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
This series of example calculations applies basic trigonometry to to calculate the altitude of satellites and Iridium satellite flares. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by...(View More) scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
Some simple arithmetic can help put the quantity of fuel in a potential oil spill - in this case 400,000 gallons - in perspective. In this example, students calculate the area that would be covered by oil from the volume measurement. This resource...(View More) is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
In this problem set, students are led through a series of calculations to determine the best launch site for a TV satellite. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and...(View More) engineers showing how math and science topics taught in K-12 classes have real world applications.(View Less)
In this exercise, learners use basic arithmetic to determine the amount that sea level would rise around the globe with the melting of the Greenland and Antarctic ice sheets. Basic data for this calculation is provided. This |
Find an Atherton Calculus State U (Calculus III for Fall 2......In school, problems will only involve skills that they have learned. More difficult problems simply try to make these rules seem more complicated. They involve negative exponents instead of positive ones, or the gravity on the moon instead of on earth. |
Key skills
Develop problem-solving skills and apply them independently to problems in one or two areas of pure and or applied mathematics.
Communicate effectively in writing about the subject (using precise notations and coherent arguments of a variety of kinds).
Improve own learning and performance (e.g. ability to organise study time, to study independently, exploit feedback and meet deadlines).
Teaching, learning and assessment methods
All relevant material is taught in the module texts and through the study of set books. Your knowledge is built up gradually, with learning fostered by in-text examples. You assess your own progress and understanding by using the in-text problems and exercises at the end of each unit. You also engage with what is taught by attempting the tutor-marked assignment (TMA) questions, and your understanding is reinforced by personal feedback from your tutor in the form of comments based on your TMA answers.
Your understanding of principles, concepts, and techniques is assessed through TMA questions and the final, unseen, three-hour examination for each |
Mathematics Olympiad activity on a national level has been one of the major initiativesof NBHM (National Board for Higher Mathematics) since 1986. The activity aims to spotmathematical talent among High School children. NBHM, with Homi Bhabha Centre forSciencec Education (HBCSE), also has taken on the responsibility of selecting and trainingthe Indian team for the International Mathematical Olympiad every year.For the purpose of the Olympiad contests, the country has been divided in to about 25 re-gions. The selection process for participation in the International Mathematical Olympiad(IMO) consists of the following stages:
Stage 1: Regional Mathematical Olympiad (RMO)
: RMO is currently held on thefirst Sunday of October each year in each of the regions in the country. The Regional coor-dinator each region holds the charge of conducting RMO in the region. All school studentsfrom Class XI are eligible to appear in RMO. Students from Class XII may also appearin RMO, but the number of students selected from Class XII is at most 6. Exceptionallybrilliant students from lower standards may also appear for RMO subject to the approvalof the Regional Coordinator. RMO is a 3-hour written test containg 6 or 7 problems. Onthe basis of the performance in RMO, students are selected for the second stage.The Regional Coordinators may charge a nominal fee to meet the expenses in organisingthe contest.
Stage 2: Indian National Mathematical Olympiad (INMO)
: INMO is currentlyheld on the third Sunday of January each year at the regional centres in all regions. Onlythose students who are selected in RMO are eligible to appear in INMO. This contest isa 4-hour written test. The evaluation of these papers is centralised, and is undertaken bythe IMO Cell of NBHM. The top 75 contestants in INMO receive Merit Certificates.
Stage 3: International Mathematical Olympiad Training Camp (IMOTC)
: Thetop 30-35 INMO certificate awardees are invited to a month long training camp in May/Juneeach year. The training camp is organised by HBCSE, Mumbai. The number of studentsfrom Class XII who are selected for IMOTC is at most 6. In addition to these 35 students,a certain number of INMO awardees of previous year(s) who have satisfactorily undergonepostal tuition over the year are also invited to a second round of training. A team of
six
students is selected from the combined pool of junior and senior batch participants, basedon a number of selection tests conducted during the camp, to represent India in the Inter-national Mathematical Olympiad.
Stage 4: International Mathematical Olympiad (IMO)
: The six member team se-lected at the end of IMOTC, accompanied by a leader and a deputy leader represent India1
at IMO, that is normally held in July each year in one of the chosen for the years IMO.IMO consists of two 4-and-a-half hour tests held on two consecutive days. The normalschedule between departure and return of the team takes about two weeks. The studentsof Indian team who win gold, silver and bronze medals at IMO receive from NBHM a cashprize of RS. 5000/-, Rs. 4000/- and Rs. 3000/- respectively. MHRD (Ministry of HumanResource Development) finances international travel of the 8-member Indian delegationto IMO, while NBHM (DAE) finances the entire in-country programme and takes care of other expenditure connected with international participation. The six students represent-ing India at IMO automatically qualify for Kishore Vaigyanik Protsahan Yojana (KVPY)scholarship (Rs 3000/- per month and some contingency) instituted by Department of Sci-ence and Technology, Government of India.
Syllabus for Mathematical Olympiad:
The syllabus for Mathematical Olympiad (re-gional, national and international) consists of pre-degree college mathematics. The dif-ficulty level increases from RMO to INMO to IMO. Broadly the syllabus for RMO andINMO is: Algebra (basic set theory, principle of Mathematical Induction,inequalities (AM-GM and Cauchy-Schwarz), theory of equations (remainder theorem, relation between rootsand coefficients, symmetric expressions in roots, applications of the Fundamental theoremof algebra and its applications), functional equations); Geometry (similarity, congruence,concurrence, collinearity, parallelism and orthogonality, tangency, concyclicity, theoremsof Appollonius, Ceva, Menelaus and Ptolemy, special points of a triangle such as circum-centre, in-centre, ex-centres, ortho-centre and centroid); Combinatorics (Basic countingnumbers such as factorial, number of permutations and combinations, cardinality of apower set, problems based on induction and bijection techniques, existence problems, pi-geonhole principle); Number theory (divisibility, gcd and lcm, primes, fundamental theoremof arithmetic (canonical factorisation), congruences, Fermat's little theorem, Wilson's the-orem, integer and fractional parts of a real number, Pythagorean triplets, polynomials withinteger coefficients). An idea of what is expected in mathematical olympiad can be hadfrom the earlier question papers (see rbb/olympiads.html) and thefollowing books:1. |
From the reviews: K.A. Ross Elementary Analysis The Theory of Calculus "This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer's opinion, has succeeded admirably."—MATHEMATICAL REVIEWS "This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." (Allen Stenger, The Mathematical Association of America, June, 2008)
Of the many analysis books I have seen, I think this is one of the best for the student approaching the subject for the first time.
It is mathematically rigourous, yet develops the major concepts of analysis in a leisurely (in the good sense of the word) way with interesting and sometimes unusual examples.
Beginners will especially appreciate the quality exercises and the solution guide in the back.
The style of this book is a bit similar to Spivak's *Calculus* in that the author is a bit wordy. I find Ross' presentation more direct and less pretentious than Spivak--and far less intimidating.
This is definitely the best introductory analysis book I know of for self-study. A student who masters the material in this book will be well prepared to tackle Rudin and other classic works in real analysis.
kwrcheng (Calgary, Alberta, Canada) |
15/01/2000
The book is rigorously written and is extremely good for math majors. I don't think this book is very suitable for non-math majors however, since they might think it's too dull. The book does not go on and on like some math textbooks with non-essential talk. It gets into the material right the way. The proofs have been carefully chosen so that they're as simple and as elegant as possible. Topology is treated in optional sections, and the focus of the book is sequences. Indeed, the treatment of sequences is very thorough. Also, many notions are also defined in terms of sequences. However, proofs that this definition and the usual delta-epsilon definition are equivalent is given. The style of writing is clear, concise, and avoids uncessaary discussion. Proofs are given out in full and are seldom left to the readers as an exercise. In keeping with the style of this book, historical facts and references are not provided. I think this book should be a must-have for all math undergrads. |
Find a Nonantum Precalculus always loved math and prealgebra is when the subject starts to get more complicated and interesting. Until now, you mostly studied the basics of addition, subtraction, multiplication and division with various numbers of digits. With prealgebra, though, you start learn more complex types of numbers like decimals, fractions and variables. |
Concise Introduction to MATLAB
9780073385839
ISBN:
0073385832
Pub Date: 2007 Publisher: McGraw-Hill Companies, The
Summary: A Concise Introduction to Matlab is a simple, concise book designed to cover all the major capabilities of MATLAB that are useful for beginning students. Thorough coverage of Function handles, Anonymous functions, and Subfunctions. In addition, key applications including plotting, programming, statistics and model building are also all covered. MATLAB is presently a globally available standard computational tool for ...engineers and scientists. The terminology, syntax, and the use of the programming language are well defined and the organization of the material makes it easy to locate information and navigate through the textbook.
Palm, William J., III is the author of Concise Introduction to MATLAB, published 2007 under ISBN 9780073385839 and 0073385832. Seven hundred thirty Concise Introduction to MATLAB textbooks are available for sale on ValoreBooks.com, one hundred fifteen used from the cheapest price of $21.93, or buy new starting at $67.21eller Rating:(0)
Ships From:Sugarland, TXShipping:StandardComments:Brand New. US Edition Book. We do not ship to Military Addresses. Fast Shipping with Order Tracki... [more]Brand New. US Edition Book. We do not ship to Military Addresses. Fast Shipping with Order Tracking. For Standard Shipping 7-8 business days & Expedite Shipping 4-6 business days, after shippingWriting programs to do tedious computations quickly and making a graphical representation of that data. One example is the differential equation solver. Very versatile built in functions to do that task. |
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 -06Algebra Open Textbook
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Look for fully developed math investigations, math challenges, Problems of the Day and standardized test practice both for SATs and Common Core assessments. The emphasis will always be on developing conceptual understanding in mathematics. There will also be dialogue on issues in mathematics education with a focus on standards, assessment, and pedagogy primarily at the 4-12 level through AP Calculus. ALSO, READ THE COMMENTS, IF ANY, BELOW THE POSTS. THEY ARE THE HEART AND SOUL OF THIS BLOG!
Wednesday, July 25, 2007
What do you think would be the results of giving the following Algebra 1 problems to your students before, during, and after the course? Do you believe that either or both of these could be or have been SAT questions? Do students normally have exposure to these kinds of problems in their regular assignments? Do these kinds of questions require a deeper conceptual understanding of algebra?
1. Given: x2 - 9 = 0 Which of the following must be true?
I. x = 3 II. x = -3 III. x2 = 9
(A) I only (B) I, II only (C) I, III only (D) I, II, III (E) none of the preceding answers is correct
The wording of the questions (even if AND were used to replace the commas) is confusing. x=3 AND x=-3 are both solutions to the first equation, but of course neither MUST be true (since the answer could be the other instead) but... well, it just feels like confusing wording to me. I think many kids would get caught up on the wording of the question, even if they understand the concepts.
mathmom-- I agree - it's confusing. However, the wording is as it typically appears on the SAT (you can verify this by looking at released tests). As you pointed out, the key word in this problem is MUST. This is about logical necessity and this is subtle and sophisticated for many students. Students reason: If x = 3 THEN x^2 - 9 = 0, so I is true! The idea that the logic must go the other way confuses strong high school students as well. That doesn't necessarily make this a poorly worded question. It may indicate that students need more experience with deductive reasoning. I always ask students: Does x have to equal 3? Yes or No? Does x have to equal -3? Y or N? "Have to" is synonymous with 'must!'
I think it takes considerable time and maturity to develop a comfort level with the language of logic.
I suspect this discussion could generate lots of heat about semantics and wording of standardized test questions!
Hmm, as most "average" students in our state take the ACT, I don't know how my students would do.
I wish I could say that these types of questions were part of our regular curriculum, but... sadly not on a consistent basis.
As to your question of "Do these kinds of questions require a deeper conceptual understanding of algebra?", my response is yes. So many of my students struggle with the difference between and/or statements. The logical thinking is not something with which they are comfortable. When I ask these questions or stress the difference between writing, "...so x = 3 and x = -3" and "...so x = 3 or x =-3"they think I'm being overly picky.
It seems to me that there are 2 things necessary here -- understanding the algebra, and understanding the SAT-style wording. I'd argue that the second is mostly only useful for taking the SAT. It's not only getting the "MUST" part but then also getting the AND/OR combinations of answers. I think if I were posing this in a non-SAT-prep class I'd ask: "Circle all the statements that must be true" or something like that, without getting into the combinations and no correct combination type multiple choice.
The must is not what makes it awkward. It was the different combinations combined with the must that I found awkward. Perhaps because of the sloppiness around the "ands" but overall I do think that adds another degree of confusion to the question that has nothing to do with "understanding algebra conceptually". I know they do that on the SAT, but that's SAT test-taking skills, not algebra. ;-)
mathmom-- Your comments are dead on! CertainlyIt's important for me to point out here that my questions were NOT actual SAT questions (I avoid this for copyright reasons). It was my lame attempt to write questions similar to a question on last October's PSAT that was missed by many. That problem avoided the issues of AND vs. OR! You and others are my excellent 'quality control' team. My question would never have made the cut' over at ETS!!
In my opinion, the underlying concept of this problem is still very important for students to grasp. My careless wording has now become more of the point of all this than my original intent, but maybe the issues of wording and item construction are just as important here! The reality is that these kinds of problems are and will be tested on standardized tests. Semantics and the form of the question are critical, since one does not want the FORM to be more critical than the content. ETS, in my opinion, generally does a good job of checking the wording (certainly better than I did).
You made some excellent suggestions for improving the question. Although it's probably not worth salvaging the problem, I'm wondering if anyone could work this as a Roman Numeral I, II, III type problem or is it not worth the effort! The original problem was multiple-choice by the way! That may be the best way to go. Of course, in my gut, the best way is to avoid this as an objective question. Having students discuss this topic in an open-ended manner is far more worthwhile, but my experience is that they take it more seriously when it appears as a standardized test problem.
Thanks again for highlighting these issues. I am fortunate to have such critical readers! Dave
CertainlyAnd... (A) doesn't make sense, IMO. X cannot equal 3 and -3 at the same time. I think that is the crux of what bothered me about the original question. the options that contained both I and II just seemed nonsensical to me, and that felt awkward.
If I were to rework it into a Roman numeral I, II, III problem, I would avoid putting I and II together with an "AND".
By substituting "are" for "must be" the problem changes. An algebra II course would move a few kids away from choosing I only for each, and I think many, would get the correct answer out of confusion, not knowledge.
I don't remember that combination of "must" with I, II, III questions from back in my day or from prep. I would have been annoyed.
We can make it clearer (although why should ETS?) by asking the almost as difficult "Which of the following does not have to be true..."
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New 2012 Challenge Math Problem/Quiz Book
NEW VERSION OF QUIZ BOOK INCLUDES DETAILED SOLUTIONS, HINTS & STRATEGIES FOR 1st 8 QUIZZES!
Click the BUY NOW PayPal Button to purchase with your PayPal acct or Credit Card. The Problem/Quiz Book with 35 Quizzes (175 questions) and Answers will be emailed to you as a secured pdf as soon as purchase is confirmed. Questions can be used for SAT I/Math I/II, Math Contest Practice and Problems of the Day. Problem types include Multiple Choice, I/II/III, and Constructed Response. Price is $9.95. Pls send email to dmarain "at gmail dot com" in addition to placing your order.
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SAT Math Tips
ZERO IS A 'WEIRDO'! (W)hole (E)ven (I)nteger (R)Rational/Real (DO) Cannot Divide by O! BUT Zero is NOT Positive and NOT Negative!
POSITIVE INTEGERS start from 1
PRIMES start from 2 (not 1)
INTEGERS can be NEGative (and zero!) as well as positive
MEMORIZE the formula for the nth term of an arithmetic sequence: a(n) = a(1) + (n-1)d. Example: Consider the sequence of positive integers which leave a remainder of 3 when divided by 4. What is the 100th term? Step 1: List the first few terms 3,7,11,15,... to see the pattern and recognize it is an arithmetic sequence. Step 2: Identify the values which are given First term or a(1) = 3 Common difference or d = 4 Number of terms or position of desired term or n = 100 Step 3: Substitute into formula and solve a(100) = a(1) + (100-1)(4) = 3 + (99)(4) = 399
Of course there are other ways to find the 100th term such as 100 x 4 - 1 but the formula is so useful for so many types of questions it is worth learning!
Know the above by heart and you are way ahead of the game! These facts will absolutely be needed on your next SAT or standardized test!
About Me
Recently retired math educator and Supervisor of Mathematics; 30 years experience as an Advanced Placement Calculus (BC) teacher; Former Author of Math Teachers of New Jersey Annual HS Math Contest; Former K-5 Chair of New Jersey Math Content Standards and Curriculum Frameworks; Former member of Math Item Review Committee for New Jersey High School Proficiency Assessment; Experienced SAT Math Instructor and author of SAT materials; speaker at many regional and national math conferences |
are vital in order to move onto more advanced skills and topics in math |
"Speed Mathematics using Vedic Math Techniques" is a 4 DVD set, which has 15+ hours of video based instruction. Take your pen and paper, and work along with the instructor, as he teaches you the techniques, and works through more than 600 problems in Addition, Subtraction, Multiplication and Division. Learn techniques that not only teach you speed, but more importantly, accuracy and error checking.
"Speed Mathematics using the Trachtenberg System" is a 2 DVD set, that has 10+ hours of video based instruction. Take your pen and paper, and work along with the instructor, as he teaches you the techniques, and works through more than 400 problems in Addition, Subtraction, Multiplication and Division. Learn techniques that not only teach you speed, but more importantly, accuracy and error checking.
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Book 1: Speed Arithmetic (Based on Vedic word – Formulas)
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Book 2: Welcome to Vedic Algebra
Multiplication of Algebraic Expressions
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HCF and LCM
Simple Equations
Quadratic Functions and Equations
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About the Author
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Beginning and Intermediate Algebra: Building a Foundation
9780201787375
ISBN:
0201787377
Pub Date: 2009 Publisher: Addison Wesley
Summary: McKenna, Paula is the author of Beginning and Intermediate Algebra: Building a Foundation, published 2009 under ISBN 9780201787375 and 0201787377. Six hundred thirty four Beginning and Intermediate Algebra: Building a Foundation textbooks are available for sale on ValoreBooks.com, one hundred thirty five used from the cheapest price of $39.60, or buy new starting at $202Authors Paula McKenna and Honey Kirk hail from the state of Texas, where they teach students of all ages, skill sets, and backgrounds. As active teachers in diverse classroom [more]
Authors Paula McKenna and Honey Kirk hail from the state of Texas, where they teach students of all ages, skill sets, and backgrounds. As active teachers in diverse classrooms, their aim is to provide88319. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less] |
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SJSU Catalog
EDEL 108D
Curriculum: Mathematics
Description
Elementary school mathematics curriculum and methodology relationships between instructional materials and how children construct knowledge; the role of technology and issues that bear on the teaching of school mathematics. May be repeated for different subtitle.
Prerequisite: Upper division standing. |
Product Reviews
Lifepac Math, Grade 9 (Algebra I), Complete Set
4.6
5
5
5
Lifepac 9 Math
Excellent as a primary math book, and the teacher's guide has all the ideas you would need for anything "extra", based on the student's needs. Combining the Grade 9 with the Grade 10 Lifepac Math is also an excellent idea, depending on your classes motivation and progress.
June 11, 2012
This is my first time to use the Lifepac curriculum and I must say I am very pleased with it. The lessons are very easy to understand. I have ordered this for a refresher for my daughter over the summer. I will most likely be using this curriculum for all of her subjects in the fall.
June 17, 2010
It is a great curriculum but it would be better served by having more self testing areas more often.
November 17, 2008
Very detail material. Make sure your student comprehends the pre-algebra first before doing this. In the beginning it's easy, as you go further it gets harder but has good examples to go by and explanations.
September 27, 2007 |
title promises, this helpful volume offers easy access to the abstract principles common to science and mathematics. It eschews technical terms and omits troublesome details in favor of straightforward explanations that will allow scientists to read papers in branches of science other than their own, mathematicians to appreciate papers on topics on which they have no specialized knowledge, and other readers to cultivate an improved understanding of subjects employing mathematical principles. The broad scope of topics encompasses Euclid's algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p-adic numbers; groups; the Galois theory of equations; algebraic geometry; matrices and determinants; invariants and tensors; algebras; group algebras; and more. "It is refreshing to find a book which deals briefly but competently with a variety of concatenated algebraic topics, that is not written for the specialist," enthused the Journal of the Institute of ActuariesStudents' Society about this volume, adding "Littlewood's book can be unreservedly recommended."
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This book, covers just about everything important in algebra from basic operations on numbers to groups and tensors, both pure and applied, and all in less than 150 pages!
Given, the above scope, it moves quickly, but should be completely comprehensible to anyone with a strong High School math background, as long as the student reads slowly and carefully. The advantage of the compression is that it is possible to see the whole field and its connections without getting mired in the details.
Fantastic for a broad overview of algebra, prior to studying in more detail (or afterwards, to see how it all fits together). Don't be put off by the age of the book and, for the money, unbeatable.
This is an old, elegantly presented, reminder of algebraic theories which should be general knowledge of the mathematics and physics students now. Disgracefully, they are not, and a short, concise review is something which could be readen in a pair of afternoons for the mere pleasure of adquiring a general idea of many theories. This book provides that, if one is prepared to cope with a little antique names. Dr. Littlewoods "Simple Account" should be amply recommended. |
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Fourier Series
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Magnetostatics
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Mathematical Application in Agriculture - 04 edition
Summary: This book teaches the many mathematical applications used in crop production, livestock production and financial management in the agriculture business, skills which are essential for success as an agriculture professional. By giving readers a solid foundation in arithmetic, applied geometry and algebra as they relate to agriculture, the material presented will help develop their ability to think through the many mathematical challenges they will face. Case studies, ...show moresample problems, charts, and graphs fully illustrate the important concepts presented.
Product Benefits:
Sample problems contain multiple operations so that students must put information together to get the desired final answer
All are real problems in agriculture, leading students to learn agricultural facts
The flexible presentation of the material lends itself to being taught in any order |
This course, presented by MIT and taught by Daniel Kleitman, provided instruction on combinatorics, graph theory and discrete mathematics. The main content provided online is a sample final paper project assignment....
This lesson from Illuminations introduces students to to basic graph theory and Euler circuits. Students will gain hands on experience using graphs. The lesson involves sketching graphs that have Euler paths and...
This lesson from illuminations helps to illustrate quadratic equations. Students will determine the maximum value of a quadratic equation and compare different equations. The lesson also asks students to move between...
Graph theory is widely used in computer science, engineering and of course, mathematics. Here, visitors will find links to information about the applications and components of graph theory, as well as its pioneers. |
MATH R115 - College Algebra
Course description: An advanced course in algebra, this course
focuses on the study of functions and their graphs, techniques of
solving equations and the recognition and creation of patterns.
Students will analyze and graph functions (constant, linear, quadratic,
absolute value, square root, cubic, polynomial, rational, exponential,
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analytic geometry of conic sections, systems of linear and nonlinear
equations and inequalities, matrices, determinants, the binomial
theorem, sequences, series, and mathematical induction. This course
includes problem-solving strategies with applications to many areas
including business and the social, biological, and physical sciences.
See a counselor for more information on IGETC or CSU GE-Breadth certification.
Some transfer information:
Credit for MATH R115 can be transferred to several universities; the
chart below shows a few of the possibilities. For more complete
transfer information, see a counselor at the Transfer Center or visit ASSIST online. |
A survey of foundations of mathematics essential to the secondary
school teacher, this course integrates secondary mathematics concepts
with problem-solving strategies and technology. Students expand on
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repertoire of classroom-tested lessons that can be used in a high
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Buy Cultural Development of Mathematical Ideas by Geoffrey B. Saxe and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
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This package consists of the textbook plus an access kit for MyMathLab/MyStatL ab.Mathematical Ideas captures the interest of non-majors who take the Liberal Arts Math course by showing how mathematics plays an important role in scenes from popular movies and television. By incorporating John Hornsby's "Math Goes to Hollywood" approach into chapter openers, margin notes, examples, exercises, and resources, this text makes it easy to weave this engaging theme into your course.The Twelfth Ed
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Merchandising Mathematics for Retailing, 5th Edition
Description
Written by experienced retailers, Merchandising Mathematics for Retailing, 5/e introduces students to the essential principles and techniques of merchandising mathematics, and explains how to apply them in solving everyday retail merchandising problems. Instructor- and student-friendly, it features clear and concise explanations of key concepts, followed by problems, case studies, spreadsheets, and summary problems using realistic industry figures. Most chapters lend themselves to spreadsheet use, and skeletal spreadsheets are provided to instructors within the Instructor's Manual. This edition is extensively updated to reflect current trends, and to discuss careers from the viewpoint of working professionals. It adds 20+ new case studies that encourage students to use analytic skills, and link content to realistic retail challenges. This edition also contains a focused discussion of profitability measures, and an extended discussion of assortment planning.
Table of Contents
1. Introduction
2. Basic Merchandising Mathematics
3. Profitability
4. Cost of Merchandise Sold
5. Markup as a Merchandising Tool
6. Retail Pricing for Profit
7. Inventory Valuation
8. The Dollar Merchandise Plan
9. Open-to-Buy and Assortment Planning
This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course. |
Pre-Calculus Demystified leads the reader through all the intricacies and requirements of this essential course
Whether you need to pass a class, a college requirement, or get a leg up on more advanced topics, this book provides clear explanation with a wealth of questions, answers and practical examples.
Packed with practical examples, graphs, and Q&As, this complete self-teaching guide from the best-selling author of Algebra Demystified covers all the essential topics, including: absolute value, nonlinear inequalities, functions and their graphs, inverses, proportion and ratio, and much more. |
Courses & Advising
Math 1150 Foundations Seminars
The MATH 1150 Math Foundations Seminars offer challenging and interesting mathematical topics with a computer science component that requires only high school mathematics. The seminar topics vary with each class and they are designed for all students.
Winter 2014
A graph in its simplest form is merely a collection of dots, called vertices, and a collection of line segments, called edges, running between some or all of the vertices. The graph could model the walking paths on campus, the preferred pizza toppings of a group of friends, or an abstract mathematical relationship. During this course, we will study the concepts and results of graph theory, how to solve problems related to graphs, and how solving graph theory problems helps us understand real world problems: scheduling, map coloring, postal delivery routes, amicable seating charts, population life cycle analysis, DNA sequencing, and more. This is a hybrid course, meaning that some of the course meetings are face-to-face (Tuesday, Thursday, Friday), while in between face-to-face meetings, you will engage with course content, complete assignments, and communicate with classmates and the instructor through our Blackboard course. No specific mathematics knowledge is presumed, but strengths in reading, writing, and reasoning will be necessary to succeed with assignments. We will do some work in this class with Mathematica, a software package which is licensed to DU and free to students, in order to compute and visualize with graphs for some online assignments.. |
All topics not listed due to character limitations set bySimilarKnowledge is life, power and road which leads to success. "Knowledge has to be improved, challenged, and increased constantly, or it vanishes" By Peter F. Drucker (1909-2005) American writer and management consultant.
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WRITE_EXTERNAL_STORAGE and READ_EXTERNAL_STORAGE: In order to share a formula on Facebook or attach it to an email, a PNG image file containing the selected formula must be created first and stored to the device. The files are very small and do not occupy any significant spaceThis Mathematics Dictionary is a comprehensive dictionary with suggestions of about thousands of internet related terms and abbreviations.Learn about the Mathematics terms and much more.Mathematics Dictionary is content all maths related Keyword description,which is used in all stream.
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Feature: Quick dynamic search of words while you type Filters to help you locate the word you are searching for. tags: math guide, maths help, mathematics, maths book, formulas bookApplication designed for beginners to learn the basics of trigonometry. This explains completely its mathematical and geometrical interpretation and physical significances. Deals all about trigonometric formulas and identities. Very helpful tutorials for students to solve mathematical problems under the category of heights and distances…try out now…
Mathematics is the abstract study of topics such as quantity (numbers), structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
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This application for probability is a great work from a team of teachers and educators.here we tried our best efforts to includes almost all topics of probability and basics of random process. This time probability tutorials also added with this application. Best to learn the topics of probabilities such as PROBABILITYINTRODUCTION, DETERMINISTIC EXPERIMENT, PROBABILISTIC OR RANDOM EXPERIMENT, CLASSICAL APPROACH TO PROBABILITY,TRIAL AND ELEMENTARY EVENTS, COMPOUND EVENTS,EXHAUSTIC NUMBER OF CASES,MUTUALLY EXCLUSIVE EVENTS, EQUALLY LIKELY EVENTS,FAVOURABLE NUMBER OF CASES,INDEPENDENT EVENTS,CLASSICAL DEFINITION OF PROBABILITY OF AN EVENT,AXIOMATIC APPROACH TO PROBABILITY,SAMPLE SPACE,EVENT,ELEMENTARY EVENTS,COMPOUND EVENTS,IMPOSSIBLE AND CERTAIN EVENTS,OCCURRENCE OR HAPPENING OF AN EVENT,MUTUALLY EXCLUSIVE EVENTS,MUTUALLY EXCLUSIVE AND EXHAUSTIVE SYSTEM OF EVENTS,FAVOURABLE EVENTS,AXIOMATIC DEFINITION OF PROBABILITY,ADDITION THEOREMS ON PROBABILITY,CONDITIONAL PROBABILITY,MULTIPLICATION THEOREMS ON PROBABILITY, INDEPENDENT EVENTS, MULTIPLICATON THEOREM FOR INDEPENDENT EVENTS, ADDITION THEOREM FOR INDEPENDENT EVENTS, THE LAW OF TOTAL PROBABILITY, BAYE'S RULE, RANDOM VARIABLE AND ITS PROBABILITY DISTRIBUTION, RANDOM VARIABLE, BINOMIAL DISTRIBUTION, MEAN AND VARIANCE OF BINOMIAL DISTRIBUTION, MEAN OF BINOMIAL DISTRIBUTION, VARIANCE OF BINOMIAL DISTRIBUTION, RELATION BETWEEN MEAN AND VARIANCE |
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