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"Mathematical Olympiad Treasures" aims at building a bridge between ordinary high school examples and exercises and more sophisticated, intricate and abstract concepts and problems in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of geometry and trigonometry, algebra, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus of "Treasures" is on engaging a wider audience of undergraduates to think creatively in applying techniques and strategies to problems in the real world.
The problems are clustered by topic into self-contained sections. Unlike "Challenges," however, "Treasures" begins with elementary facts, followed by a number of carefully selected problems and an extensive discussion of their solutions. This discussion then leads to more complicated and more intellectually challenging problems as well as their solutions.
Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools and strategies that will be useful beyond the classroom and in a number of disciplines.
"Mathematical Olympiad Treasures" reflects the experience of two experienced professors and coaches from the United States and Romanian Olympiad teams.
buy read books online Mathematical Olympiad Treasures
M. Wang |
21/08/2006
A good pedagogical aid for math competition
" from the same authors, but this book poses so little challenge that there is virtually no risk of stumbling over any problem. The authors acknowledge the difference in difficulty levels in the promotional literature. Perhaps they will publish a collection of harder problems separately.
Math_Kid_25 |
01/05/2005
Helpful for the experience, but not beginners
I would recommend this book if you have already developed a repretoire for solving olympiad (USAMO, IMO, etc) level problems. This book teaches a couple more interesting startegies to add to your olympiad bag of tricks. However, a beginner to olympiad problems may wish to consider a different book first.
I bought this book this year before my first USAMO. I wanted to acquaint myself with important problem solving techniques I would need for this test. Whiel this book provided many important insights and tricks, It was not helpful for my purposes. Basically, it gave plenty of extra tricks, but very, very little on where to apply these tricks and how a student would know to use a given technique.
In all, I'd rate this book a 5 for advanced problem solvers who know what they are doing but want a good set of problems and extra techniques. However, a newcomer to olympiads may wish to consider a different book to start educating themselves in problem-solving
SCK |
30/01/2004
Definitely a treasure!
Andreescu delivered again! This book teaches powerful math problem solving techniques through a series of graded problems. The insight from these two renounced problem solvers of elementary problems at the olympiad level is prevalent throughout the book, which is what makes this book a treasure. You'll learn wonderful techniques and come away with a satisfying feeling after you can solve some of the problems that seem impossible to you before. I hope these authors continue to put out such gems in the near future. Enjoy! |
Definitely
Memorization is very useful in advanced mathematics. However beyond memorizing the formulas you need to know how to apply then, alter them to fit new situations, etc. I you memorize the basic formula like the area of a rectangle. width * length = area Then later you are given just an area and a width and have to find length. You must be able to adapt the memorized to fit the new data. So area/width=length. Without the understanding of basic algebra some people would be unable to solve this new problem. So make sure that you not only memorize put understand exactly what the formula does and its uses.
Memorization is essential. And understanding facilitates the memorization process. Math is a cumulative discipline - each concept is stack upon another. Here is a comprehensive geometry formulas list. Hope this helps.
is it usually required in more advanced math to memorize mensuration formulas such as sphere and cone volumes. etc?
Are you asking about the practice of mathematician-ing, or about passing advanced exams in maths?
For the first the answer is no, you have to understand how to derive things if you need to, but when you need them you will look them up. For the second the answer yes, its a hoop you are made to jump through. |
30328391 / ISBN-13: 9780130328397
Introductory Algebra for College Students
The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer's ...Show synopsisTheIntroductory Algebra for College Students (Prentice Hall) – Hardcover (2001)
by
Robert F Blitzer
Hardcover, Prentice Hall 2001
English
3rd ed.
699 pages
ISBN: 0130328391 ISBN-13: 9780130328397
...Show more prepare students for subsequent Algebra courses as well as "service" math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving Introductory Algebra for College Students
tHIS IS NOT THE COVER Of the book. Its orange and has a bottle cap on the cover. BUUT this book is great. It clearly lists the steps and reasons for the math eq. and such. Although I DESPISE the ANSWER KEY in the back because it only lists the answers for ODD NUMBERS. Other than that, the condition ...
More
Unfortunately, this text was required for my class. I got to use the Lial series for PreAlgebra, and I will get to for Intermediate as well. They are much better for those who need more examples, description, worked problems, etc. This one assumes you know a lot |
201312220 / ISBN-13: 9780201312225
Basic Mathematics Through Applications
KEY MESSAGE Presented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that are ...Show synopsisKEY MESSAGE Presented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that are fully integrated throughout the text and exercise sets. Akst/Bragg's user-friendly design offers a distinctive side-by-side format that pairs each example and its solution with a corresponding practice exercise. The concise writing style keeps readers' interest and attention by presenting the mathematics with minimal distractions, and the motivating real-world applications demonstrate how integral mathematical understanding is to a variety of disciplines, careers, and everyday situations. KEY TOPICS Whole Numbers, Fractions, Decimals, Basic Algebra: Solving Simple Equations, Ratio and Proportion, Percents, Signed Numbers, Basic Statistics, More on Algebra, Measurement and Units, Basic Geometry MARKET For all readers interested in Basic MathematicsHide synopsis
...Show more Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section incorporating related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and historical connections. Compelling Historical Notes give students further evidence that mathematics grew out of a universal need to find efficient solutions to everyday problems. Plenty of practice exercises provide ample opportunity for students to thoroughly master basic mathematics skills and develop confidence in their understanding |
Designed for students intending to earn an Associate of Science degree and ...
(more)
Designed for students intending to earn an Associate of Science degree and then transfer to a mathematics, engineering program, or other calculus-based major at a four-year institution. Students will gain a basic understanding of calculus, the mathematics of motion and change. Topics include limits and continuity, differentiation, applications of differentiation, integration, applications of integration, derivatives of exponential functions, logarithmic functions, inverse trigonometric functions, hyperbolic functions and related integrals. Students must have a working knowledge of college algebra and trigonometry.
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You get the general idea that taking a definite integral of a ...
(more)
You get the general idea that taking a definite integral of a function is related to evaluating the antiderivative, but where did this connection come from. This tutorial focuses on the fundamental theorem of calculus which ties the ideas of integration and differentiation together. We'll explain what it is, give a proof and then show examples of taking derivatives of integrals where the Fundamental Theorem is directly applicable.
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In this course, we will study the foundations of calculus, the study ...
(more)
In this course, we will study the foundations of calculus, the study of functions and their rates of change. We want you to learn how to model situations in order to solve problems. If you have already taken calculus before, we want you to gain an even deeper understanding of this fascinating subject.
The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two ideas form the basis for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way.
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This page emphasizes the practical concepts of calculus, and is intended to ...
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This page emphasizes the practical concepts of calculus, and is intended to provide a new context for the student already familiar with much of the material. The emphasis is on how calculus can actually be used outside of the classroom, and how the language of calculus is important in many other disciplines. It features articles for download, on topics from exponential growth and decay to discontinuities, vector fields and differential equations. All of the articles include extensive notes, examples, and figures. This resource is part of the Teaching Quantitative Skills in the Geosciences collection.
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This is a two-semester course in n-dimensional calculus with a review of ...
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This is a two-semester course in n-dimensional calculus with a review of the necessary linear algebra. It covers the derivative, the integral, and a variety of applications. An emphasis is made on the coordinate free, vector analysis.
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This is a text on elementary multivariable calculus, designed for students who ...
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This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.
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COW is an internet utility for learning and practicing calculus. The principal ...
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COW is an internet utility for learning and practicing calculus. The principal purpose of COW is to provide you, the student or interested user, with the opportunity to learn and practice problems in calculus (and in the future other topics in mathematics) in a friendly environment via the internet. The most important feature of the COW is that you get to know whether your answer is correct almost immediately. It is as if you had a tutor looking over your shoulder and helping you along as you work. This will be true no matter where you are or what computer you use, as long as it is connected to the internet and has a web browser. The student component of COW (called the Manager) generates calculus examples and exercises in "modules" for studying, tutoring and practice. A number of the modules allow you to experiment by letting you change values or parameters in a function or graph and then see the effect. These modules are called "hands on" modules, and are marked with an asterisk. The component of the COW accessible by instructors (called the Reporter) handles assignment and automatic grading of homework, reporting on student work and class management.
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This course begins with a review of algebra specifically designed to help ...
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This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)
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Calculus Revisited is a series of videos and related resources that covers ...
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Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series, consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.
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Higher order thinking, even in mathematics, is
not a unitary phenomenon. There is not one
form of higher order thinking but, rather, many
forms. It might be argued that each form is the
same complex of cognitive processes applied
to differing domains of knowledge and tasks.
However, as seen in this volume, the task and
knowledge domains differ so greatly that, even
if there are important commonalities in the
cognitive processes involved in complex thinking in those domains, pragmatically, it may be
more useful to consider the thinking tasks of
each domain in terms of their specificity, with
a focus on the tasks particular to the knowledge
of the domain and the forms of higher order
thinking critical to such tasks. Such is the case
with the critical evaluation of quantitative arguments.
The entrance of our society into the information age, with its ubiquity of computer-enhanced publishing and presentation graphics,
has led to a virtual bombardment of both
citizen and student with numerical data and,
moreover, with numerical data embedded not
in the context of separate treatises or texts on
mathematics, but in the context of informative
articles which often contain either central or
peripheral arguments that have essential
quantitative elements. In particular, the quantum leap in the ease with which presentation
graphics can be generated has resulted in constant exposure to information presented in
graphical form. The ability to think critically in
the presence of arguments with essential
quantitative elements, often graphical elements, has become an essential skill for educated citizens in our society and will be so
even more in the future. Instruction related to
the skills necessary for such quantitatively
oriented critical thinking will certainly enter
the curricula of school mathematics if the new
standards for mathematics as reasoning and
communication promulgated by the National
Council of Teachers of Mathematics ( NCTM, 1989) have their hoped-for impact.
Even with the emergence of these new
essential skills of critical thinking that utilize
tools for quantitative reasoning and graphical
interpretation in contexts that are not "mathematical" in the narrow or disciplinary sense,
little investigation has yet been done of the
nature of these cognitive skills, their characterization in information-processing terms,
and their interaction with noncognitive factors
such as anxiety about mathematics. Anecdotal
evidence suggests that mathematics anxiety
results in the paralysis of critical thinking
abilities when quantitative elements are included in the contexts in which individuals
must think critically. Further, it has been suggested that the presumed fact of this paralysis
of critical facilities, along with the wide spread
of such mathematics anxiety, provides at least
the possibility for use of numerical data and
presentation graphics precisely to eliminate
critical evaluation of arguments and claims |
Compact Calculator - CompactCalc You can build linear, polynomial and nonlinear equation set. You are not limited by the size or the complexity of your mathematical expressions. CompactCalc has almost hundred of physical and mathematical constants built in, which can be easily accessed and used in calculations. No longer do you have to search the physic textbook for that common physical constant |
Scientific/Graphing Calculator Workshop
The Academic Support Center is offering scientific and graphing calculator (TI 84 and TI 84 plus) workshops. The workshop will focus on basic use of scientific and graphing calculators to the more advanced uses of the graphing calculator. The workshop will be helpful for all mathematics students who would like to know specific functions of the calculator and how they can be helpful in specific mathematics courses.
Workshops will be held in the Academic Support Center's satellite location in Anderson Library room 2120 at the times listed below. To register, click on the time and fill out the registration form. An email will be sent to you to confirm your attendance for the workshop. Keep in mind that the workshop's capacity is 12 students, so sign up early to reserve your spot!
If none of these times work for you, keep checking back because additional sections may be offered in the future. |
Algebra 1
Description
An outstanding text that presents mathematics as a study of absolutes with a logical approach from one concept to another. Concepts are developed and mastered through an abundance of worked examples and student exercises. Many application problems relate algebra to the physical world |
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...
With this lesson, students will use tables of fees from a few different cell phone providers to create an algebraic expression that reflects billing for services. The example helps students apply algebraic functions to...
This lesson helps students further their understanding of linear functions by applying the material to a real-world example. The class will use data on an airline flight including travel time, ground speed, time...
With this algebra lesson, students will gather data about different airlines, including flight delays, mishandled baggage and other consumer complaints. The material helps students learn how to effectively analyze data,...
This algebra lesson demonstrates exponential growth and decay. The document includes three different ways in which students will retrieve data from the internet, formulate a function, perform calculations and then... |
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Physics online is an interesting, innovative and very creative in the style and presentation for young students of all ages. Most of the physics online courses separate into three categories with the sub-categories listed for the convenience of the students. These main categories are mechanics, light and waves, and electricity.... |
Department Members
Core Academic Departments
Mathematics Department
Curriculum
Standards and Item Specifications
For 2013-2014, the Mathematics curriculum is defined by a combination of the Common Core State Standards and the Next Generation Sunshine State Standards. You may read more about the "blended" standards by viewing the course descriptions below. Detailed information about the kinds of problems students are expected to solve on this year's FCAT, including sample problems, can be found in the FCAT Item Specifications (scroll down to find the specifications in PDF format).
Course Descriptions
Resources for Students and Parents
Mathematics is a challenging subject for many middle school students. However, there are many online resources available to help.
Department of Education Resources
FCAT Explorer is "a free, online educational program for Florida's students that reinforces reading and math skills outlined in the Sunshine State Standards." Students are provided sign-in names and passwords may be requested from your Mathematics teacher.
The Florida Standards web site provides information about the standards Florida's students are expected to meet and the courses they will take during their K-12 education.
The Success Measures web site provides "in-depth information about all of Florida's student assessments in a timely and meaningful way...including details on what your children are being taught in our classrooms and how their learning will be assessed."
Textbook Web Sites
The publishers of WBMS's math textbooks maintain useful web sites that include many additional resources, such as study guides, remedial skills worksheets, tutorial videos, and more.
Regular Mathematics: The textbook for sixth, seventh, and eighth grade regular mathematics is published by Big Ideas Learning. Click here to visit the Big Ideas Math web site. No login credentials are required, but be sure to choose Florida from the drop-down menu, then explore the "Students" and/or "Parents" tabs.
Advanced Mathematics: The textbook for sixth, seventh, and eighth grade advanced mathematics is published by Glencoe/McGraw-Hill. Usernames and passwords will be provided by your teacher.
Algebra: The textbook for eighth grade Algebra I and Algebra I Honors is published by Pearson. Login information will be provided by your teacher.
Resources for Algebra I Students
Students in Algebra I should begin by visiting our Algebra I teacher's blog, the Mathlete Corner.
On his blog, Mr. Baugus presents his own tutorial videos covering every topic in Florida's Algebra I curriculum.
Unaffiliated Online Resources
Khan Academy provides free tutorial videos and practice modules on most K-12 mathematics topics (as well as topics in various sciences, history, and finance). The practice modules are especially helpful in allowing students to practice math skills by providing immediate feedback on their answers. The site allows students to track their progress by logging in with a Google or Facebook account, though logging in is not required to make use of the site's resources. Parents looking for extra practice for their students beyond homework assignments will find what they need here.
The National Library of Virtual Manipulatives provides interactive practice tools ("virtual manipulatives") for mathematics topics such as fractions, integers, equations, and more. The virtual manipulatives are free to use.
Tutoring
Tutoring is available at WBMS on a limited basis. Tutoring begins during the first quarter and ends just before FCAT. Ask your mathematics teacher for a letter explaining tutoring at WBMS and a tutoring application form. Visit the tutoring page for more information.
This website may contain links and/or advertisements to websites maintained by companies and persons unrelated to the School Board of Santa Rosa County, Florida. An advertisement of, or link to, a non-School Board website does not mean that SBSRC approves, endorses or accepts any responsibility for that website, its content or use, or the use of products and services made available through such website. SBSRC is not responsible for the actions, content, accuracy, opinions expressed, privacy policies, products or services provided through these links or made available through these resources or appearing in such websites, nor for any damages or losses, directly or indirectly, caused or alleged to have been caused as a result of your use on such websites. If you decide to leave this website and access hyperlinks to other websites, you do so at your own risk. |
what is the best calculator?I'm planning to take calculus throughout high school and college. Which one did you have, TI-89?
what is the best calculator?
I'm really a big fan of the under $10 solar-cell type (with trig functions). Buy a few of these, and keep them in various places around the house, in the office, etc. Of course, I'm the type to misplace such things as keys, cellphones, etc. (and drop expensive cellphones). I do still have my TI-something high-school/college calculator somewhere in my office, but it has a solvent "burn hole" from organic chem.
I know at least one person online here who will likely point you to a slide rule.
I'm planning to take calculus throughout high school and college. Which one did you have, TI-89?No, it's quite easy. The problem is, I don't know if they're allowed on standardized tests, and some classes disallow them. My first physics professor was an electrical engineer, and he said he used the TI-89 all the time in his engineering work.Do you have a strong preference for where you will attend Uni, and for what courses you want? If so, contact the engineering school and ask for their guidelines, so you'll know what calculators are allowable for tests. Your current TI-84 might be the most advanced calculator allowed, so you wouldn't benefit from an upgrade unless the school loosened their rules. You have plenty of time... Good luck!
It depends on the school, I think. Where I am, the math and physics departments don't allow calculators of any kind (physics exams are symbolic, math exams have contrived numbers such that calculations are easy), the chemistry department only allows scientific calculators, and the engineering department allows all calculators.
Where I come from; mathematics is all symbolic, no calculators; physics has some calculation involved, we are allowed a TI-30X, after, we can use whatever with some exceptions (like no calculators on tests). I'm not sure about engineering, I know in first year they use TI-30X's too, but I'm not sure of any year after. |
books.google.com - R... Geometry
Riemannian Geometry(Google eBook)
R of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.
A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.
User ratings
Review: Riemannian Geometry: Theory & Applications
Review: Riemannian Geometry: Theory & Applications
User Review - Bogdan Suceava - Goodreads
The best introduction in the fundamental topics of Riemannian Geometry. This book helped me a lot. MP do Carmo accomplished a very useful construction that most probably will help several generations of mathematicians as they advance in this topic.Read full review |
More About
This Textbook
Overview
Essential VCE Mathematics has a reputation for mathematical excellence, developed by a highly regarded team of teachers and mathematicians. This approach encourages understanding through a wealth of examples and exercises, an emphasis on VCE examination-style questions. The series has expanded to allow teachers and students to use textbooks geared to their choice of CAS and graphics calculators. Essential Mathematical Methods Units 1 & 2 CAS for the 2006 study design features TI-Nspire and Casio ClassPad calculator explanations, examples and problems in the text. Features: foundation questions allow students to grasp concepts before moving to higher order questions, examples are now cross-referenced to problems, independent learning chapter reviews that include a summary, multiple-choice, short-answer (technology-free), extended-response questions, a comprehensive glossary of terms, a free student CD-ROM containing a PDF of the book with links to additional features, interactive multiple-choice, drag-and drop-tests.
Product Details
Meet the Author
Dr Michael Evans has gained a wealth of experience whilst Head of Mathematics at Scotch College. He is heavily involved in curriculum development both at a Victorian and national level. Michael is a vastly experienced writer of mathematical texts and he is lead author on a number of the texts in the Essential VCE Mathematics series.
Associate Professor Kay Lipson currently teaches statistics at undergraduate and graduate level, as well as conducting courses for industry and government. She is the co-author of several current secondary mathematics textbooks.
Doug Wallace has been a Senior Mathematics Teacher at Wesley College, Melbourne for 20 years. He was Head of Mathematics from 1990 to 2000 and is now Senior College Curriculum and International Baccalaureate Co-ordinator |
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Professional Learning Day
"Math talks" are quick routines that you can implement in your classroom within days. They can raise engagement, build efficient, accurate, and flexible mental math strategies, and help students construct arguments and critique reasoning. We will engage in math talks, analyzing how they can be enacted in the classroom and designed for specific goals or respond to specific misconceptions. Participants will learn about math talks that support understanding of number, algebra, and other domains.
Session A-2: Cycloids!, Ruth Dover
Professional Learning Day
This session includes a hands-on exploration to see graphs of different types of cycloids. Participants will use trigonometry to create the parametric equations for the graphs. This topic lends itself nicely to projects for pre-calculus students. Software will be shown to help see more examples and patterns.
The Nature And Nurture Of Intuition, Thomas Q. Sibley
Forum Lectures
Are people just innately good at mathematics or not? My teaching experience suggests mathematical ability is not just fate: Students develop their mathematical abilities by doing mathematics. In particular we discuss geometric intuition, its connection with geometric reasoning and the possibility of developing them, using examples to get the listeners actively thinking about their own geometric thinking.
Charles G. Torre
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from ...
Workshop On Beauty And Explanation In Mathematics, Manya Raman-Sundström
Journal of Humanistic Mathematics
On March 10-12, 2014, Umeå University in Sweden will host a workshop on mathematical beauty and explanation. The goal of this workshop is explore the question of whether beauty and explanation are related in mathematics. The workshop will bring together top researchers from fields such as mathematics, philosophy, and mathematics education for which this topic is relevant. Many of these researchers have till now worked within their own discipline boundaries on related topics, but have not met or worked with each other. We hope the workshop not only develops the programs of these established researchers, but also sparks interest in ...
Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman
Journal of Humanistic Mathematics
This review discusses Brams' wide-ranging book Game Theory and the Humanities and gives some basic examples of the methodology and style, including how the Theory of Moves contributes to understanding such games.
Journal of Humanistic Mathematics
We explore using a "Study Challenge" to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students' to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
Journal of Humanistic Mathematics
While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly thatLiberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson
Journal of Humanistic Mathematics
This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the ...
Extracting Vessel Structure From 3d Image Data, Yuchen Zhong
University of Western Ontario - Electronic Thesis and Dissertation Repository
This thesis is focused on extracting the structure of vessels from 3D cardiac images. In many biomedical applications it is important to segment the vessels preserving their anatomically-correct topological structure. That is, the final result should form a tree. There are many technical challenges when solving this image analysis problem: noise, outliers, partial volume. In particular, standard segmentation methods are known to have problems with extracting thin structures and with enforcing topological constraints. All these issues explain why vessel segmentation remains an unsolved problem despite years of research.
Algebraic Detection Of Flexibility Of Polyhedral Structures With Applications To Robotics And Chemistry, Stephen Fox Fcrh '11, Robert Lewis
Fordham Undergraduate Research Journal
Many problems arise in biochemistry, robotics, and other fields in which flexibility of a polygonal or polyhedral structure plays an important role. In biochemistry, the flexibility and folding of molecules is an important factor in drug design and is a subject of ongoing research (Erickson et al. 2004). In robotics, stable configurations of manipulators (e.g., a mechanical arm grasping) as well as mechanical joints for locomotion (e.g., walking) must be calculated for safe, smooth movement.
A Sampling Of Popular Books For Numeracy Readers, Michael T. Catalano
Numeracy
Popular books on quantitative themes are seemingly more available than ever. In this book review, we look at five such books from a wide range of authors. Although the books are written for diverse audiences, all provide examples and discussion of concepts that could be used in courses with quantitative literacy objectives. The books are Guesstimation and Guesstimation 2.0 by Lawrence Weinstein and John A. Adam, and Weinstein, respectively; Turning Numbers into Knowledge: Mastering the Art of Problem Solving, by Jonathan G. Koomey; How to Measure Anything: Finding The Value of "Intangibles" in Business, by Douglas W. Hubbard; and ...
Jeffrey Keisler
In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbors in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider's sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of ... |
Prentice hall gold algebra
Prentice hall gold algebra worksheet answers downloads. I dont know but you shoud do the work yourself cause if theres a test or sumthin you wont be able to use a answer key! and if you use an answer key. Prentice hall geometry practice workbook answers key. Prentice hall worksheets answer sheets answers. |
Introduction to Analysis
9780821847879
ISBN:
0821847872
Edition: 5 Pub Date: 2009 Publisher: American Mathematical Society
Summary: Gaughan, Edward is the author of Introduction to Analysis, published 2009 under ISBN 9780821847879 and 0821847872. Three hundred eight Introduction to Analysis textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $47.12, or buy new starting at $55.00.
Ships From:Boonsboro, MDShipping:Standard, ExpeditedComments:Brand new. We distribute directly for the publisher. Introduction to Analysis is designed to bri... [more][ experience with proofs in analysis. A considerable amount of time is spent motivating the theorems and proofs and developing the reader's intuition. Of course, that intuition must be tempered with the realization that rigorous proofs are required for theorems. The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section. Also, at the end of each section, one finds several Projects. The purpose of a Project is to give the reader a substantial mathematical problem and the necessary guidance to solve that problem. A Project is distinguished from an exercise in that the solution of a Project is a multi-step process requiring assistance for the beginner student |
Elementary Differential Equations Bound with IDE CD Package
1 rating:
5.0
A book by Werner E. Kohler
Elementary Differential Equations integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. For example, whenever a new type of problem is introduced (such as first-order … see full wiki
A worthy selection for a text in a differential equations course
As a teacher at a small college, at some point I will be required to teach just about every class in the math and computer science curriculum. Therefore, I examined this book for possible adoption as a text in our differential equations course and found it to be appropriate in all ways. In my opinion, differential equations is a retro course as far as proofs are concerned Meaning that although it is an upper division math course, proofs are best when they are few and far between. That was the strategy taken in this book. Each section opens with a discussion of the new solution strategy, followed by some examples of how it is applied, additional explanation if warranted and then a set of exercises. Solutions to the odd-numbered exercises are included at the end. The quality of the explanations is quite good; the student who has done well in their three-semester calculus sequence will have little difficulty understanding it. The coverage is exactly what I consider to be the necessary material for an introductory course in differential equations. The chapter titles are: |
online course offered by the Saylor Foundation.'...
More
This is a free online course offered by the Saylor Foundation.
' applications. Additionally, you will study trigonometric equations and identities, the laws of sines and cosines, polar coordinates and graphs, parametric equations and elementary vector operations.
You might be curious how the study of trigonometry, or "trig," as it is more often referred to, came about and why it is important to your studies still. Trigonometry, from the Greek for "triangle measure," studies the relationships between the angles of a triangle and its sides and defines the trigonometric functions used to describe those relationships. Trigonometric functions are particularly useful when describing cyclical phenomena and have applications in numerous fields, including astronomy, navigation, music theory, physics, chemistry, and—perhaps most importantly, to the mathematics student—calculus.
In this course, you will begin by establishing the definitions of the basic trig functions and exploring their properties and then proceed to use the basic definitions of the functions to study the properties of their graphs, including domain and range, and to define the inverses of these functions and establish the properties of these. Through the language of transformation, you will explore the ideas of period and amplitude and learn how these graphical differences relate to algebraic changes in the function formulas. You will also learn to solve equations, prove identities using the trig functions, and study several applications of these functions.' |
Elementary Algebra by Schaums Outlines
393
Practice Questions
2
Quizzes
1056
Lessons
216
Flashcards
Overview
Covering everything from Signed Numbers, to Quadratic Equations, Schaum's Outline in Elementary Algebra is so thorough, both struggling and confident students can expect to achieve their personal best on exams. Equipped with 433 practice questions, 2 mini-tests and 216 flashcards, students will get the thorough review they need to better acquaint them with Elementary Algebra.
Topics Covered
Topics and concepts covered in Elementary Algebra by Schaums Outlines
From Arithmetic To Algebra
Representing Numbers By Letters
Representing Numbers By Letters
Stating Products Without Multiplication Signs
Changing Verbal Statements To Algebraic Equations
Interchanging Numbers In Addition
Interchanging Numbers In Addition
Interchanging Addends To Simplify Addition
Rearranging Addends
Interchanging Numbers In Multiplication
Interchanging Numbers In Multiplication
Simplifying Multiplication
Rearranging Factors
Symbolizing The Operations In Algebra
Symbolizing The Operations In Algebra
Symbols In Multiplication
Division By Zero
Expressing Addition And Subtraction Algebraically
Expressing Addition And Subtraction Algebraically
Expressing Addition Algebraically
Expressing Subtraction Algebraically
Changing Verbal Statements Into Algebraic Expressions
Expressing Multiplication And Division Algebraically
Expressing Multiplication And Division Algebraically
Representing Multiplication Or Division
Division And Its Relationship To Multiplication
Expressing Two Or More Operations Algebraically
Expressing Two Or More Operations Algebraically
Expressing Two Operations Algebraically
More Difficult Expressions
Changing Verbal Statements Into Algebraic Expressions
Order In Which Fundamental Operations Are Performed
Order In Which Fundamental Operations Are Performed
To Evaluate A Numerical Expression Not Containing Parentheses
To Evaluate An Algebraic Expression Not Containing Parentheses
Evaluating Numerical Expressions
Evaluating Algebraic Expressions
Evaluating When A Letter Represents
The Uses Of Parentheses
Changing The Order Of Operations
To Evaluate An Algebraic Expression Containing Parentheses
Evaluating Numerical Expressions Containing Parentheses
Evaluating Algebraic Expressions Containing Parentheses
Evaluating When A Letter Represents Zero
Multiplying Factors In Terms Numerical And Literal Coefficients
Multiplying Factors In Terms Numerical And Literal Coefficients
Expressions Containing Terms
Factors Of Terms
Numerical And Literal Coefficients
Repeated Multiplying Of A Factor Base Exponent And Power
Repeated Multiplying Of A Factor Base Exponent And Power
Table Of Powers
Literal Bases Squares And Cubes
Reading Powers
Writing As Bases And Exponents
Writing Without Exponents
Evaluating Powers
Evaluating Powers Of Fractions And Decimals
Evaluating Powers Of Literal Bases
Combining Like And Unlike Terms
Combining Like And Unlike Terms
To Combine Like Terms Being Added Or Subtracted
Combine Like Terms
Simplifying Expressions By Combining Like Terms
Combining Like Terms With Fractional And Decimal Coefficients
Combining Like Terms Representing Line Segments 9
Supplementary Problem 10
Supplementary Problem 12
Supplementary Problem 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 18
Supplementary Problem 22
Supplementary Problem 23
Supplementary Problem 24
Supplementary Problem 25
Simple Equations And Their Solutions
Kinds Of Equalities
Equations And Identities
Checking An Equation
Checking An Identity
Translating Verbal Statements Into Equations
Translating Verbal Statements Into Equations
Translating Statements Into Equations
Matching Statements And Equations
Representing Unknowns
Solving Simple Equations By Using Inverse Operations
Solving Simple Equations By Using Inverse Operations
Addition And Subtraction Are Inverse Operations
Multiplication And Division Are Inverse Operations
Solving By Using Inverse Operations
Rules Of Equality For Solving Equations
Rules Of Equality For Solving Equations
The Rule Of Equality For All Operations
Using Rules Of Equality
Using Division To Solve An Equation
Division Rule Of Equality
Division Rule Of Equality
To Solve An Equation By Using The Division Rule Of Equality
Solving Equations With Integral Coefficients
Division In Equations With Decimal Coefficients
Solving Equations With Percents As Coefficients
Solving Equations With Like Terms On One Side
Division Rule In A Wage Problem
Division Rule In A Commission Problem
Using Multiplication To Solve An Equation
Multiplication Rule Of Equality
Multiplication Rule Of Equality
To Solve An Equation By Using The Multiplication Rule Of Equality
Dividing By A Fraction
Dividing By A Fraction
To Solve An Equation Whose Unknown Has A Fractional Coefficient
Solving Equations With Integral Divisors
Solving Equations With Decimal Divisors
Solving Equations With Fractional Coefficients
Solving Equations With Percents As Coefficients
Multiplication Rule In Distance Problem
Multiplication Rule In Investment Problem
Using Subtraction To Solve An Equation
Subtraction Rule Of Equality
Subtraction Rule Of Equality
To Solve An Equation By Using The Subtraction Rule Of Equality
Subtraction Rule In Equations Containing Integers
Subtraction Rule In Equations Containing Fractions Or Decimals
Subtraction Rule In Problem Solving
Using Addition To Solve An Equation
Addition Rule Of Equality
Addition Rule Of Equality
To Solve An Equation By Using The Addition Rule Of Equality
Addition Rule In Equations Containing Integers
Addition Rule In Equations Containing Fractions Or Decimals
Addition Rule In Problem Solving
Using Two Or More Operations To Solve An Equation
Using Two Or More Operations To Solve An Equation
To Solve Equations By Using Two Inverse Operations
Using Two Inverse Operations To Solve An Equation
Solving Equations With Like Terms On The Same Side
Solving Equations With Like Terms On Both Sides
Solving Equations In Which The Unknown Is A Divisor
Solving Equations In Which The Unknown Is Being Subtracted
Solving Equations Whose Unknown Has A Fractional Coefficient
Using Two Operations In Problem Solving 18
Supplementary Problem 19
Supplementary Problem 20
Supplementary Problem 21
Supplementary Problem 22
Supplementary Problem 23
Signed Numbers
Understanding Signed Numbers Positive And Negative Numbers
Understanding Signed Numbers Positive And Negative Numbers
Words Opposite In Meaning
Expressing Quantities As Signed Numbers
Absolute Value Of Signed Numbers
Using Number Scales For Signed Numbers
Using Number Scales For Signed Numbers
Number Scales
Two Meanings Of Signed Numbers
Comparing Signed Numbers
Use A Number Scale To Solve Problems
Adding Signed Numbers
Adding Signed Numbers
Rules For Adding Signed Numbers
Combining By Means Of Signed Numbers
Adding Signed Numbers With Like Signs
Adding Signed Numbers With Unlike Signs
Adding Signed Numbers Which Are Opposites Of Each Other
Adding Signed Numbers
Simplifying The Addition Of Signed Numbers
To Simplify The Writing Used In Adding Signed Numbers
To Simplify The Writing Used In Adding Signed Numbers
To Simplify Adding Signed Numbers
Simplifying The Addition Of Signed Numbers
Adding Positives And Negatives Separately
Using Signed Numbers And Number Scales To Solve Problems
Subtracting Signed Numbers
Subtracting Signed Numbers
Using Subtraction To Find The Change From One Position To Another
Using Subtraction To Find The Change From One Position To Another
Rule For Subtracting Signed Numbers
Subtracting A Positive Number
Subtracting A Negative Number
Subtracting Vertically
Subtracting Signed Numbers
Combining Addition And Subtraction Of Signed Numbers
Finding The Change Between Two Signed Numbers
Finding The Distance Between Two Levels
Finding A Temperature Change
Multiplying Signed Numbers
Rules For Multiplying Two Signed Numbers
Rules For Multiplying More Than Two Signed Numbers
Multiplying Signed Numbers With Like Signs
Multiplying Signed Numbers With Unlike Signs
Multiplying Signed Numbers
Multiplying More Than Two Signed Numbers
Using Signed Numbers To Solve Problems
Finding Powers Of Signed Numbers
Rules For Finding Powers Of Signed Numbers
Finding Powers When Base Is Positive
Finding Powers When Base Is Negative
Finding Powers Of Signed Numbers
Finding Bases Exponents Or Powers
Dividing Signed Numbers
Rules For Dividing Signed Numbers
Combining Multiplying And Dividing Of Signed Numbers
Dividing Signed Numbers With Like Signs
Dividing Signed Numbers With Unlike Signs
Dividing Signed Numbers
Combining Multiplying And Dividing Signed Numbers
Zero In Dividend Or Divisor
Evaluating Expressions Having Signed Numbers
Evaluating Expressions Having Signed Numbers
Evaluating Expressions Having One Letter
Evaluating Expressions Having Two Letters
Evaluating Expressions Having Three Letters
Summary Of Rules For Computations Involving Signed Numbers
Supplementary Problems
Supplementary Problem 1
Supplementary Problem 5
Supplementary Problem 7
Supplementary Problem 9
Supplementary Problem 14
Supplementary Problem 16
Supplementary Problem 17
Supplementary Problem 21
Supplementary Problem 22
Supplementary Problem 24
Supplementary Problem 25
Supplementary Problem 26
Supplementary Problem 27
Introduction To Monomials And Polynomials
Understanding Monomials And Polynomials
Understanding Monomials And Polynomials
Selecting Like Terms
Adding Monomials
Adding Monomials
Adding Like Terms
Adding Like Terms Horizontally
Adding Like Terms Vertically
Adding Like And Unlike Terms
Arranging And Adding Polynomials
Arranging The Terms Of A Polynomial In Descending Or Ascending Order
To Add Polynomials
Arranging Polynomials And Combining Like Terms
Adding Arranged Polynomials
Adding Polynomials
Checking The Addition Of Polynomials
Subtracting Monomials
Subtracting Monomials
Subtracting Like Terms
Different Subtraction Forms
Combining Adding And Subtracting Of Like Terms
Subtracting Polynomials
To Subtract Polynomials
Subtracting Arranged Polynomials
Arranging Polynomials And Subtracting
Different Subtraction Forms
Checking The Subtraction Of Polynomials
Using Parentheses And Other Grouping Symbols To Add Or Subtract Polynomials
Using Parentheses And Other Grouping Symbols To Add Or Subtract Polynomials
Rules For Removing Parentheses And Grouping Symbols
Removing Parentheses Preceded By A Plus Sign
Removing Parentheses Preceded By A Minus Sign
Brackets Containing Parentheses
Using Grouping Symbols To Add Or Subtract Polynomials
Removing Symbols Of Grouping
Multiplying Monomials And Powers Of The Same Base
Multiplying Monomials And Powers Of The Same Base
Multiplying Powers Of The Same Base
Finding The Power Of A Power Of A Base
Multiplying Monomials
Multiplying A Polynomial By A Monomial
Multiplying A Polynomial By A Monomial
Multiplying A Polynomial By A Monomial Horizontally
Multiplying A Polynomial By A Monomial Vertically
Removing Parentheses
Removing Brackets Containing Parentheses
Removing Symbols Of Grouping
Multiplying Polynomials
To Multiply Polynomials
Multiplying Polynomials
Checking Multiplication
Extended Multiplication
Dividing Powers And Monomials
Dividing Powers And Monomials
To Divide Monomials
To Divide Monomials
To Check Division Of Monomials
Dividing Powers Of The Same Base
Dividing Monomials
Checking Division
Dividing A Polynomial By A Monomial
Dividing A Polynomial By A Monomial
Dividing A Polynomial By A Monomial
Checking Division
Multiplying And Dividing Polynomials By A Monomial
Dividing A Polynomial By A Polynomial
To Divide Polynomial
To Divide Polynomial
To Check The Division
Dividing A Polynomial By A Polynomial No Remainder
Arranging Polynomials And Dividing
Terms Missing In Dividend
Dividing Polynomials With Remainder 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 20
Supplementary Problem 22
Supplementary Problem 23
Supplementary Problem 25
Supplementary Problem 27
Supplementary Problem 28
Supplementary Problem 32
Supplementary Problem 33
Supplementary Problem 34
Supplementary Problem 35
Supplementary Problem 37
Supplementary Problem 38
Supplementary Problem 39
Supplementary Problem 40
Supplementary Problem 41
First Degree Equations
Reviewing The Solution Of First Degree Equations Having Positive Roots
Reviewing The Solution Of First Degree Equations Having Positive Roots
Inverse Operations
Using Subtraction S To Undo Addition A
Using Addition A To Undo Subtraction S
Using Division D To Undo Multiplication M
Using Multiplication M To Undo Division D
Using Two Operations To Solve Equations
Equations Containing More Than One Term Of The Unknown
Equations Having Fractional Coefficients
Number Problems Leading To First Degree Equations
Solving First Degree Equations Having Negative Solutions
Solving First Degree Equations Having Negative Solutions
Using Addition Or Subtraction To Solve Equations
Using Multiplication Or Division To Solve Equations
Using Two Operations To Solve Equations
Equations Having Fractional Coefficients
More Difficult Equations
Problems Having Negative Roots
Solving Equations By Transposing
Rule Of Transposition
Rule Of Transposition
To Solve Equations By Transposing Terms
Transposing Terms In An Equation
More Difficult Equations
Solving Equations Containing Parentheses
To Solve Equations By Removing Parentheses
Removing Parentheses To Solve Equations
More Difficult Equations With Parentheses
Problems Leading To Equations With Parentheses
Solving Equations Containing One Fraction Or Fractions Having The Same Denominator
To Solve Equations Having Same Denominator By Clearing Of Fractions
Fractional Equations Having The Same Denominator
Fractional Equations Having Binomial Numerator Or Denominator
Solving Equations Containing Fractions Having Different Denominators
Lowest Common Denominator
To Solve Equations Having Different Denominators By Clearing Of Fractions
Fractional Equations Having Numerical Denominators
Fractional Equations Having Literal Denominators
Fractional Equations Having Binomial Numerators
Fractional Equations Having Binomial Denominators
Solving Equations Containing Decimals
Solving Equations Containing Decimals
To Solve An Equation Having Decimals
Equations With One Decimal
Solving Equations Without Clearing Of Decimals
Equations With Two Or More Decimals
Equations Containing Percents
Equations Containing Decimals And Parentheses
More Difficult Decimal Equations
Solving Literal Equations
Solving Literal Equations
Solving Literal Equations By Using One Operation
Solving For One Of The Letters In A Formula
Solving And Checking Literal Equations
Solving A Literal Equation For Each Letter
Solving More Difficult Literal Equations
The Graphing Calculator
Graphing Calculators Are Used To Solve Equations. 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 17
Supplementary Problem 18
Supplementary Problem 19
Supplementary Problem 20
Supplementary Problem 21
Supplementary Problem 22
Supplementary Problem 23
Formulas
Points And Lines
Points And Lines
Undefined Terms Of Geometry Point Line And Plane
Point
Line
Planes
Line Segments
Dividing A Line Segment Into Parts
Congruent Segments
Understanding Polygons Circles And Solids
Understanding Polygons In General
Understanding Circles
Understanding Triangles
Understanding Quadrilaterals
Understanding Solids
Formulas For Perimeters And Circumferences Linear Measure
Formulas For Perimeters And Circumferences Linear Measure
Perimeter Formulas For Triangles And Quadrilaterals
Perimeter Formulas For Polygons
Finding A Side Of An Equilateral Polygon
Finding Perimeters Of Regular Polygons
Finding Perimeters Of Quadrilaterals
Finding The Perimeter Of A Rectangle
Finding The Length Or Width Of A Rectangle
Perimeter Of An Isoceles Triangle
Circumference And Arc Formulas
Circumference Of A Circle
Perimeters Of Combined Figures
Formulas For Areas Square Measure
Formulas For Areas Square Measure
Area Formulas Using A For Area Of Figure
Area Formulas For Solids Using T For Total Area Of Solid
Relations Among Square Units
Finding The Area Of Squares
Finding Areas
Area Of Circle Formulas
Area Of A Circle
Formulas For Combined Areas
Formulas For Reduced Areas
Finding Total Areas Of Solids
Formulas For Volumes Cubic Measure
Formulas For Volumes Cubic Measure
Volume Formulas
Relations Among Cubic Units
Finding Volumes Of Cubes
Finding Volumes Of Rectangular Solid Prism And Pyramid
Finding Volumes Of Sphere Cylinder And Cone
Deriving Formulas From V Bh
Formulas For Combined Volumes
Deriving Formulas
To Derive A Formula For Related Quantities
Obtaining Formulas From A More General Formula
Deriving A Coin Formula
Deriving Coin Formulas
Deriving Time Formulas
Deriving Length Formulas
Obtaining Formulas From D and Rt
Transforming Formulas
Transforming Formulas
Use Inverse Operations To Transform Formulas
Transformations Requiring Division
Transformations Requiring Multiplication
Transformations Requiring Addition Or Subtraction
Transformations Requiring Two Operations
More Difficult Transformations
Finding The Value Of An Unknown In A Formula
Finding The Value Of An Unknown In A Formula
Finding The Value Of An Isolated Unknown
Finding The Value Of An Unknown That Is Not Isolated
More Difficult Evaluations Using Transformations
Finding An Unknown In A Problem 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 17 31
Supplementary Problem 32
Supplementary Problem 34
Supplementary Problem 35
Graphs Of Linear Equations
Understanding Graphs
Reviewing Number Scales
Forming A Graph By Combining Number Scales
Comparing A Map And A Graph
Locating Points On A Graph
Locating Positions On A Map
Coordinates Of Points In The Four Quadrants
Coordinates Of Points Between The Quadrants
Graphing A Quadrilateral
Graphing A Triangle
Graphing Linear Equations
Graphing Linear Equations
To Graph A Linear Equation
To Graph A Linear Equation
To Graph A Linear Equation By Using Intercepts
Equations Of The First Degree
Making Tables Of Coordinate Values
Graphing Linear Equations
Graphing Linear Equations Using Intercepts
Graphing Equations Of First Degree In Only One Unknown
Coordinate Values Of Any Point On A Line
Coordinate Values Of Any Point Not On A Line
Intercepts And Points Of Intersection
Solving A Pair Of Linear Equations Graphically
Solving A Pair Of Linear Equations Graphically
Consistent Inconsistent And Dependent Equations
To Solve A Pair Of Linear Equations Graphically
Finding Common Solutions Graphically
Consistent Equations And Their Graphic Solution
Inconsistent Equations
Dependent Equations
Deriving A Linear Equation From A Table Of Values
Deriving A Simple Linear Equation By Inspection
Deriving A Linear Equation By The Ratio Method
Deriving Simple Linear Equations By Inspection
Deriving Linear Equation Of Form By Ratio Method
Midpoint Of A Segment
Midpoint Of A Segment
Applying The Midpoint Formula
Determining If Segments Bisect Each Other
Distance Between Two Points
Distance Between Two Points
Finding The Distance Between Two Points By Using The Distance Formula
Applying The Distance Formula To A Triangle
Applying The Distance Formula To A Parallelogram 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16
Supplementary Problem 17
Supplementary Problem 19
Supplementary Problem 20
Introduction To Simultaneous Equations
Solving A Pair Of Equations By Addition Or Subtraction
To Solve A Pair Of Equations By Adding Or Subtracting
Using Addition Or Subtraction To Eliminate One Unknown
Solutions Not Requiring Multiplication
Solutions Requiring Multiplication
Solutions Requiring Rearrangement Of Terms
Fractional Pairs Of Equations
Decimal Pairs Of Equations
Solving A Pair Of Equations By Substitution
To Solve A Pair Of Equations By SubstitutionProblem Solving And Mathematical Modeling
Problem Solving And Mathematical Modeling
Number Problems Having One Unknown
Number Problems Having One Unknown
To Solve A Number Problem Having One Unknown
Translation Of Statements Into Equations
Verification Or Check In Original Statement
Complete Solutions Of Number Problems
Number Problems Having Two Unknowns
Number Problems Having Two Unknowns
To Solve A Number Problem Having Two Unknowns
Representing Two Unknowns By Using One Letter
Using One Equation For Two Unknowns
Using Two Equations For Two Unknowns
Complete Solution Of Number Problem Having Two Unknowns
Consecutive Integer Problems
Consecutive Integer Problems
Representation Using N For First Integer
Representation Using N For Middle Integer
Translation In Consecutive Integer Problems
Translation In Consecutive Even Integer Problems
Complete Solutions Of An Integer Problem
Age Problems
Age Problems
Representing Ages On Basis Of Present Age
Representing Ages
Using One Equation For Two Unknowns In Age Problems
Using Two Equations For Two Unknowns In Age Problems
Complete Solution Of An Age Problem Two Methods
Ratio Problems
Ratio Problems
Ways Of Expressing A Ratio
General Principles Of Ratios
Ratio Of Two Quantities With Same Unit
Ratio Of Two Quantities With Different Units
Continued Ratio Of Three Quantities
Numerical Ratios
Algebraic Ratios
Representation Of Numbers In A Fixed Ratio
Ratio In Number Problems
Ratio In A Triangle Problem
Ratio In A Money Problem
Ratio In A Will Problem
Ratio In A Wage Problem
Angle Problems
Pairs Of Angles
Using One Equation For Two Unknowns In Angle Problems
Using Two Equations For Two Unknowns In Angle Problems
Three Angles Having A Fixed Ratio
Supplementary Angles Problem
Sum Of Angles Of A Triangle Problem
Perimeter Problems
Perimeter Problems
One Equation Method Perimeter Of Rectangle
Two Equation Method Perimeter Of Triangle
One Equation Method Perimeter Of Trapezoid
Perimeter Of A Quadrilateral Ratio Of Sides
Perimeter Of An Isosceles Triangle Problem
Perimeter Of A Square Problem
Coin Or Stamp Problems
Coin Or Stamp Problems
Finding Total Values
Representation In Coin Or Stamp Problems
Using One Equation In Coin Or Stamp Problems
Using Two Equations In Coin Or Stamp Problems
Complete Solution Of Coin Problem
Complete Solution Of A Change Problem
Complete Solution Of A Fares Problem
Cost And Mixture Problems
Cost And Mixture Problems
Representation In Mixture Problems T and Nv
Representation In Cost Problems
Translation In Value And Cost Problems
Complete Solution Blending Coffee Problem
Complete Solution Selling Tickets Problem
Investment Or Interest Problems
Investment Or Interest Problems
Representation In Interest Problems I and Pr
Translation In An Interest Problem
Complete Solution Ratio In An Interest Problem
Alternate Methods In An Investment Problem
Alternate Methods In A Profit And Loss Investment Problem
Complete Solution Adding A Third Investment
Motion Problems
Motion Problems
Representation Of Distance
Representation Of Time
Separation Situation
Closure Situation
Round Trip Situation
Gain Or Overtake Situation
Motion Problem A Trip In Two Stages
Mathematical Modeling
Mathematical Modeling
Example 10
Supplementary Problem 11
Supplementary Problem 12
Supplementary Problem 13
Supplementary Problem 14
Supplementary Problem 15 33
Supplementary Problem 34
Supplementary Problem 35
Supplementary Problem 36
Supplementary Problem 38
Supplementary Problem 39
Supplementary Problem 40
Supplementary Problem 43
Supplementary Problem 44
Supplementary Problem 45
Supplementary Problem 46
Supplementary Problem 47
Supplementary Problem 48
Supplementary Problem 49
Supplementary Problem 50
Supplementary Problem 51
Supplementary Problem 52
Supplementary Problem 54
Supplementary Problem 55
Supplementary Problem 56
Supplementary Problem 58
Supplementary Problem 60
Supplementary Problem 62
Supplementary Problem 64
Supplementary Problem 65
Supplementary Problem 66
Products And Factoring
Understanding Factors And Products
A Product And Its Factors
Finding The Product Of Monomial Factors
Finding The Product Of Two Factors A Monomial And A Polynomial
Finding Products Involving Fractions And Decimals
Factoring A Polynomial Having A Common Monomial Factor
Factoring A Polynomial Having A Common Monomial Factor
To Factor A Polynomial Having A Common Monomial Factor
Factoring Polynomials Having A Common Monomial Factor
Factoring Numerical Polynomials
Squaring A Monomial
Squaring A Monomial
Squaring Numbers
Squaring Monomials
Finding Areas Of Squares
Finding The Square Root Of A Monomial
Finding The Square Root Of A Monomial
Finding Principal Square Roots
Finding Sides Of Squares
Finding The Product Of The Sum And Difference Of Two Numbers
Finding The Product Of The Sum And Difference Of Two Numbers
Multiplying The Sum Of Two Numbers By Their Difference
Multiplying Two Numbers By The Sum Product Method
Multiplying A Monomial By Sum And Difference Factors
Factoring The Difference Of Two Squares
Factoring The Difference Of Two Squares
To Factor The Difference Of Two Squares
Procedure For Factoring The Difference Of Two Squares
Complete Factoring Involving The Difference Of Two Squares
Finding The Product Of Two Binomials With Like Terms
Finding The Product Of Two Binomials With Like Terms
To Multiply Two Binomials By Inspection
Products Of Binomials By Steps
Products Of Two Binomials Mentally
Representing Areas Of Rectangles
Factoring Trinomials In Form Of X2 Bx C
Factoring Trinomials In Form Of X2 Bx C
To Factor A Trinomial In Form Of X2 Bx C
Factoring Trinomials In Form Of X2 Bx C
Factoring Trinomials In Form Of X2 Bx C
Factoring Trinomial In Form Of Ax2 Bx C
To Factor A Trinomial In Form Of Ax2 Bx C
Factoring Trinomials In Form Of Ax2 Bx C
Squaring A Binomial
Squaring A Binomial
To Square A Binomial
Factoring A Perfect Square Trinomial
Factoring A Perfect Square Trinomial
To Factor A Perfect Square Trinomial
Factoring A Perfect Square Trinomial
Representing The Side Of A Square
Completely Factoring Polynomials
Completely Factoring Polynomials
Procedure To Completely Factor Expressions Having Common Monomial Factor
Procedure To Completely Factor Expressions Having No Common Monomial Factor
Factoring Completely Expressions Having Common Monomial Factor
Factoring Completely Expressions Having No Common Monomial Factor
The Variable Direct And Inverse Variation
The Variable Direct And Inverse Variation
Measuring The Change In A Variable
Using Division To Measure The Change In A Variable
Multiplying Or Dividing Variables
Understanding Direct Variation
Understanding Direct Variation
Multiplication And Division In Direct Variation
Direct Variation In Formulas
Multiplication And Division In Direct Variation
Applying Direct Variation To Statements
Finding Values For Directly Varying Variables
Applying Direct Variation To A Motion Problem
Applying Direct Variation To An Interest Problem
Understanding Inverse Variation
Understanding Inverse Variation
Multiplication And Division In Inverse Variation
Inverse Variation In Formulas
Multiplication And Division In Inverse Variation
Applying Inverse Variation To Statements
Finding Values For Inversely Varying Variables
Supplementary Problems
Supplementary Problem 1
Supplementary Problem 2
Supplementary Problem 3
Supplementary Problem 4
Supplementary Problem 5
Supplementary Problem 6
Supplementary Problem 8
Supplementary Problem 9
Supplementary Problem 10
Supplementary Problem 12
Supplementary Problem 13
Supplementary Problem 14
Supplementary Problem 15
Supplementary Problem 16 26
Supplementary Problem 27
Supplementary Problem 28
Supplementary Problem 29
Supplementary Problem 30
Supplementary Problem 31
Supplementary Problem 34
Supplementary Problem 35
Supplementary Problem 36
Fractions
Understanding Fractions
Understanding Fractions
Zero Numerators Or Zero Denominators
Fractions Meaning Division
Fractions Meaning Ratio
Fractions Meaning Parts Of A Whole Or Of A Group
Fractions Having Zero Numerators
Fractions Having Zero Denominators
Changing Fractions To Equivalent Fractions
Changing Fractions To Equivalent Fractions
Using Multiplication To Obtain Equivalent Fractions
Using Division To Obtain Equivalent Fractions
Obtaining Missing Terms
Reciprocals And Their Uses
Reciprocal Of A Number
Rules Of Reciprocals
Are Reciprocal Of Each Other
The Product Of Two Reciprocals Is 1
Using Reciprocals To Change Division To Multiplication
Using Reciprocals To Solve Equations
Reducing Fractions To Lowest Terms
Reducing Fractions To Lowest Terms
To Reduce A Fraction To Lowest Terms
Binomials Which Are Negatives Of Each Other
Reducing Fractions Whose Terms Have Common Monomial Factors
Reducing Fractions Whose Terms Have A Common Binomial Factor
Reducing Fractions Having Binomial Factors Which Are Negatives Of Each Other builtPerfect for beginning math students, this program is designed by curriculum experts and experienced teachers to bring students up to speed in the most challenging areas of early-level algebra. Concepts include real…
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NROC's Algebra 1 course is designed to be used with high school and college algebra students at a broad range of ability levels, from remedial to advanced. The content is correlated to all US state algebra frameworks…
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Perfect for beginning math students, the NROC developmental math program is designed by curriculum experts and experienced teachers to bring students up to speed in the most challenging areas. |
Mathematics in Fun and in Earnest
A world-renowned mathematician takes a lighthearted look at the philosophy, form, and recreations of mathematics in this fascinating book. In lucid and witty language, he discusses and illustrates the charm of mathematics as well as the science's vast practical utility and its vital significance to our cultural history. 1958 edition.
What is the role of mathematics in the secondary classroom? What is expected of a would-be maths teacher? How is mathematics best taught and learnt? This book combines theory and practice to present ...
Essential Mathematics for Economics and Business has become established as one of the leading introductory textbooks on mathematics for students of these subjects. It combines a non-rigorous approach ... |
Mathematical Experience, Study Edition
"This is a people-centered book about mathematics, and as such it provides an opportunity to explore fundamental issues that are typically absent ...Show synopsis"This is a people-centered book about mathematics, and as such it provides an opportunity to explore fundamental issues that are typically absent from the experience of most college and university students (as well as their teachers). This new edition provides an excellent initiation of students into some of the more challenging aspects of mathematics The study edition of The Mathematical Experience will help its readers acquire a real understanding of mathematics." -Notices of the AMS "Two distinguished mathematicians...have written a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." --The New Yorker (1984 American Book Award Edition) |
: Applications and Concepts: Course 3
Setting the standard in middle school mathematics "Mathematics: Applications and Concepts" is a three-course middle school series intended to bridge ...Show synopsisSetting the standard in middle school mathematics "Mathematics: Applications and Concepts" is a three-course middle school series intended to bridge the gap from elementary mathematics to Algebra 1. The program is designed to motivate your students, enable them to see the usefulness of mathematics in the world around them, enhance their fluency in the language of mathematics, and prepare them for success in algebra and geometry78652653652653 0078652650 MULTIPLE COPIES AVAILABLE-COVER IS TATTERED...Fair. 007865265078652650 MULTIPLE COPIES AVAILABLE-Very Good...Very Good. 0078652650 |
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Related Information
COMMON MATH ASSIGNMENT - RUBRIC
Suggestions for Correcting CMAs and General Guide for Rating the Level of Accomplishment
A reader will evaluate the responses to the questions on a scale of 1 to 4. Based on evaluations of designated subsets of the questions, the reader will evaluate each dimension (A,B,C,D) on a scale of 1 to 4. Finally, the reader will review his/her assigned scores (1,2,3,4) for each of the dimensions (A,B,C,D) and assign to the CMA Project a holistic score for quantitative reasoning.
4.- (85%-100% correct) Nearly flawless
3.- (70%-85% correct) Equations are nearly correct. Models will be reasonable. Models will be meaningful. There is much better use of equations than for "essential". For the most part, graphs will be correct.
2.- (30%-70% correct) There is evidence of progress. There be errors and little discernible logic, estimates will be better than for "in progress" scores. There may be an attempt to use an equation.
1. - (0-30% correct) Floundering, very little idea of what is to be done |
Geometry FlexBook is a clear presentation of the essentials of geometry for the high school student. Topics include: Proof, Congruent Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations Trigonometry FlexBook is an introduction to trigonometry for the high school student. Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.'The study of sequences, although seen as an incipient numerical progression, is the foundation of mathematical analysis. This...
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The study of sequences, although seen as an incipient numerical progression, is the foundation of mathematical analysis. This concept in turn is based on set theory and Dedekind cuts, and is studied by mathematical analysisYes, this is the Lewis Carroll who wrote Alice in Wonderland, and these two works show the same quirky humor. Here you see Carroll the mathematician at his playful best. Don't let the title of the first work mislead you--this isn't about modern symbolic logic but about ways of expressing classical logic with symbols. It's loaded with amusing problems to delight any mathematical puzzler. In the second work he turns logic into a game played with diagrams and colored counters, giving you hundreds of challenging and witty syllogisms to solve. Great mind-stretching funA System of Logic was first published in 1843 and immediately enjoyed a wide circulation, going through numerous editions. Mill himself made substantial changes in the third edition, published in 1850, and the eighth edition, published in 1872, a year before his death. This book is Mill's most comprehensive and systematic philosophical work, elaborating his inductive method, which helped to free the empirical sciences from the rigidity of analysis by way of syllogisms. Syllogisms are arguments grounded in general principles, in which two premises are used to deduce a third premise, or conclusion. In A System of Logic, Mill breaks away from this age-old practice and instead proposes the use of a form of logic derived from the principles of the natural sciences. He uses his method to address questions of language and logic, induction, the relativity of knowledge, the structure of the scientific method, the structure of arithmetic and geometry, and the principles of the moral sciences. In effect, Mill provides a solid, scientific methodology for reasoning and for philosophy, derived from science and mathematics.The introduction discusses the role and purpose of logic in human understanding. Logic is the art and science of reasoning, a means for the pursuit of truth. However, logic is only concerned with making inferences from observed phenomena, not with intuitive truths. Logic does not produce new evidence, but it can determine whether something offered as evidence is valid. Logic judges but does not observe, invent, or discover. Logic serves a purpose in some larger project of inquiry that gives it meaning. Fundamentally, logic is a method of evaluating evidence covers |
The purpose of this study was to determine the effect of TI-Nspire graphing calculator use on student achievement and on teacher behavior variables of planning, teaching, and assessing. This study investigated the teaching of functions by teachers...
Computer scientists studying formal languages have made use of a variety of representations to both reason, and communicate their ideas to others. Symbolic representations have proved useful for rigorously defining the theoretical objects of |
AQA Certificate in Further Mathematics (Paperback)
Motivates and challenges more able students by providing more complex introductions, worked examples and exercises for all topics. This specification is ideal for students to prepare for A level mathematics. A range of algebraic and geometric topics are covered and it provides an introduction to Matrices and Calculus. Written by experienced teachers, this book: - Offers complete support for students throughout the course as it is an exact match to this new specification - Includes an introduction to each topic followed by worked examples with commentaries - Provides plenty of practice with hundreds of questions Contents Section 1: Algebra 1. Number and algebra I 2. Algebra II 3. Algebra III 4. Algebra IV Section 2: Geometry 5. Co-ordinate geometry 6. Geometry I 7. Geometry II Section 3: Calculus 8. Calculus Section 4: Matrices 9. Matrices |
Nonmathematician
Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the ...Show synopsisErudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems486248232 Paperback. Minor wear and discoloration on...Good. 0486248232 Paperback. Minor wear and discoloration on cover. Mild corner bump and edge |
Survey Of Mathematics I –
mth361
(3 credits)
This is the first course of a two-part course sequence presenting a survey of mathematics. This course addresses the conceptual framework for mathematics. The focus of this course is on real number properties, patterns, operations, and algebraic reasoning and problem solving |
This site is the parent site of an extensive collection of interactive mathematics authored by Alexander Bogomolny and...
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This site is the parent site of an extensive collection of interactive mathematics authored by Alexander Bogomolny and includes an interactive monthly column . The content is accessible to the casual reader but offers much depth along with links to other high-quality resources. Altogether, this site is a mathematician's delight.
This excellent site contains a large and interesting selection of material on Fibonacci Numbers and their myriad related...
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This excellent site contains a large and interesting selection of material on Fibonacci Numbers and their myriad related concepts. It includes web and text references to the rich literature of Fibonacci numbers. It also features a variety of images, graphics and animations. Many of the topics include student investigations for NCTM standard type explorations. The content includes standard motivational examples and applications in nature, but also mathematical explanations and puzzle pages. The site has already won several awards.
GeoGebra is a free and multi-platform dynamic mathematics software for education in secondary schools that joins geometry,...
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GeoGebra is a free and multi-platform dynamic mathematics software for education in secondary schools that joins geometry, algebra and calculus. On the one hand, GeoGebra is a dynamic geometry system--you can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards; on the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGebra: an expression in the algebra window corresponds to an object in the geometry window and vice versa.
site contains an extensive collection of games and puzzles in the form of java applets including Nim, the Tower of...
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This site contains an extensive collection of games and puzzles in the form of java applets including Nim, the Tower of Hanoi, Cryptarithms, Latin Squares, and much more. Written by Alexander Bogomolny, these applets are designed to engage the reader in interactive investigations. Background material is provided and the site serves as an excellent educational resource.
This site provides an extremely large encyclopedia-style collection of material related to mathematics at the college level...
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This site provides an extremely large encyclopedia-style collection of material related to mathematics at the college level and beyond. Much of the material deals with advanced topics. A large number of animated GIFs and java applets are presented as visual aids and the site has won numerous web awards. The World of Mathematics is hosted by Wolfram Research, Inc., and is offered as a free service to the mathematics community.
This site contains an extensive collection of java applets involving arithmetic and algebra miscellany and puzzles. Written...
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This site contains an extensive collection of java applets involving arithmetic and algebra miscellany and puzzles. Written by Alexander Bogomolny, these applets are designed to engage the reader in interactive investigations. Background material is provided and the site serves as an excellent educational resource. |
Math Advising
THIS PAGE IS INTENDED TO GIVE YOU A LITTLE MORE INFORMATION ABOUT RVC MATH COURSES TO HELP YOU PLAN YOUR SCHEDULE.
It is best to talk to an RVC counselor who can advise you about what math classes you should take for your specific program of study or intended transfer school.
Who is MTH 096A (Mathematical Literacy for College Students) for?
If you know the only college-level math class you will need to take is MTH 115 (General Education Mathematics) or MTH 220 (Statistics), consider taking MTH 096A. MTH 096A is a 6-hour course focused on problem solving in real-world contexts. By taking MTH 096A you can satisfy the algebra and geometry prerequisites for MTH 115 and MTH 220 in one semester. The prerequisite for the course is grades of C or higher in MTH 088 & 089 or a sufficiently high placement test score.
Who can take MTH 096S (Combined Beginning and Intermediate Algebra)?
MTH 096S is a fast paced 6-hour course that covers all the content of both Beginning Algebra (MTH 091-092) and Intermediate Algebra (MTH 093-094) in one semester. Students who scored a 45 or higher on the RVC Placement Test (ACCUPLACER) Elementary Algebra Test or earned A's in both MTH 088 & 089 are eligible to enroll in MTH 096S.
If you take MTH 097 (Geometry), when should you take it?
Once you've earned a "C" or higher in beginning algebra, you may enroll in MTH 097. You have the option of taking MTH 097 before, in the same semester as, or after taking intermediate algebra. (Unless mathematics is a fairly easy subject for you, it is not recommended that you take both geometry and intermediate algebra in the same semester.) If you will eventually be taking MTH 100, MTH 120 or MTH 132, it is best to take intermediate algebra in the semester right before taking those math courses.
NOTE: You may not have to take MTH 097 if you qualify for a MTH 097 Waiver or pass the RVC Geometry Competency Test--see Geometry Options
What should you take after completing geometry and intermediate algebra?
Once you have satisfactorily completed geometry and intermediate algebra, there are a variety of college-level math courses that you can choose from at Rock Valley College. The class you should choose depends on your intended major.
Are you planning to get an AA or AS degree at RVC?
Who should take MTH 120 (College Algebra)?
MTH 120 is primarily intended for students who need it as a prerequisite for another math course such as MTH 125, MTH 135, MTH 160, and MTH 211.
Who is MTH 132 (Precalculus) recommended for?
MTH 132 is 5-hour course that is intended for students preparing for MTH 135 (Calculus I). It covers the content of both College Algebra (MTH 120) and Trigonometry (MTH 125). Because MTH 132 covers the topics at a more rapid pace than those individual courses, it is recommended that students have earned an "A" or "B" in intermediate algebra (MTH 093 & 094 or MTH 096S) before enrolling in MTH 132. Also, if you recently took the equivalent of college algebra and trigonometry in high school and want a "refresher" before enrolling in calculus, MTH 132 would be a good option for you. |
MatBasic Desciption:
The MatBasic is the language of mathematical calculations. Strong mathematical base: full complex arithmetic's, linear algebra and operations, nonlinear methods and graphical visualization.
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MatBasic is a calculating, programming and debugging environment using special high-level programming language designed for solving mathematical problems. MatBasic programming language allows execution of difficult mathematical calculations, involving an exhaustive set of tools for the purpose of creation of algorithmic programs. It also allows a user to abstract his mind from the type of working data which can be either real-valued, or complex numbers, or matrices, or strings, or structures, etc. The MatBasic supports both the text and the graphical data visualization.
MatBasic is fast language interpreter and its environment application field is wide: from solving the school problem to executing different engineering and mathematical computations. The MatBasic programming language combines; simplicity of BASIC language, flexibility of high-level languages such as C or Pascal and at the same time turns up to be a powerful calculation tool. By means of a special operating mode, Matbasic it is possible to use as the powerful calculator. Also the MatBasic can be used for educational purpose as a matter of studying the bases of programming and raising algorithmization skills.
Differential Equations is a handy application designed to help you solve equations with minimum effort. The program enables you to specify the coefficients by using the keyboard on the main window.It is designed to calculate the solution to homogeneous...
Linear Algebra Decoded is a program designed to assist students in the subject of Linear Algebra, although it has features for professors, including the ability to generate tests where problems are customized and solutions are in the field of integers....
This script defines the Matrix class, an implementation of a linear algebra matrix. Arithmetic operations, trace, determinant, and minors are defined for it. This is a lightweight alternative to a numerical Python package for people who need to do...
System of Equations is an educational software designed to provide teachers with an automated generator of equations for exams.The final quiz can be customized to include unique solutions (or no solutions at all), integer or fraction answers, custom...
Efficient Java Matrix Library or EJML is an Java based linear algebra library designed to help you with the manipulation of dense matrices. Its design goals are: to be as computationally efficient as possible for both small and large matrices and to beThe Bluebit .NET Matrix Library provides classes for object-oriented linear algebra in the .NET platform. It can be used to solve systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalues and...
Diofantos is a library for the solution of equations that arise in physics. It deals with ordinary differential equations (ODE), partial differential equations (PDE), including grid generation, and integral equations |
Discussing functions can be a tricky endeavor, but having a handy interactive way to talk about functions can relieve a great deal of stress. As part of the Mathematical Sciences Digital Library, this Functions Grapher...
The home of the World Wide Algebra project. This international megaproject has several principal parts, including Algebraic Cryptography, The World of Groups, and The World of Polynomials. These include lists of open...
Grace plotting software with convenient graphical interface and publication quality output is available at this site for free download (under public license). The software was developed by the Plasma Laboratory of...
Designed as an educational reference for graduate and upper-level undergraduate students, this site confers information about computer animation techniques. The site's author, Dr. Richard Parent, Associate Professor of...
Trying to find patterns in numbers is one of the greatest challenges in mathematics. Some researchers make it their primary area of investigation, perhaps with entire projects devoted to developing algorithms for the... |
More About
This Textbook
Overview
Takes a unique approach by developing fluency in the abstract and symbolic language of algebra to ensure that readers learn, understand, and think mathematical thoughts. The goal of this book is to develop the readers' ability to read, write, think and do mathematics. The book emphasizes the appropriate and creative use of technology, but even more, the understanding of concepts and symbolism. Graphing Calculators are required. The usual topics required to prepare students for calculus are covered. However, the text is different because it identifies and emphasizes the concepts of algebra that will remain essential for students to grasp regardless of what present or future calculators can do. To this end, the symbolic language is explicitly studied because it is the way in which thoughts about algebraic processes are best expressed and remembered. Numerous specially designed examples and problems focus on key concepts. This unique approach improves: conceptualization and understanding; the rate of current and future mathematics learning; the ability to work with problems in which genuinely algebraic concepts are essential, such as word problems and retention |
Graphing
Author:
Unknown
ISBN-13:
9780768202335
ISBN:
0768202337
Publisher: Schaffer Publications, Frank
Summary: Help students succeed in math! Math Minders provide students with the self-confidence they need to succeed in math. Students learn one step at a time, reviewing skills learned in earlier grades, then moving to skills appropriate for their grade level. They progress gradually, giving them the constant feeling of success! Vocabulary is kept at a level appropriate for each grade level to help ensure success. Fun and sim...ple formats help maintain a high level of student interest. Perfect for home or school, or to reinforce any existing math program0768202337 Top of book wavy, as if was in humid environment, but no stains and covers are shiny and bright. Binding tight, pages crisp and clean. Some dents, light scuffs and [more]
0768202337 Top of book wavy, as if was in humid environment, but no stains and covers are shiny and bright. Binding tight, pages crisp and clean. Some dents, light scuffs and rubs. Minimal tip wear at corners.[less] |
Brand new. We distribute directly for the publisher. This thorough and detailed exposition is the result of an intensive month-long course sponsored by the Clay Mathematics ...Institute. It develops mirror symmetry from both mathematical and physical perspectives. The material will be particularly useful for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics.This one-of-a-kind volume offers the first comprehensive exposition on this increasingly active area of study. It is carefully written by leading experts who explain the main concepts without assuming too much prerequisite knowledge. The book is an excellent resource for graduate students and research mathematicians interested in mathematical and theoretical physics.This is an oversized or heavy book that requires additional postage for international delivery outside of Canada and the US. Read moreShow Less
More About
This Textbook
Overview
Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ''mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar Vafa invariants. This book aims to give a single, cohesive treatment of mirror symmetry from both the mathematical and physical viewpoint. Parts 1 and 2 develop the necessary mathematical and physical background ''from scratch,'' and are intended for readers trying to learn across disciplines. The treatment is focussed, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ''pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topics in mirror symmetry, including the role of D-branes in the context of mirror symmetry, and some of their applications in physics and mathematics: topological strings and large $N$ Chern-Simons theory; geometric engineering; mirror symmetry at higher genus; Gopakumar-Vafa invariants; and Kontsevich's formulation of the mirror phenomenon as an equivalence of categories. This book grew out of an intense, month-long course on mirror symmetry at Pine Manor College, sponsored by the Clay Mathematics Institute. The lecturers have tried to summarize this course in a coherent, unified |
Translation Of Geometric Figures Pdf
Math by Design Lesson Plan Transformations to describe this transformation lead a discussion about ways to describe the transformation of a figure encourage descriptions that include up down and right left Math by Design Lesson Plan Transformations
Mathematics Geomet and Spatial Sense - New Jersey new jersey mathematics curriculum framework standard 7 geometry and spatial sense 209 all students will develop spatial sense and an ability to use geometric Mathematics Geomet and Spatial Sense - New Jersey
Translation of terms used on the statewide mathematics translation of terms used on the statewide mathematics assessments spanish over english each year as oregon presents more mathematics items in Translation of terms used on the statewide mathematics
Geometry Curriculum Map Table of Contents Unit 1 Basic build on rigid motions as a familiar starting point for development of concept of geometric proof use the definition of congruence in terms of rigid motions to Geometry Curriculum Map Table of Contents Unit 1 Basic
Mathematics Standards of Learning for Virginia Public mathematics standards of learning for virginia public schools february 2009 4 11 the student will a investigate congruence of plane figures after geometric Mathematics Standards of Learning for Virginia Public
New Advances in Geometric Algebra - University of Cambridge 28 10 2003 geometric computation 2001 3 what is geometric algebra geometric algebra is a universal language for physics based on the mathematics of clifford New Advances in Geometric Algebra - University of Cambridge
Transformations in the Coordinate Plane - Gaston County 518 chapter 10 geometric figures computer graphicscomputer and video game programmers use transformations to create patterns and animations how can you use Transformations in the Coordinate Plane - Gaston County |
year students often use a functional language in their introductory programming classes today. Experiences gained in this way allows them to build mathematical concepts quickly and properly. On the other hand, modern algebra systems, such as MATLAB, accelerate advanced calculation and offer an excellent platform for experimentation, but they do not facilitate understanding of fundamental concepts. It is proposed to use jointly the functional approach and a modern algebra system (in this instance, the MATLAB software). This would reduce a danger of creating a clutter of unrelated procedures in place of a coherent system of concepts. |
Intermediate Algebra-Student Support Edition - 4th edition
Summary: Designed for first-year developmental math students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra owes its success to the hallmark features for which the Larson team is known: learning by example, accessible writing style, emphasis on visualization, and comprehensive exercise sets. These pedagogical features are carefully coordinated to ensure that students are better able to make connections between mathematical concepts and under...show morestand the content.
The new Student Support Edition continues the Larson tradition of guided learning by incorporating a comprehensive range of student success materials throughout the text. Additionally, instructors and students alike can track progress with HM Assess, a new online diagnostic assessment and remediation tool from Houghton Mifflin.
New! An extensive student support section, Your Guide to Success in Algebra, contains all the tools the student needs to succeed in the course. Your Guide to Academic Success includes a review of math study skills, learning styles, test-taking strategies, time management tips, unique study strategies, course progress tracker, and comprehensive guides to using the textbook and study aids effectively. Your Guide to the Chapters includes progress trackers that outline each chapter's topics and learning objectives, along with a checklist of all the study aids available for that chapter.
New! HM Testing (Powered by Diploma) provides instructors with wide array of algorithmic test items, and improved functionality and ease of use, including the ability to author and edit algorithmic questions.
New! Eduspace Houghton Mifflin's Online Learning Tool (powered by Blackboard), now includes enhanced algorithmic exercises which are supported by a new math symbol palette for inputting free-response answers and are closely correlated to the end of section/chapter exercises. It also includes HM Assess, a new online diagnostic assessment and remediation program that tests the student's understanding of core concepts and develops individual study paths for self-remediation753524 Teacher Edition. Used texts may NOT contain supplemental materials such as CD00 +$3.99 s/h
VeryGood
Gab's Book Bag Books Mount Morris, MI
Jan 02, 2007 Very good Clean and crisp |
Designed to incorporate the power of a graphing calculator into the classroom, Discovering Algebra presents step-by-step keystroke instruction in a convenient, easy to follow format. This manual is intended as a supplement to any standard algebra text and provides beginners with the tools necessary to succeed in algebra without anxiety |
In some cases these chapters will be covered quite thoroughly and in
others
only selected topics will be discussed.
COURSE GRADE:
Two hour exams
25% of grade each
Quizzes and homework
20% of grade
Final exam
30% of grade
UNGRADED
HOMEWORK: Assignments from the textbook will be
made
for each class, which are not meant to be handed in. Working these
problems in a careful and timely manner is the most important way
you
have to learn the material. Click
here
to get
an up-to-date list of homework assignments. A little class
time will be taken from time to time to go over some of the
assigned homework. If
you want to request that a certain problem be discussed, let
me know ahead of time by
e-mail.
EXAMS:
These will take place
during the regular class period on October 2 and November 6
(both Wednesdays). Exam problems
will be
very similar to homework problems. I will clarify a week
or so ahead of time exactly what
topics will be covered on each exam. The final exam time will be posted
here as soon as it is available.
CALCULATORS:
Calculators
of four function, scientific, or graphing type are allowed,
but not required, on quizzes and exams unless
otherwise stated. You may not use a calculator
which is also a
communications device or which has a built in computer algebra system.
Calculators are meant as a convenience
for
the routine aspects of problem solving, but not as a replacement for
the understanding of the concepts and methods which make up this
course. As in any other mathematics course you should expect to have to
demonstrate your competence by showing your work on anything which gets
graded.
ELECTRONIC
DEVICES:
Cell phones and other communications devices should be turned off
during class time. In the event that a student needs to keep his/her
cell
phone on for an emergency, please notify the instructor before class.
During class time, laptop computers should only be used for class
appropriate purposes.
OTHER RESOURCES: Course information and
announcements can also be found via Blackboard
Learn where you can also keep track of your grades. Click here for Mathematics department syllabus and class policies, including policies about make-up exams.
If
a student has a disability that qualifies under the Americans with
Disabilities Act and Section 504 of the Rehabilitation Act and requires
accommodations, he/she should contact the Disability Resources (DR)
office for information on appropriate policies and procedures. DR is
located on the main floor of the Student Services Building, Room 1076;
their phone is 515-294-7220. |
fun and easy way to learn pre-calculus
Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations.
With this guide's help you'll quickly and painlessly get a handle on all of the concepts — not just the number crunching — and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for how these concepts are used in the real world, and find out that getting a decent grade in pre-calc isn't as impossible as you thought.
Updated with fresh example equations and detailed explanations
Tracks to a typical pre-calculus class
Serves as an excellent supplement to classroom learning
If "the fun and easy way to learn pre-calc" seems like a contradiction, get ready for a wealth of surprises in Pre-Calculus For Dummies! |
Problem Sets
All homework assignments are due on Thursday at 7pm. Except for
the first problem set, the solutions are to be submitted via the
hand-in server, for which you will get instructions in lab. The first
problem set is submitted on paper to Prof. Van Horn's office: 350 WVH.
All problem sets consist of two parts:
a set of finger exercises
a set of numbered problems.
Solve the finger exercises as you read the book. Solve as many as
you can. For some a paper-and-pencil solution is enough; for others, you
really want to open DrRacket and experiment/play. Feel free to discuss the
problems and the solutions with classmates.
You will not get a grade for the finger exercises. But, when you ask for
help with homework problems, we may ask you to solve one of these finger
exercises or explain its solution.
Of the numbered problems, we pick between one and three to grade on a
weekly basis. Which ones we will grade will be decided after you hand in
the solutions. |
Pre-Calculus: Exponents and Logarithms Help & Problems
Find study help on exponents and logarithms for pre-calculus. Use the links below to select the specific area of exponents and logarithms you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn exponents and logarithms for pre-calculus.
Introduction to Applications of Logarithm and Exponential Equations
Now that we can solve exponential and logarithmic equations, we can solve many applied problems. We will need the compound growth formula for an investment earning interest rate r , ...
Introduction to Finding the Growth Rate
We can find the growth rate of a population if we have reason to believe that it is growing exponentially and if we know the population level at two different times. We will use the first population level as n
Introduction to Radioactive Decay
Some radioactive substances decay at the rate of nearly 100% per year and others at nearly 0% per year. For this reason, we use the half-life of a radioactive substance to describe how fast its radioactivity decays. For ... |
Find a Richmond, CA Algebra 2This serves you better than merely answering the specific question or problem at hand. I work with you to develop the ability to understand and to define the immediate problem, to identify potential routes of solving the problem, to solve the problem itself, and then to critically evaluate the a... latter has problems taken from algebra 2 and some introductory trigonometry, which are subjects beyond algebra 1. Contents of CBEST include: arithmetic, algebra, geometry, and formulas. Actually problems in the "formulas" category are formulas taken from the previous three categories.
...It's a great tool and a big confidence booster when you can master this subject. The concepts behind Calculus are actually simple and few in number. But they are often introduced in ways that seem complex and confusing. |
Algebra 2 students are tasked with putting their previous knowledge to the test. This is where we first see conic sections, the unit circle, and roots of real and complex functions. Inverse functions are introduced as well. |
the right solution every time!
Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence. You'll understand how to factor fearlessly, conquer the quadratic formula, and solve linear equations.
Other titles by Sterling: Algebra II For Dummies and Algebra Workbook For Dummies
Whether you're currently enrolled in a high school or college algebra course or are just looking to brush-up your skills, Algebra I For Dummies, 2nd Edition gives you friendly and comprehensible guidance on this often difficult-to-grasp subject.
Mary Jane Sterling has been teaching algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook |
More About
This Textbook
Overview
In mathematics, "buildings" are geometric structures that represent groups of Lie type over an arbitrary field. This concept is critical to physicists and mathematicians working in discrete mathematics, simple groups, and algebraic group theory, to name just a few areas.
Almost twenty years after its original publication, Mark Ronan's Lectures on Buildings remains one of the best introductory texts on the subject. A thorough, concise introduction to mathematical buildings, it contains problem sets and an excellent bibliography that will prove invaluable to students new to the field. Lectures on Buildings will find a grateful audience among those doing research or teaching courses on Lie-type groups, on finite groups, or on discrete groups.
"Ronan's account of the classification of affine buildings [is] both interesting and stimulating, and his book is highly recommended to those who already have some knowledge and enthusiasm for the theory of buildings."—Bulletin of the London Mathematical |
Linear Equation Practice in Elementary Algebra, Grades 6-8
Overview
Practice solving linear equations with these fifty problems in elementary algebra. The student selects a single variable linear equation, solves for the variable, and checks the answer by viewing the step-by-step solution. Problems start with low diffic65842947
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The branch of mathematics that treats the relations and properties of quantity by means of letter and other symbols. It is applicable to those relations that are true of every kind of magnitude. Source: Websters Dictionary....hide
Education in a free society must prepare citizens to make informed choices in all areas of their lives. They must be able to grasp the information being presented, analyze it, and make reasoned decisions. To accomplish these goals, students learn to collect, organize, and display relevant data to answer questions that can be addressed with data; use appropriate statistical methods and predictions that are based on data; develop and evaluate inferences and predictions that are based on data; and apply basic concepts of probability. Probability is the study of chance and the possibility that an event will occur....hide
In earth and space science, students study the origin, structure, and physical phenomena of the earth and the universe. Earth and space science studies include concepts in geology, meteorology, oceanography, and astronomy....hide
Geometry is the branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles. It is the science of the relations of space. Sourse: Webster's Dictionary...hide
The life sciences investigate the diversity, complexity, and interconnectedness of life on earth. Students are naturally drawn to examine living things, and as they progress through the grade levels, they become capable of understanding the theories and models that scientists use to explain observations of nature....hide
Measurement is best learned through direct applications or as part of other mathematical topics. A measurable attribute of an object is a characteristic that is most readily quantified and compared. Many attributes, such as length, perimeter, area, volume, and angle measure, come from the geometric realm. Other attributes are physical, such as temperature and mass. Still other attributes, such as density, are not readily measurable by direct means....hide
The study of numbers and operations is the cornerstone of the mathematics curriculum. Learning what numbers mean, how they may be represented, relationships among them, and computations with them is central to developing number sense....hide
Physical science is the science of matter and energy and their interactions and examines the physical world around us. Using the methods of the physical sciences, students learn about the composition, structure, properties, and reactions of matter and the relationships between matter and energy. Students are best able to build understanding of the physical sciences through hands-on exploration of the physical world....hide
Problem solving is the thought processes involved in solving a problem. It is both a means of developing students' knowledge of mathematics and a critical outcome of a good mathematics education. A mathematical problem, as distinct from an exercise, requires the solver to search for a method for solving the problem rather than following a set procedure. Mathematical problem solving, therefore, requires an understanding of relevant concepts, procedures, and strategies. To become good problem solvers, students need many opportunities to formulate questions, model problem situations in a variety of ways, generalize mathematical relationships, and solve problems in both mathematical and everyday contexts....hide
From the early grades on, students develop their reasoning skills by making and testing mathematical conjectures, drawing logical conclusions, and justifying their thinking in developmentally appropriate ways. As they advance through the grades, students' arguments become more sophisticated and they are able to construct formal proofs. By doing so, students learn what mathematical reasoning entails....hide
The goal of engineering is to solve practical problems through the development or use of technologies. Technology/engineering works in conjunction with science to expand our capacity to understand the world....hide
Chemistry is the scientific study of matter and its interaction with other matter and with energy. It is the branch of natural science that deals with the composition of substances and their properties and reactions....hide
Physics is the scientific study of the basic principles of the universe, including matter, energy, motion and force, and their interactions. Major topics include classical mechanics, thermodynamics, light and optics, electromagnetism and relativity....hide
Computer science is the study of computational systems and their use in representing important problems in science and society. Major topics include computational science, software systems, network systems, theory of computation, machine learning, and human-computer interaction....hide |
Date of Examination
Time of Examination
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Quick Links
About Mathematics Association
The Mathematics Association of IIT Bombay was formed in 1978 as a student body organization aimed to bring about awareness, generate and promote interest,
and facilitate communication among students of various age groups with an interest in Mathematics. It has been very successful in identifying and nurturing
young talent in Mathematics. Targeted at motivating and encouraging student participation, this association aims to host activities at national level in the coming
years. The quickly growing popularity of the association is not only a success for the association but for Mathematics itself. The most important and widespread activity
of the Association is the Mathematics Olympiad, a mathematical talent search examination, conducted every year.
About Mathematics Olympiad
Mathematics Olympiad is a talent search event involving schools from Mumbai and nearby districts. The 1st Mathematics Olympiad was held in 1981.
This year the Mathematics Association is organizing the 33rd Mathematics Olympiad. This is a platform for students to challenge themselves and test their Mathematical knowledge and skills.
The goal of Mathematics Olympiad is to stimulate enthusiasm and love for mathematics, to strengthen mathematical intuition, foster mathematical creativity and provide satisfaction, joy and thrill of meeting challenges.
It is a great opportunity for the participating students to experience the atmosphere of IIT Bombay, which is one of the premium academic institutions of the country.
The Olympiad is overseen by some of the most renowned professors of the country, who are faculty at the Mathematics Department of IIT Bombay. |
Mathematics
"Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about ...Show synopsis"Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about specialized fields, they provide little help for the nonspecialist; and other books, some of them semipopular in nature, give an overview of mathematics while omitting some necessary details. "Fundamentals of Mathematics strikes a unique balance, presenting an irreproachable treatment of specialized fields and at the same time providing a very clear view of their interrelations, a feature of great value to students, instructors, and those who use mathematics in applied and scientific endeavors. Moreover, as noted in a review of the German edition in "Mathematical Reviews, the work is "designed to acquaint [the student] with modern viewpoints and developments. The articles are well illustrated and supplied with references to the literature, both current and 'classical.'"The outstanding pedagogical quality of this work was made possible only by the unique method by which it was written. There are, in general, two authors for each chapter: one a university researcher, the other a teacher of long experience in the German educational system. (In a few cases, more than two authors have collaborated.) And the whole book has been coordinated in repeated conferences, involving altogether about 150 authors and coordinators.Volume I opens with a section on mathematical foundations. It covers such topics as axiomatization, the concept of an algorithm, proofs, the theory of sets, the theory of relations, Boolean algebra, and antinomies. The closing section, on the real number system and algebra, takes up natural numbers, groups, linear algebra, polynomials,rings and ideals, the theory of numbers, algebraic extensions of a fields, complex numbers and quaternions, lattices, the theory of structure, and Zorn's lemma.Volume II begins with eight chapters on the foundations of geometry, followed by eight others on its analytic treatment. The latter include discussions of affine and Euclidean geometry, algebraic geometry, the Erlanger Program and higher geometry, group theory approaches, differential geometry, convex figures, and aspects of topology.Volume III, on analysis, covers convergence, functions, integral and measure, fundamental concepts of probability theory, alternating differential forms, complex numbers and variables, points at infinity, ordinary and partial differential equations, difference equations and definite integrals, functional analysis, real functions, and analytic number theory. An important concluding chapter examines "The Changing Structure of Modern MathematicsHardcover,
MIT,
1974
Description:First edition. Very good in very good dustwrapper. Vol. 3 only....First edition. Very good in very good dustwrapper. Vol. 3 only. Bottom edge of cover slightly rubbed. Dustwrapper shelf rubbed. Top edge of dustwrapper have minor tears. Small tear in middle of dustwrapper near spine. Foxing on dustwrapper spine.
Description:Good. Fundamentals of Mathematics, Vol. 1: Foundations of...Good. Fundamentals of Mathematics, Vol. 1: Foundations of Mathematics: The Real Number System and Algebra |
Student Resources
As noted in our mission statement, we are strongly committed to providing students with a solid and broad-based mathematical foundation that helps prepare them for a variety of careers as well as graduate study in mathematics and the mathematical sciences.
CSBSJU Mathematics Colloquium
The CSBSJU Mathematics Colloquium meets roughly every other Thursday. Here is a schedule for Spring 2014:
3/20: Professor Jennifer Galovich will speak on "The Secret Lives of Bacteria" at 2:40 pm in PENGL 229
Abstract: While you weren't looking, that E coli in your gut was doing amazing things! Some of which you can't do, like make tryptophan and some of which you can, like make lactose. Well, at least some of us can.
In this talk I will reveal the secret machinery (AKA gene regulatory networks AKA operons) that E coli uses, and describe mathematical models that predict the long term behavior of these cellular machines. There will be ZERO (count 'em) differential equations. However there will be surprising (perhaps) references to the content of Math 241 and 331!
This talk is also shameless promotion of the fall Topics course (Math 340) which will look at a variety of differential equation-free mathematical models of biological phenomena.
Abstract: A simple puzzle starts with 8 small cubes, each painted with one of four colors. The cubes are to be stacked into a bigger cube so that each face of the larger cube has all four colors. A natural generalization considers n³ cubes and n² colors. What happens when we also increase the number of dimensions?
Abstract: To "color" a graph, graph parts (vertices, edges, both, etc.) are partitioned into different colors. We will look at how some classical ideas from graph theory behave once a coloring is applied to the graph. (No prior knowledge of graph theory will be needed.) Along with the founding ideas and new avenues to pursue in this area, some results from CSBSJU students will also be presented.
Mathematical Competitions
Each year students from the College of Saint Benedict and Saint John's University participate in two mathematical competitions. Each November students may participate in the NCS/MAA team competition. This contest consists of ten problems, which are graded with a value of ten points per problem. The problems typically range in difficulty from fairly easy to extremely difficult. Students work in groups of three and submit their work as a team.
Every February students may particpate in the Mathematical Contest in Modeling or MCM. The MCM is a contest where teams of undergraduates use mathematical modeling to present their solutions to real world problems. Students in teams of three work on one problem over an entire weekend. Not only is their work graded on mathematical correctness, but also on clarity and ease of understanding. For additional information see the COMAP website.
Actuary
A good number of our students pursue a career as an Actuary, a person who calculates risk for insurance companies. For further information contact Phil Byrne or Kris Nairn.
Student Employment Opportunities
Students with an aptitude for mathematics have the option to work for the department as a course assisstant, teaching assistant and work in the Math Skills Center. This opportunity not only help students prepare for teaching mathematics in the secondary and college level, but also they get paid! For more information contact Phil Byrne.
Summer Experiences
Every summer the math department sponsers students to do summer research with an advisor. CSB/SJU also has a strong tradition of students particpating in Research Experiences for Undergraduates (REUs) around the country. For further information contact Bret Benesh and visit our page on summer research experiences. |
Find a Sunol Algebra 2However, commands such as Print and Open are now in the Backstage View instead of on the Microsoft Office Button. I tutored students in the use of Word in order to gain initial knowledge, use of information, content skills, and improve understanding / performance with the software. Prealgebra is the study of numbers, ratios and proportions, factoring, and fractions. |
Linear Algebra withKEY BENEFIT: This trusted reference offers an intellectually honest, thought-provoking, sound introduction to linear algebra.Enables readers to grasp the subject with a challenging, yet visually accessible approach that does not sacrifice mathematical integrity. Adds over 400 new exercises to the problem sets, ranging in difficulty from elementary to more challenging. Adds new historical problems taken from ancient Chinese, Indian, Arabic, and early European sources. Strengthens geometric and conceptual emphasis.A comprehensive, thorough reference for anyone who needs to brush up on their knowledge of linear algebra. |
The materials in this book lay a conceptual foundation for understanding mathematical ideas; promote reasoning and problem solving; and show contemporary applications of mathematics using contemporary methodologies.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
Product Description
About the Author
Don Cohen was born in Jersey City, N.J. He has a B.A. and M.A. from SUNY-Albany, NY and M.S.from RPI,in Troy, NY. He has taught all ages of students for 44 years, the last 22 of these as co-founder and teacher of The Math Program. After 7 years of teaching in a junior high school, he realized there must be a more enjoyable and effective way to teach math. He searched for alternatives. This led to designing new curriculum for N.Y. State; learning about mathematics and creativity from Bob Davis with The Madison Project; learning what real teaching is about by observing great teachers such as Sue Monell; teaching teachers; working on Plato (a computer-based education system at the U of I); all before Don and his partner invented The Math Program. These are the good old days! Don has three fine sons and six terrific grandchildren. He is a watercolor artist (see cover).Calculus as everyone should first come to know it!Sept. 3 1999
By A Customer - Published on Amazon.com
Format:Paperback
Calculus By and For Young People-- Worksheets by Don Cohen is a book of wonderfully visual worksheets which lead young people (and their parents ) into the joy and science that is math at its best. Somewhere between kindergarten and high school graduation the concept of math as a joyful, experimental science disappeared for most of us. The drudgery of repetitious arithmetic with right and wrong answers is NOT the approach taken in Cohen's book. My kids are primarily visual learners who do math in a non linear fashion and suffer with current school curriculum. The workbook's emphasis on ideas rather than methods has supported their learning style and increased their confidence. The author and the young students who work with him present calculus in a format which can be (and is) followed by seven year olds, yet is clear and appealing to all ages. The workbook has been designed by someone familiar with keen problem solvers, as well as math phobes, or those who have become math shy as a result of the standard right/wrong approach. Best of all parent input is rarely needed, (speaking of calculus phobes). Each page deals with options for solving involved calculus problems. You have to flip over the page to see the next step (which helps with my sons who are speed readers and often read the solution before mulling over the problem). All kinds of problem solving options are explored and discussed, with an emphasis on pattern recognition and visual and practical methods of examining calculus problems. Lots of examples share the ways other people solved the problem and explain why they tried what they did in a truly collaborative fashion. The book is designed to be used to work on observing (creating) and solving problems. It is not a text or a curriculum based book. It is a wonderful way to introduce any keen or math shy child to the joy of working on and solving what appear to be difficult problems using examples from real life. Despite the visual format there is a refreshing lack of cute characters or sugary language. You don't need to be a math whiz kid to use this book. Basic knowledge of math and a mind open to exploring are enough to get you in the door and down the path (solving common physical puzzles like the shuttle puzzle and the tower puzzle on your way). In a very nice touch, graph paper of different sizes useful for physically and visually working out the problems, is included in a format for copying at the back of the workbook. Highly recommended!
20 of 21 people found the following review helpful
5.0 out of 5 starsConstructing Calculus Concepts-a Method for all AgesJan. 27 1997
By A Customer - Published on Amazon.com
Format:Paperback
Sure, your children are doing great in elementary school, and that's probably due to the time you have taken to work with them...to prepare them for school. But do you ever wonder what will happen to that success later on when the concepts get tougher--like when they study calculus?
Your children CAN be ready for calculus--and Don Cohen's book, written for young people by young people, will prepare them. "Calculus By and for Young People" will empower your children to construct the conceptual associations necessary to understand calculus. It is as simple as that!
A specialist in Instructional Design and Psychology and a veteran, myself, of calculus training at Iowa State University of Science and Technology, I have used Don's book with learners age 8 through 72 (you are never too old) for three years now. Don's stuff is EXCITING! I give his books as Christmas presents to my favorite nieces and nephews. I take copies of the book on trips, and PLAY at math with the children at the homes I visit.
With Don as a guide and mentor, I love to play with mathematics. I have seen my students jump up in the air with glee when they solve one of Don't challenges--or giggle as they work at an assignment. I have a video tape of my students at work with Cohen's materials. Watching it always amazes me. This is education at its best.
Don Cohen and you. What a team, working together to help your children reach their potential in tomorrow's world.
P.S. Don't think this book is kid-stuff. Your high school student, or college student will benefit from Don's training as much as your younger child. Don't be surprised when your son or daughter confides: "I've been working on this calculus stuff all year, and getting A's, but I never really understood what it all meant, or what I was doing, until I worked through this book. Gee, thanks for helping me out."
13 of 13 people found the following review helpful
4.0 out of 5 starsConversations about math with kids...June 29 2005
By Stephen Armstrong - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
Don Cohen's book testifies to his love of math and kids. While other reviewers speak of how informative, diverse, and refreshing his book is, I want to make a few brief comments on materials required and what instruction for young children presumes. (1) Children will have to know about number lines, fractions-to-decimals, and will have to be curious. (2) This is definitely not a remedial book for the un-curious. (3) The methods in this book are really for small group tutorials. (4) This book requires that the teacher understand high school geometry and algebra. (5) It is very helpful to have graphing calculators or a computer that kids can use to write programs in BASIC. (6) Students will learn about (in no particular order) topics in measurement, number theory and number patterns, algebraic thinking, geometric reasoning, and a little bit about graph theory. These materials are not simply about calculus.
Some of the more powerful things that children will learn are: (1) indexing of numbers; (2) fractions; (3) programming in BASIC; (4) iteration; (5) exponents, and e; (6) ratios (such as t he golden ratio, etc.). I had the hardest time with (7) continuing fractions, which are rarely taught these days and which, to me, are not intuitive.
Perhaps the word "intuitive" sums up Cohen's approach: his skills at math are sufficient enough that he can see connections and help youngsters intuit connections, which are then their "discoveries." He does not mind youngsters making mistakes, and he believes in constructionist math.
I used Cohen's materials in a summer program with first graders, to solve Zero's Paradox, which, in calculus terms is: What is the limit of the sum of (1/2)^nth power? It took five weeks of daily discussion to help them learn about fractions, adding fractions, fractions less than one, graphing the sum, and understanding the idea of when "close enough" is a "good enough" limit. We had a great time and the youngsters enjoyed the project.
10 of 12 people found the following review helpful
5.0 out of 5 starsThe ONLY text for EVERYONE to learn calculus!Aug. 19 1999
By Lori Johnson - Published on Amazon.com
Format:Paperback
I had been searching for years for a text that would enable me to teach myself calculus. So when I found Don's book I couldn't believe my eyes. I had always done very well in mathematics but there were always missing pieces: Don's book filled those gaps. I devoured the worksheet book with the excitement of a child. The puzzles are engaging, dare I say fun, never monotonous. I especially love the way Don relates the questions and exercises to everyday things: sunflowers, shells, spaghetti, why mice are nocturnal, etc. The book answers the questions WHY and HOW. I understand the college texts better and I believe I scored in the 95th percentile and up ONLY with the help of Don's book. It should be everyone's FIRST math book! As a math tutor my proficiency and my mathematical creativity have grown, it seems without bound, for Don's book makes new ideas flow out of my head! I conducted my first workshops this summer. One mom couldn't believe that the 7-10 year olds worked on infinite series and sums (CH 1&2), Fibonacci numbers (CH 7), and basic integrals (CH 13). Their level of understanding amazed even me! When asked if they wanted to have individual sessions after the workshop several children jumped up and down saying, "Yeah, yeah, yeah!!!" Parents get this book for your children AND yourselves. If you love math, get this book. If you hate, are afraid of or intimidated by math, DEFINITELY GET THIS BOOK! Go at your own pace and you will overcome your fears. Share what you learn with everyone you know. I believe only with this book will you begin to increase your confidence in all things mathematical and be enriched for a lifetime.
2 of 3 people found the following review helpful
3.0 out of 5 starsUnrealisticOct. 4 2013
By Elizabeth - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
I'm a math teacher and I have my own tutoring company. I've wanted to buy this book for a LONG time because I was so curious - how could a 7 year old do calculus?! I'm always searching for material that engages my really advanced young students (late elementary and middle school). I want to give them material that is a challenging version of whatever they're learning in school, instead of constantly moving them on to the next level of math. I thought this book would offer just that.
The two chapters could be done by a very motivated, intelligent 7 year old. Of those motivated, intelligent 7 year olds, few would be able to see the point that Don Cohen is trying to make. Few students this age know multiplication and fractions, though! More ideally, the first two chapters could reasonably be done by an intelligent, above-average 5th grader.
Chapter 3 and above, though? Some of the material is suitable for middle school students, some of it is just too abstract.
This book is designed for students who are seriously intrigued by math. I've worked with very advanced students, and this is still beyond most of them.
I also got this booked used for $19. I can't believe it's $150+. Trust me - get a used version! I thought this would be a mind-blowing math breakthrough. It's a more interesting read for math nerds like me who have already been through calculus. |
Calculus for the Utterly Confused - 2nd edition
Summary: 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 into easy-to-understand chunks.
Calculus for the Utterly Confused shows you how to apply calculus concepts to p...show moreroblems in business, medicine, sociology, physics, and environmental science. You'll get on the road to higher grades and greater confidence, and go from utterly confused to totally prepared in no time!
Inside, you'll learn about
Calculus problems with applications to business and economics
How to use spreadsheets for business analysis
Growth and decay models including exponential and logarithmic models for biology |
More About
This Textbook
Overview
Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail.
* This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory
* Includes a concise and self contained introduction to differential equations
* Easy to follow and comprehensive introduction to Lie group analysis
* The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural |
Basic Engineering Mathematics
Synopses & Reviews
Publisher Comments: level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, especially for those who find the theoretical side of mathematics difficult.
Now in its fifth edition, Basic Engineering Mathematics is an established textbook, with the previous edition selling nearly 7500 copies. All students that require a fundamental knowledge of mathematics for engineering will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering, the Diploma, and the BTEC First specifications. Level 3 students will also find this text to be a useful resource for getting to grips with essential mathematics concepts, because the compulsory topics in BTEC National and A Level Engineering courses are also addressed.
• Numerous worked examples supported by 600 worked problems and 1050 further problems within exercises included throughout the text. Additionally, there are 15 assignments included at regular intervals.
• Free instructor's manual available for download, which includes solutions to assignments.
AboutRoyal Naval School of Marine Engineering, HMS Sultan, Gosport; formerly University of Portsmouth and Highbury College, UK |
$100Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.
Contains 300 exercises to help readers master new material
Numerous illustrations, many in color, assist in visualizing geometric concepts and highlight the results of computer simulations
Covers applications to topics of current physical and astrophysical significance
Reviews & endorsements
Pre-publication Praise:"Over the last five years, there have been impressive advances in numerical relativity. It has now become a central area in the fast growing field of gravitational wave physics. These tools have played an important role also in the theory of critical phenomena associated with gravitational collapse, loop quantum cosmology and the discussion of quantum black holes and black branes. The book by Baumgarte and Shapiro provides an excellent introduction to the subject covering both, mathematical aspects and numerical techniques. The authors are world leaders in numerical relativity and their contributions have shaped neutron star simulations, the new frontier of this field. This book will soon become the standard advanced text for younger researchers entering the field and will also serve as the authoritative reference for senior researchers in numerical relativity and neighboring fields."
Abhay Ashtekhar, Director, Institute for Gravitation and the Cosmos, The Pennsylvania State University
Pre-publication Praise:"Numerical relativity has come of age with a number of recent breakthroughs. Two leading experts give a lucid as well as richly detailed account building a bridge from the basics to current research -- highly recommended."
Bernd Brügmann, Friedrich-Schiller-Universität
Pre-publication Praise:"Numerical relativity has come of age in the last few years, and Baumgarte and Shapiro have produced the first textbook on the subject. And what a book this is! Sufficiently complete to be an encyclopedia, yet accessible enough to be a genuine learning manual, the book is exceedingly well written. It covers virtually all aspects of numerical relativity, from formalism to the most modern application, and it is replete with beautiful and helpful diagrams. The book will serve as a useful reference to the researcher, and a source of enlightenment to many a student."
Eric Poisson, University of Guelph
Pre-publication Praise:"Quiescent black holes are well understood, but until recently nobody could calculate how they behave when they collide with each other, or are in the process of formation. Recent breakthroughs make such computations possible -- an advance that is crucially important for understanding galactic nuclei and gravitational waves. Baumgarte and Shapiro are established leaders in this subject. Their book is a timely contribution to the literature, and the ideal primer for researchers newly attracted to the burgeoning field of computational relativity."
Martin Rees, Astronomer Royal and Master of Trinity College, Cambridge
"This is an extraordinary, big, dense book. It captures much of the recent advance in computational modeling of gravitational systems via Einstein's description of gravity (General Relativity [1]) which subsumes Special Relativity [2] (high velocity systems with no gravity)... No book can cover all aspects of any modern field, and the experience of the authors is visible in the subjects they present. But this book is satisfyingly thorough on what it covers. If you want to understand how the merger of compact astrophysical objects (e.g. spinning black holes) is modeled
and what signal the produced waveform will create in a gravitational wave detector, this book is essential. There is none other like it."
Richard Matzner, Computers in Science and Engineering
"It is difficult to imagine that a book covering a field at the intersection of multiple disciplines could please all possible audiences. Nonetheless, Numerical Relativity hits the mark in its comprehensive coverage; it will be useful to practitioners in the field and especially graduate students wishing to join them in this active and exciting area of research."
Jorge Pullin, Louisiana State University, Baton Rouge for Physics Today
"Numerical Relativity is a comprehensive introduction to the numerical solution of the equations of general relativity. Numerical Relativity will be widely used as a handbook for those entering the field, as a reference for active investigators, and as a source for scholars in related fields. Libraries at any institution with an active research program in astrophysics or general relativity should have a copy. Scientists working in numerical relativity will want their own copies."
M.C. Ogilvie, Choice Magazine
"Numerical Relativity hits the mark in its quite comprehensive coverage; it will be useful to practitioners in the field and especially to graduate students wishing to join them in this active and exciting area of research."
Jorge Pullin, Physics Today
"This book provides a comprehensive reference on numerical relativity by familiarizing its readers with the fundamental concepts of general relativity and relevant numerical methods, with a view toward the most important applications. The authors recommend their book to students and researchers with a solid background in the basic theory of general relativity. However, based on the systematic organization of the book and its clear and adequate content, it could also be useful to those in other disciplines with related skills."
Hamid R. Noori, Computing Reviews
Look Inside
Authors
Thomas W. Baumgarte, Bowdoin College, Maine Thomas W. Baumgarte is a Professor of Physics at Bowdoin College, and an Adjunct Professor of Physics at the University of Illinois at Urbana-Champaign. He received his Diploma (1993) and Doctorate (1995) from Ludwig-Maximilians-Universität, München, and held postdoctoral positions at Cornell University and the University of Illinois before joining the faculty at Bowdoin College. He is a recipient of a John Simon Guggenheim Memorial Foundation Fellowship. He has written over 65 research articles on a variety of topics in general relativity and relativistic astrophysics, including black holes and neutron stars, gravitational collapse, and more formal mathematical issues.
Stuart L. Shapiro, University of Illinois, Urbana-Champaign Stuart L. Shapiro is a Professor of Physics and Astronomy at the University of Illinois at Urbana-Champaign. He received his A.B. from Harvard (1969) and his Ph.D. from Princeton (1973). He has published over 335 research articles spanning many topics in general relativity and theoretical astrophysics and co-authored the widely used textbook Black Holes, White Dwarfs and Neutron Stars; The Physics of Compact Objects (John Wiley, 1983). In addition to numerical relativity, Shapiro has worked on the physics and astrophysics of black holes and neutron stars, relativistic hydrodynamics, magnetohydrodynamics and stellar dynamics, and the generation of gravitational waves. He is a recipient of an IBM Supercomputing Award, a Forefronts of Large-Scale Computation Award, an Alfred P. Snow Research Fellowship, a John Simon Guggenheim Memorial Foundation Fellowship, and several teaching citations. He has served on the editorial boards of The Astrophysical Journal Letters and Classical and Quantum Gravity. He was elected Fellow of both the American Physical Society and Institute of Physics (UK |
The Basic Mathematics
portion of the M.S. in Ed is designed
to increase a teacher's knowledge
of mathematics as a preparation
for taking Basic Mathematics exam.
All classes are designed with
the practicing middle school teacher
in mind and feature hands-on and
active classroom experiences with
the appropriate use of technology
and mathematical models.
NOTE: Students pursuing a M.S. in Ed with a Mathematics endorsement
will take written comprehensive exams to finish the degree. There is no option for thesis or presentation.
Math
589: Algebraic
Structures for Middle School Teachers
The study of integers and algebraic
skills; solving linear and quadratic
equations, inequalities, functions,
graphing and complex numbers.
Connection of visual methods (using
Math in the Mind's Eye curriculum
and materials) to the NCTM standards
with extensive use of group activities
and hands-on models.
Math
591: Historical
Topics in Mathematics for Middle
School Teachers
A survey of the historical development
of topics in mathematics from
ancient to modern times, with
special emphasis on topics in
arithmetic, algebra and informal
geometry. Applications to middle
school mathematics.
Math
592: Abstract
Algebra for Middle School Teachers
An introduction to abstract
mathematics as a structured mathematical
systems. This course will explore
number sets and properties, and
beginning group theory with concrete
applications for the elementary
and middle school classroom.
Math 593:
Experimental Probability & Statistics
for Middle School Teachers
Advanced study of using basic
elements of probability and statistics
to solve problems involving the
organization, description and
interpretation of data. Concrete
application will be explored through
laboratory experiments, simulations
and computer programs suitable
for use in the middle school classroom.
Math
594: Geometry
for Middle School Teachers
Selected topics in informal geometry
through the use of discovery and
technology. Studies in how students
learn geometry will be used in
the development of geometric ideas.
Math 595:
Calculus Concepts for Middle School
Teachers
An introduction to the limit concept
and its role in defining the derivative,
the integral and infinite series.
Applications to middle school
mathematics.
Math
597: Discrete
Mathematics for Middle School
Teachers
In this course we will explore
the topics of logical operators
and sets, experimental vs. theoretical
probability, the multiplication
rule, permutations and combinations,
and an introduction to graph theory. |
Jobs
Mathematics AS
Introduction to course
Interested in Maths? It's a popular choice and useful for many degree and career choices but you must enjoy maths to consider taking it as one of your AS/A Level options. - you'll need to get a kick out of solving problems and enjoy a challenge. In the first year, you'll study two pure maths modules and decision maths, while in the second year topics include more pure maths and mechanics.
Course Details
You must enjoy Mathematics to consider it for an A Level subject; you should get a kick out of solving problems correctly and enjoy a challenge. In the first year, students study two Pure Maths modules (C1, C2) and Decision Maths (D1).
In the second year, you will study C3, C4 and Mechanics (M1). We follow the AQA syllabus.
Entry Requirements
In addition to the general entry requirements you will need at least a grade B in GCSE Maths.
This course combines well with
This course combines well with Economics and the Sciences. However, students studying Humanities and the Social Sciences are also well represented in Maths classes.
Course Assessment
3 x 1 and a half hour exams at AS
3 x 1 and a half hour exams at A2
Course Progression
Maths is essential if you want to study for a degree in Maths and is usually also a requirement for Physics, Engineering or Computing. It also provides useful support for further studies in Biology, Chemistry, Finance, Business, Economics and Social Sciences. An A and AS Level in Maths demonstrates that you have a level of numerical and problem solving skills which are well above average, making you particularly valued by employers and higher education establishments.
Links
mathscareers.org (an excellent site for researching careers in maths and lots of exciting examples of how maths can be used in the real world)
What help is available?
Clearly most of your learning will take place inside the classroom, but as well as excellent teaching we also provide
Timetabled workshops for students who need extra help
Drop-in workshops for all students
Up-to-date textbooks
A range of resources, web-links and all assessment materials available on the college intra-net (moodle)
A good range of additional textbooks in the library
Revision, study guides and graphical calculators for sale |
Prealgebra and Introductory Algebra (Paper) - 3rd edition
Summary: Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Prealgebra& Introductory Algebra, Third 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 successUsed - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000
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I tutor several people in a "Mathematics for the Social Sciences" course at a local university. This semester the material is focused on matrix algebra. For the most part, they have no trouble wrapping their heads around the notions of basic vector operations, row reduction, systems of equations, inverse matrices and determinants. But, they have a lot of problems with more abstract concepts such as linear independence, subspaces, basis and dimension. I'm wondering if anyone has any tips on helping them visualize and understand these ideas more clearly. posted by Proginoskes to Education (7 answers total) 8 users marked this as a favorite
The way I'd do it is with a 2-D example. Two arrows drawn on the board. If they point the same direction or exact opposite directions, they're not linearly independent and thus form a 1-D subspace. Otherwise, they're a basis for the whole board, because any point on the board can be expressed as a linear combination of the two. Then just talk through extending that to higher dimensions, if necessary. posted by wanderingmind at 7:43 PM on March 30, 2008
Demonstrate the abstract concepts using metaphors from computer graphics. posted by Blazecock Pileon at 7:44 PM on March 30, 2008
I'd say pictures help. vectors and a 3d cartesian plot. 2 vectors on the X-Y plane clearly cannot cover all of 3D space, but they can form a 2d subspace, etc etc. posted by Large Marge at 8:20 PM on March 30, 2008
You might try a little dip into color spaces and color theory (at the very shallow oversimplified end). They might intuitively believe that if you show them a color and ask them to mix red, yellow, and blue paints to match the color, that there will be just one correct recipe. And obviously if, instead of red, you gave them some other paint that was already a mixture of blue and yellow, well, that wouldn't do shit for them.
Of course this won't hold up if you go too far, but the point is to get away from the arrows and axes and mindless grinding out of matrix operations. Treat the coordinates as amounts of some concrete property and think up some goofy examples. Determinants are more abstract than basis and dimension! posted by fleacircus at 1:31 AM on March 31, 2008
This site is great for learning to visualize concepts in linear algebra. The only downside is that it uses somewhat non-standard terminology. posted by dfan at 7:27 AM on March 31, 2008 [1 favorite]
The most important (constructive) concept I think is the idea of basis elements. Once people get them intuitively at a gut level, criteria for bases (linear independence) can be formalized, and the importance is manifest. But the basis lets you describe your space (physical space, state space, personality space, analytical space, etc....), so if you're going to be talking about STUFF, you gotta understand your basis.
I'm with wanderingmind: 1D is boring, 2D is interesting and non-trivial, so I'd start there. Later 2D can be described as a subspace of 3D. The idea is to build people's intuition with something that is a real honest linear space, so I'd stay away from color mixing for a bit. Let people navigate physical space, which is what they've been doing all their lives, then you can give them other things to think about later. Here's a sketch off the top of my head of how I'd play with this given a TA section or 2.
First, orthogonal:
Everyone can navigate Manhattan, given directions, yeah? There are two nice basis vectors (North and East), that I think everyone gets. People can see that there's no way you can describe east in terms of north (without rotation), and vice versa, but with both you can describe every cardinal direction, in a way you couldn't if all you had was a "West arrow" and an "East arrow". There's loads of examples in Real City Life you can use to discuss normalization, superposition, all applied linear algebra fun. So you can play with different representations using orthogonal 2-d basis.
Then, linear independence:
Can you get everywhere if someone gives you NEE and East? Sure, all you need is a little of the north, and you can still get everywhere. Important bit is the spanning of the space.
But what about getting to the 21st floor? We need a new linearly independent vector to get to 3D (2D was a subspace etc). If these were entry-physicists, this would be the time to introduce the Minkowski metric, and Time for 4D, social scientists should know this too, but you might have a rebellion on your hands.
So after people have this language for talking about physical space, let them relax and encourage them to start thinking about everything in terms of spanning basis (personality === Cambell's archetypes. taste === salty, sweet, etc. fashion, music, ..., everything you can describe you can whip up some sort of basis for, although for some things (functions of real variables, eg.) you need infinite bases). Some of these things don't really encourage the analogy of linear superposition, some do, and it's valuable for scientists (even the social kind) to learn the boundaries of the language their using.
I think that there are very few concepts in elementary linear algebra that can't be visualized in two or three dimensions.
linear independence, subspaces, basis and dimension
Draw R^2. Two vectors are linearly independent if they point in different directions. A subspace is any line through the origin. A basis for that subspace is any nonzero vector pointing in the direction of that line. Maybe move to R^3 to illustrate the difference between subspaces of dimension 1 and 2. |
Prerequisite: MATH 099 or Level II placement on the Basic Math Skills Inventory or permission of the instructor. Open to early childhood and elementary/special education majors with sophomore standing; open to others with permission of the instructor. Not intended for first-year students. Credit by exam. (First semester/3 credits)
An introduction to mathematical concepts, their understanding and communication.Topics include place value, multidigit calculations, the properties of integers and rationals, representing and justifying arithmetic claims, the power of algebraic notation, the field axioms of the real numbers and representing functions by graphs, tables and formulas. Emphasis is on developing a deep understanding of the fundamental ideas of elementary school mathematics. An integrated mathematics laboratory approach will be used, including the use of appropriate technology |
Precalculus Mathematics for Calculus - 6th edition
Summary: This bestselling 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, the book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop i...show morensight 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 leaderL
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Highlights of Calculus - MIT OpenCourseWare Highlights of Calculus is a series of videos that introduce the fundamental concepts of calculus to both high school and college students. Renowned mathematics professor, GilbertStrang, will guide students through a number of calculus topics to help them understand why calculus is relevant and important to understand. View the complete course at: License: Creative Commons BY-NC-SA More information at More courses at Keywords:Gilbert Strang; Calculus; Highlights; Fundamentals Downloads: 53,584 (1 review) |
modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. It covers topics including tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory.Read more... |
To begin the exploration of what algebraic thinking looks like in a classroom at your grade level, watch a video segment of a teacher who has taken the "Patterns, Functions, and Algebra" course and has adapted the mathematics to her own teaching situation. When viewing the video, keep the following three questions in mind:
Note 2
a.
What fundamental algebraic ideas (content) is the teacher trying to teach? Think back to the big ideas of the previous sessions: patterns, functions, linearity, proportional reasoning, nonlinear functions, and algebraic structure.
b.
What mathematical thinking tools (process) does the teacher expect students to demonstrate? Think back to the processes you identified in the first session: problem solving skills, representation skills, and reasoning skills.
c.
How do students demonstrate their knowledge of the intended content? What does the teacher do to elicit student thinking?
Video Segment In this video segment, Lolita Mattos introduces her students to the process of backtracking. She begins by giving her students an algorithm. She then asks them to undo the algorithm by reversing operations.
You can find this segment on the session video, approximately 46 minutes and 3 seconds after the Annenberg Media logo. |
These video lectures of Professor Gilbert Strang teaching 18.06 were recorded in Fall 1999 and do not correspond precisely to the current edition of the textbook. However, this book is still the best reference for more information on the topics covered in each lecture.
Related Resources
We've reached twelve lectures. And this one is more than the others about applications of linear algebra.
And I'll confess. When I'm giving you examples of the null space and the row space, I create a little matrix. You probably see that I just invent that matrix as I'm going.
And I feel a little guilty about it, because the truth is that real linear algebra uses matrices that come from somewhere. They're not just, like, randomly invented by the instructor.
They come from applications. They have a definite structure.
And anybody who works with them gets, uses that structure.
I'll just report, like, this weekend I was at an event with chemistry professors. OK, those guys are row reducing matrices, and what matrices are they working with? Well, their little matrices tell them how much of each element goes into the -- or each molecule, how many molecules of each go into a reaction and what comes out.
And by row reduction they get a clearer picture of a complicated reaction. And this weekend I'm going to -- to a sort of birthday party at Mathworks. So Mathworks is out Route 9 in Natick.
That's where Matlab is created. It's a very, very successful, software, tremendously successful. And the conference will be about how linear algebra is used. And so I feel better today to talk about what I think is the most important model in applied math.
And the discrete version is a graph. So can I draw a graph? Write down the matrix that's associated with it, and that's a great source of matrices. You'll see. So a graph is just, so a graph -- to repeat -- has nodes and edges. OK.
And I'm going to write down the graph, a graph, so I'm just creating a small graph here.
As I mentioned last time, we would be very interested in the graph of all, websites.
Or the graph of all telephones. I mean -- or the graph of all people in the world. Here let me take just, maybe nodes one two three -- well, I better put in an -- I'll put in that edge and maybe an edge to, to a node four, and another edge to node four. How's that? So there's a graph with four nodes.
So n will be four in my -- n equal four nodes.
And the matrix will have m equal the number -- there'll be a row for every edge, so I've got one two three four five edges. So that will be the number of rows. And I have to to write down the matrix that I want to, I want to study, I need to give a direction to every edge, so I know a plus and a minus direction. So I'll just do that with an arrow. Say from one to two, one to three, two to three, one to four, three to four.
That just tells me, if I have current flowing on these edges then I know whether it's -- to count it as positive or negative according as whether it's with the arrow or against the arrow. But I just drew those arrows arbitrarily. OK.
Because I -- my example is going to come -- the example I'll -- the words that I will use will be words like potential, potential difference, currents. In other words, I'm thinking of an electrical network.
But that's just one possibility.
My applied math class builds on this example.
It could be a hydraulic network, so we could be doing, flow of water, flow of oil.
Other examples, this could be a structure.
Like the -- a design for a bridge or a design for a Buckminster Fuller dome. Or many other possibilities, so many. So l- but let's take potentials and currents as, as a basic example, and let me create the matrix that tells you exactly what the graph tells you. So now I'll call it the incidence matrix, incidence matrix. OK. So let me write it down, and you'll see, what its properties are.
So every row corresponds to an edge.
I have five rows from five edges, and let me write down again what this graph looks like.
OK, the first edge, edge one, goes from node one to two. So I'm going to put in a minus one and a plus one in th- this corresponds to node one two three and four, the four columns. The five rows correspond -- the first row corresponds to edge one. Edge one leaves node one and goes into node two, and that -- and it doesn't touch three and four.
Edge two, edge two goes -- oh, I haven't numbered these edges.
I just figured that was probably edge one, but I didn't say so. Let me take that to be edge one. Let me take this to be edge two. Let me take this to be edge three. This is edge four. Ho, I'm discovering -- no, wait a minute.
Did I number that twice? Here's edge four. And here's edge five. OK? All right. So, so edge one, as I said, goes from node one to two.
Edge two goes from two to three, node two to three, so minus one and one in the second and third columns.
Edge three goes from one to three.
I'm, I'm tempted to stop for a moment with those three edges.
Edges one two three, those form what would we, what do you call the, the little, the little, the subgraph formed by edges one, two, and three? That's a loop. And the number of loops and the position of the loops will be crucial.
OK. Actually, here's a interesting point about loops. If I look at those rows, corresponding to edges one two three, and these guys made a loop. You want to tell me -- if I just looked at that much of the matrix it would be natural for me to ask, are those rows independent? Are the rows independent? And can you tell from looking at that if they are or are not independent? Do you see a, a relation between those three rows? Yes.
If I add that row to that row, I get this row.
So, so that's like a hint here that loops correspond to dependent, linearly dependent column -- linearly dependent rows. OK, let me complete the incidence matrix. Number four, edge four is going from node one to node four.
And the fifth edge is going from node three to node four.
OK. There's my matrix.
It came from the five edges and the four nodes.
And if I had a big graph, I'd have a big matrix.
And what questions do I ask about matrices? Can I ask -- here's the review now.
There's a matrix that comes from somewhere.
If, if it was a big graph, it would be a large matrix, but a lot of zeros, right? Because every row only has two non-zeros.
So the number of -- it's a very sparse matrix.
The number of non-zeros is exactly two times five, it's two m. Every row only has two non-zeros. And that's with a lot of structure. And -- that was the point I wanted to begin with, that graphs, that real graphs from real -- real matrices from genuine problems have structure. OK.
We can ask, and because of the structure, we can answer, the, the main questions about matrices.
So first question, what about the null space? So what I asking if I ask you for the null space of that matrix? I'm asking you if I'm looking at the columns of the matrix, four columns, and I'm asking you, are those columns independent? If the columns are independent, then what's in the null space? Only the zero vector, right? The null space contains -- tells us what combinations of the columns -- it tells us how to combine columns to get zero.
Can -- and is there anything in the null space of this matrix other than just the zero vector? In other words, are those four columns independent or dependent? OK. That's our question.
Let me, I don't know if you see the answer.
Whether there's -- so let's see.
I guess we could do it properly. We could solve Ax=0. So let me solve Ax=0 to find the null space. OK.
Ax now is that matrix times x. And what do I get for Ax? If the camera can keep that matrix multiplication there, I'll put the answer here. Ax equal -- what's the first component of Ax? Can you take that first row, minus one one zero zero, and multiply by the x, and of course you get x2-x1. The second row, I get x3-x2. From the third row, I get x3-x1. From the fourth row, I get x4-x1. And from the fifth row, I get x4-x3. And I want to know when is the thing zero. This is my equation, Ax=0. Notice what that matrix A is doing, what we've created a matrix that computes the differences across every edge, the differences in potential.
Let me even begin to give this interpretation.
I'm going to think of this vector x, which is x1 x2 x3 x4, as the potentials at the nodes. So I'm introducing a word, potentials at the nodes. And now if I multiply by A, I get these -- I get these five components, x2-x1, et cetera. And what are they? They're potential differences. That's what A computes.
If I have potentials at the nodes and I multiply by A, it gives me the potential differences, the differences in potential, across the edges. OK.
When are those differences all zero? So I'm looking for the null space.
Of course, if all the (x)s are zero then I get zero.
That, that just tells me, of course, the zero vector is in the null space. But w- there's more in the null space. Those columns are -- of A are dependent, right -- because I can find solutions to that equation. Tell me -- the null space.
Tell me one vector in the null space, so tell me an x, it's got four components, and it makes that thing zero.
So what's a good x to do that? One one one one, constant potential. If the potentials are constant, then all the potential differences are zero, and that x is in the null space.
What else is in the null space? If it -- yeah, let me ask you just always, give me a basis for the null space. A basis for the null space will be just that.1 That's --, that's it.
That's a basis for the null space.
The null space is actually one dimensional, and it's the line of all vectors through that one. So there's a basis for it, and here is the whole null space.
Any multiple of one one one one, it's the whole line in four dimensional space. Do you see that that's the null space? So the, so the dimension of the null space of A is one. And there's a basis for it, and there's everything that's in it.
Good. And what does that mean physically? I mean, what does that mean in the application? That guy in the null space.
It means that the potentials can only be determined up to a constant. Potential differences are what make current flow. That's what makes things happen. It's these potential differences that will make something move in the, in our network, between x2- between node two and node one. Nothing will move if all potentials are the same. If all potentials are c, c, c, and c, then nothing will move. So we're, we have this one parameter, this arbitrary constant that raises or drops all the potentials.
It's like ranking football teams, whatever.
We have a, there's a, there's a constant -- or looking at temperatures, you know, there's a flow of heat from higher temperature to lower temperature. If temperatures are equal there's no flow, and therefore we can measure -- we can measure temperatures by, Celsius or we can start at absolute zero.
And that arbitrary -- it's the same arbitrary constant that, that was there in calculus. In calculus, right, when you took the integral, the indefinite integral, there was a plus c, and you had to set a starting point to know what that c was. So here what often happens is we fix one of the potentials, like the last one.
So a typical thing would be to ground that node.
To set its potential at zero. And if we do that, if we fix that potential so it's not unknown anymore, then that column disappears and we have three columns, and those three columns are independent.
So I'll leave the column in there, but we'll remember that grounding a node is the way to get it out.
And grounding a node is the way to -- setting a node -- setting a potential to zero tells us the, the base for all potentials. Then we can compute the others. OK. But what's the -- now I've talked enough to ask what the rank of the matrix is? What's the rank then? The rank of the matrix.
So we have a five by four matrix.
We've located its null space, one dimensional.
How many independent columns do we have? What's the rank? It's three.
And the first three columns, or actually any three columns, will be independent. Any three potentials are independent, good variables. The fourth potential is not, we need to set, and typically we ground that node. OK.
Rank is three. Rank equals three.
OK. Let's see, do I want to ask you about the column space? The column space is all combinations of those columns. I could say more about it and I will. Let me go to the null space of A transpose, because the equation A transpose y equals zero is probably the most fundamental equation of applied mathematics. All right, let's talk about that. That deserves our attention. A transpose y equals zero. Let's -- let me put it on here. OK. So A transpose y equals zero.
So now I'm finding the null space of A transpose.
Oh, and if I ask you its dimension, you could tell me what it is. What's the dimension of the null space of A transpose? We now know enough to answer that question. What's the general formula for the dimension of the null space of A transpose? A transpose, let me even write out A transpose. This A transpose will be n by m, right? n by m.
In this case, it'll be four by five.
Those columns will become rows. Minus one zero minus one minus one zero is now the first row. The second row of the matrix, one minus one and three zeros. The third column now becomes the third row, zero one one zero minus one. And the fourth column becomes the fourth row.
OK, good. There's A transpose.
That multiplies y, y1 y2 y3 y4 and y5.
OK. Now you've had time to think about this question. What's the dimension of the null space, if I set all those -- wow.
Usually -- sometime during this semester, I'll drop one of these erasers behind there. That's a great moment.
There's no recovery. There's -- centuries of erasers are back there. OK. OK, what's the dimension of the null space? Give me the general formula first in terms of r and m and n.
This is like crucial, you -- we struggled to, to decide what dimension meant, and then we figured out what it equaled for an m by n matrix of rank r, and the answer was m-r, right? There are m=5 components, m=5 columns of A transpose. And r of those columns are pivot columns, because it'll have r pivots.
It has rank r. And m-r are the free ones now for A transpose, so that's five minus three, so that's two. And I would like to find this null space. I know its dimension.
Now I want to find out a basis for it.
And I want to understand what this equation is.
So let me say what A transpose y actually represents, why I'm interested in that equation.
So I'll call these -- these are currents on the edges, y1 y2 y3 y4 and y5. Those are currents on the edges. And this relation between current and potential difference is Ohm's Law.
This here is Ohm's Law. Ohm's Law says that the current on an edge is some number times the potential drop. That's -- and that number is the conductance of the edge, one over the resistance. This is the old current is, is, the relation of current, resistance, and change in potential. So it's a change in potential that makes some current happen, and it's Ohm's Law that says how much current happens. OK.
And then the final step of this framework is the equation A transpose y equals zero. And that's -- what is that saying? It has a famous name.
It's Kirchoff's Current Law, KCL, Kirchoff's Current Law, A transpose y equals zero. So that when I'm solving, and when I go back up with this blackboard and solve A transpose y equals zero, it's this pattern of -- that I want you to see. That we had rectangular matrices, but -- and real applications, but in those real applications comes A and A transpose.
So our four subspaces are exactly the right things to know about. All right.
Let's know about that null space of A transpose.
Wait a minute, where'd it go? There it is. OK.
OK. Null space of A transpose.
We know what its dimension should be.
Let's find out -- tell me a vector in it.
Tell me -- now, so what I asking you? I'm asking you for five currents that satisfy Kirchoff's Current Law. So we better understand what that law says. That, that law, A transpose y equals zero, what does that say, say in the first row of A transpose? That says -- the so the first row of A transpose says minus y1 minus y3 minus y4 is zero. Where did that equation come from? Let me -- I'll redraw the graph. Can I redraw the graph here, so that we -- maybe here, so that we see again -- there was node one, node two, node three, node four was off here. That was, that was our graph.
We had currents on those. We had a current y1 going there. We had a current y -- what were the other, what are those edge numbers? y4 here and y3 here. And then a y2 and a y5.
I'm, I'm just copying what was on the other board so it's ea- convenient to see it. What is this equation telling me, this first equation of Kirchoff's Current Law? What does that mean for that graph? Well, I see y1, y3, and y4 as the currents leaving node one. So sure enough, the first equation refers to node one, and what does it say? It says that the net flow is zero.
That, that equation A transpose y, Kirchoff's Current Law, is a balance equation, a conservation law.
Physicists, be overjoyed, right, by this stuff.
It, it says that in equals out. And in this case, the three arrows are all going out, so it says y1, y3, and y4 add to zero. Let's take the next one.
The second row is y1-y2, and that's all that's in that row. And that must have something to do with node two. And sure enough, it says y1=y2, current in equals current out. The third one, y2 plus y3 minus y5 equals zero. That certainly will be what's up at the third node. y2 coming in, y3 coming in, y5 going out has to balance.
And finally, y4 plus y5 equals zero says that at this node, y4 plus y5, the total flow, is zero. We don't -- you know, charge doesn't accumulate at the nodes.
It travels around. OK.
Now give me -- I come back now to the linear algebra question.
What's a vector y that solves these equations? Can I figure out what the null space is for this matrix, A transpose, by looking at the graph? I'm happy if I don't have to do elimination. I can do elimination, we know how to do, we know how to find the null space basis.
We can do elimination on this matrix, and we'll get it into a good reduced row echelon form, and the special solutions will pop right out. But I would like to -- even to do it without that. Let me just ask you first, if I did elimination on that, on that, matrix, what would the last row become? What would the last row -- if I do elimination on that matrix, the last row of R will be all zeros, right? Why? Because the rank is three. We only going to have three pivots. And the fourth row will be all zeros when we eliminate. So elimination will tell us what, what we spotted earlier, what's the null space -- all the, all the information, what are the dependencies. We'll find those by elimination, but here in a real example, we can find them by thinking.
OK. Again, my question is, what is a solution y? How could current travel around this network without collecting any charge at the nodes? Tell me a y. OK.
So a basis for the null space of A transpose.
How many vectors I looking for? Two.
It's a two dimensional space. My basis should have two vectors in it. Give me one.
One set of currents. Suppose, let me start it.
Let me start with y1 as one. OK.
So one unit of -- one amp travels on edge one with the arrow. OK, then what? What is y2? It's one also, right? And of course what you did was solve Kirchoff's Current Law quickly in the second equation.
What shall we do now? Well, what shall I take for y3 in other words? Oh, I've got a choice, but why not make it what you said, negative one.
So I have just sent current, one amp, around that loop.
What shall y4 and y5 be in this case? We could take them to be zero. This satisfies Kirchoff's Current Law. We could check it patiently, that minus y1 minus y3 gives zero.
We know y1 is y2. The others, y4 plus y5 is certainly zero. Any current around a loop satisfies -- satisfies the Current Law. OK. Now you know how to get another one. Take current around this loop. So now let y3 be one, y5 be one, and y4 be minus one.
And so, so we have the first basis vector sent current around that loop, the second basis vector sends current around that loop. And I've -- and those are independent, and I've got two solutions -- two vectors in the null space of A transpose, two solutions to Kirchoff's Current Law.
Of course you would say what about sending current around the big loop. What about that vector? One for y1, one for y2, nothing f- on y3, one for y5, and minus one for y4. What about that? Is that, is that in the null space of A transpose? Sure.
So why don't we now have a third vector in the basis? Because it's not independent, right? It's not independent. This vector is the sum of those two. If I send current around that and around that -- then on this edge y3 it's going to cancel out and I'll have altogether current around the whole, the outside loop. That's what this one is, but it's a combination of those two.
Do you see that I've now, I've identified the null space of A transpose -- but more than that, we've solved Kirchoff's Current Law.
And understood it in terms of the network.
OK. So that's the null space of A transpose. I guess I -- there's always one more space to ask you about. Let's see, I guess I need the row space of A, the column space of A transpose. So what's N, what's its dimension? Yup? What's the dimension of the row space of A? If I look at the original A, it had five rows.
How many were independent? Oh, I guess I'm asking you the rank again, right? And the answer is three, right? Three independent rows. When I transpose it, there's three independent columns. Are those columns independent, those three? The first three columns, are they the pivot columns of the matrix? No. Those three columns are not independent. There's a in fact, this tells me a relation between them. There's a vector in the null space that says the first column plus the second column equals the third column.
They're not independent because they come from a loop. So the pivot columns, the pivot columns of this matrix will be the first, the second, not the third, but the fourth. One, columns one, two, and four are OK. Where are they -- those are the columns of A transpose, those correspond to edges.
If I just look at the part of the graph that I've, that I've, thick -- used with thick edges, it has the same four nodes. It only has three edges.
And the, those edges correspond to the independent guys. And in the graph there -- those three edges have no loop, right? The independent ones are the ones that don't have a loop. All the -- dependencies came from loops. They were the things in the null space of A transpose. If I take three pivot columns, there are no dependencies among them, and they form a graph without a loop, and I just want to ask you what's the name for a graph without a loop? So a graph without a loop is -- has got not very many edges, right? I've got four nodes and it only has three edges, and if I put another edge in, I would have a loop. So it's this graph with no loops, and it's the one where the rows of A are independent.
And what's a graph called that has no loops? It's called a tree. So a tree is the name for a graph with no loops. And just to take one last step here. Using our formula for dimension. Using our formula for dimension, let's look -- once at this formula.
The dimension of the null space of A transpose is m-r.
OK. This is the number of loops, number of independent loops. m is the number of edges.
And what is r? What is r for our -- we'll have to remember way back. The rank came -- from looking at the columns of our matrix. So what's the rank? Let's just remember. Rank was -- you remember there was one -- we had a one dimensional -- rank was n minus one, that's what I'm struggling to say. Because there were n columns coming from the n nodes, so it's minus, the number of nodes minus one, because of that C, that one one one one vector in the null space.
The columns were not independent.
There was one dependency, so we needed n minus one.
This is a great formula. This is like the first shall I, -- write it slightly differently? The number of edges -- let me put things -- have I got it right? Number of edges is m, the number -- r- is m-r, OK. So, so I'm getting -- let me put the number of nodes on the other side. So I -- the number of nodes -- I'll move that to the other side -- minus the number of edges plus the number of loops is -- I have minus, minus one is one.
The number of nodes minus the number of edges plus the number of loops is one. These are like zero dimensional guys. They're the points on the graph. The edges are like one dimensional things, they're, they connect nodes. The loops are like two dimensional things. They have, like, an area. And this count works for every graph.
And it's known as Euler's Formula.
We see Euler again, that guy never stopped.
OK. And can we just check -- so what I saying? I'm saying that linear algebra proves Euler's Formula. Euler's Formula is this great topology fact about any graph. I'll draw, let me draw another graph, let me draw a graph with more edges and loops. Let me put in lots of -- OK. I just drew a graph there.
So what are the, what are the quantities in that formula? How many nodes have I got? Looks like five. How many edges have I got? One two three four five six seven.
How many loops have I got? One two three.
And Euler's right, I always get one.
That, this formula, is extremely useful in understanding the relation of these quantities -- the number of nodes, the number of edges, and the number of loops. OK.
Just complete this lecture by completing this picture, this cycle. So let me come to the -- so this expresses the equations of applied math. This, let me call these potential differences, say, E. So E is A x.
That's the equation for this step.
The currents come from the potential differences. y is C E. The potential -- the currents satisfy Kirchoff's Current Law. Those are the equations of -- with no source terms. Those are the equations of electrical circuits of many -- those are like the, the most basic three equations. Applied math comes in this structure. The only thing I haven't got yet in the picture is an outside source to make something happen.
I could add a current source here, I could, I could add external currents going in and out of nodes.
I could add batteries in the edges.
Those are two ways. If I add batteries in the edges, they, they come into here.
Let me add current sources. If I add current sources, those come in here. So there's a, there's where current sources go, because the F is a like a current coming from outside. So we have our edges, we have our graph, and then I send one amp into this node and out of this node -- and that gives me, a right-hand side in Kirchoff's Current Law. And can I -- to complete the lecture, I'm just going to put these three equations together.
So I start with x, my unknown.
I multiply by A. That gives me the potential differences. That was our matrix A that the whole thing started with. I multiply by C.
Those are the physical constants in Ohm's Law.
Now I have y. I multiply y by A transpose, and now I have F. So there is the whole thing.
There's the basic equation of applied math.
Coming from these three steps, in which the last step is this balance equation. There's always a balance equation to look for. These are the -- when I say the most basic equations of applied mathematics -- I should say, in equilibrium.
Time isn't in this problem. I'm not -- and Newton's Law isn't acting here. I'm, I'm looking at the -- equations when everything has settled down, how do the currents distribute in the network.
And of course there are big codes to solve the -- this is the basic problem of numerical linear algebra for systems of equations, because that's how they come. And my final question. What can you tell me about this matrix A transpose C A? Or even A transpose A? I'll just close with that question.
What do you know about the matrix A transpose A? It is always symmetric, right.
OK, thank. So I'll see you Wednesday for a full review of these chapters, and Friday you get to tell me |
Shows definite wear, and perhaps considerable marking on inside. Find out why millions of customers rave about Better World Books. Experience the best customer care and a 100% ...satisfaction guarantee.Read moreShow Less
Ships from: Mishawaka classic in the series of highly respected Swokowski/Cole mathematics texts retains the elements that have made it so popular with instructors and students alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. The goal of this text is to prepare students for further courses in mathematics. This book is set apart from the competition in a number of ways: it is mathematically sound, it focuses on preparing students for further courses in mathematics, and it has excellent problem sets. This edition has been improved in many respects. All of the chapters include numerous technology inserts with specific keystrokes for the TI-83 Plus and the TI-86, ideal for students who are working with a calculator for the first time. The new design of the text makes the technology inserts easily identifiable, so if a professor prefers to skip these sections it is simple to do |
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Overview
The History of Mathematics is a six-volume set that examines the development of the science through discovery, innovation, collaboration, and experimentation. Designed to complement mathematics curricula, each volume covers a significant development in recent mathematical history as well as the subject's origins. The books represent a fascinating overview of the contributions that mathematical research has made to the physical world.
Probability and Statistics, Revised Edition details the evolution of these two disciplines and their relevance to the scientific and lay communities. Probability and statistics are two of the youngest branches of mathematics, having been discovered in the 17th and 18th centuries, respectively, yet in modern-day language and thinking, they have become omnipresent. The book discusses how probability and statistics pervade our world, from the nature of randomness to the role of statistics in developing vaccines. It also includes an exclusive interview with Dr. Michael Stamatelatos, director of the safety and assurance requirements division in the Office of Safety and Mission Assurance at NASA, who suggests how the use of probability in risk assessments leads to improved safety and reliability in space exploration.
The volume includes information on
the bell curve
the birth of modern statistics
credit default swaps
data analysis and precision
Edmund Halley
randomness
smallpox and public health
vaccinations and statistics
The book contains 40 color photographs and four-color line illustrations, sidebars, a chronology, a glossary, a detailed list of print and Internet resources, and an index. The History of Mathematics is essential for high school students, teachers, and general readers who wish to understand the contributions of the major branches of |
Math 215
Analysis in a Single Variable
Aimed primarily at future math majors, this course covers calculus more thoroughly and more theoretically, giving an introduction to important mathematical techniques and results that give a foundation for further work in analysis. It serves as an introduction to the rigorous proofs and formal mathematical arguments needed in all upper division math courses.
EqualTopics: include the rigorous epsilon-delta treatment of limits, convergence, and uniform convergence of sequences and series, continuity, uniform continuity, and differentiability of functions, the Heine-Borel Theorem, the Rieman integral, conditions for integrability of a function and term by term differentiation and integration of series of functions, Taylor's Theorem.
Classes: are usually taught in a two sections in the fall semester and a single section in the spring semester. The two fall sections are closely coordinated, with the same problem sets and exams.
Alternatively, prospective math majors can take
214 for a more algebraic introduction to rigorous proofs and formal mathematical arguments in the context of classical number theory.
This course is usually followed by 217 (linear algebra) and then 218 (analysis in several variables).
Who Takes This Course?
Primarily incoming students who seriously consider majoring in math.
Students who are choosing between math and physics as a major should perhaps consider
203 instead.
Students who are choosing between math and computer science might consider
214 instead argument, separate from considerations of real-world applications or utility?
Typically students have a 5 on the BC calculus exam together with a math SAT score of at least 760.
A very solid knowledge of one-variable calculus is assumed, and this course will build on that knowledge to give you a much deeper understanding of the concepts and theorems you first saw in high school.
Sample Problems
A math major who took this course in the Fall of 2010 has prepared this list of Sample Problems designed to help you understand for yourself what 215 will be like. If these questions seem intriguing to you, then take the course to find the solutions! 214 |
Trigonometry FlexBook is an introduction to trigonometry for the high school student. Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex NumbersThis is a supplement to the author's Introduction to Real Analysis. It has been judged to meet the evaluation criteria set...
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'.'Introduction to Real Analysis: NOTE: This book meets the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. a parent struggling to help your child with geometry homework, this is a short book that will help you. It covers plane geometry and touches on beginning trigonometry. You will find 70 illustrations and 25 problems with detailed solutions. Whether you are new to geometry or just need to brush up on the things you learned in school, this is the book for you. Give your child the gift of learning along with you. This book can be useful for students as well. ' |
Visualizing Quaternions
Steve Cunningham
By
Andrew Hanson
Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions.
Audience Programmers and developers in computer graphics and the game industry, scientists and engineers working in aerospace and scientific visualization, students of game development and computer graphics, and those interested in quaternions but who have limited math background.
Reviews
"Almost all computer graphics practitioners have a good grasp of the 3D Cartesian space. However, in many graphics applications, orientations and rotations are equally important, and the concepts and tools related to rotations are less well-known. Quaternions are the key tool for understanding and manipulating orientations and rotations, and this book does a masterful job of making quaternions accessible. It excels not only in its scholarship, but also provides enough detailed figures and examples to expose the subtleties encountered when using quaternions. This is a book our field has needed for twenty years and I'm thrilled it is finally here." —Peter Shirley, Professor, University of Utah
"This book contains all that you would want to know about quaternions, including a great many things that you don't yet realize that you want to know!" —Alyn Rockwood, Vice President, ACM SIGGRAPH
"We need to use quaternions any time we have to interpolate orientations, for animating a camera move, simulating a rollercoaster ride, indicating fluid vorticity or displaying a folded protein, and it's all too easy to do it wrong. This book presents gently but deeply the relationship between orientations in 3D and the differential geometry of the three-sphere in 4D that we all need to understand to be proficient in modern science and engineering, and especially computer graphics." —John C. Hart, Associate Professor, Department of Computer Science, University of Illinois Urbana-Champaign, and Editor-in-Chief, ACM Transactions on Graphics
"Visualizing Quaternions is a comprehensive, yet superbly readable introduction to the concepts, mechanics, geometry, and graphical applications of Hamilton's lasting contribution to the mathematical description of the real world. To write effectively on this subject, an author has to be a mathematician, physicist and computer scientist; Hanson is all three. Still, the reader can afford to be much less learned since the patient and detailed explanations makes this book an easy read." —George K. Francis, Professor, Mathematics Department, University of Illinois at Urbana-Champaign
"The new book, Visualizing Quaternions, will be welcomed by the many fans of Andy Hanson's SIGGRAPH course." —Anselmo Lastra, University of North Carolina at Chapel Hill
"Andy Hanson's expository yet scholarly book is a stunning tour de force; it is both long overdue, and a splendid surprise! Quaternions have been a perennial source of confusion for the computer graphics community, which sorely needs this book. His enthusiasm for and deep knowledge of the subject shines through his exceptionally clear prose, as he weaves together a story encompassing branches of mathematics from group theory to differential geometry to Fourier analysis. Hanson leads the reader through the thicket of interlocking mathematical frameworks using visualization as the path, providing geometric interpretations of quaternion properties. The first part of the book features a lucid explanation of how quaternions work that is suitable for a broad audience, covering such fundamental application areas as handling camera trajectories or the rolling ball interaction model. The middle section will inform even a mathematically sophisticated audience, with careful development of the more subtle implications of quaternions that have often been misunderstood, and presentation of less obvious quaternion applications such as visualizing vector field streamlines or the motion envelope of the human shoulder joint. The book concludes with a bridge to the mathematics of higher dimensional analogues to quaternions, namely octonians and Clifford algebra, that is designed to be accessible to computer scientists as well as mathematicians." —Tamara Munzner, University of British Columbia
Contents
ABOUT THE AUTHOR
FOREWORD by Steve Cunningham
PREFACE
ACKNOWLEDGMENTS
PART I ELEMENTS OF QUATERNIONS
01 THE DISCOVERY OF QUATERNIONS
1.1 Hamilton's Walk
1.2 Then Came Octonions
1.3 The Quaternion Revival
02 FOLKLORE OF ROTATIONS
2.1 The Belt Trick
2.2 The Rolling Ball
2.3 The Apollo 10 Gimbal-lock Incident
2.4 3D Game Developer's Nightmare
2.5 The Urban Legend of the Upside-down F16
2.6 Quaternions to the Rescue
03 BASIC NOTATION
3.1 Vectors
3.2 Length of a Vector
3.3 3D Dot Product
3.4 3D Cross Product
3.5 Unit Vectors
3.6 Spheres
3.7 Matrices
3.8 Complex Numbers
04 WHAT ARE QUATERNIONS?
05 ROAD MAP TO QUATERNION VISUALIZATION
5.1 The Complex Number Connection
5.2 The Cornerstones of Quaternion Visualization
06 FUNDAMENTALS OF ROTATIONS
6.1 2D Rotations
6.1.1 Relation to Complex Numbers
6.1.2 The Half-angle Form
6.1.3 Complex Exponential Version
6.2 Quaternions and 3D Rotations
6.2.1 Construction
6.2.2 Quaternions and Half Angles
6.2.3 Double Values
6.3 Recovering Θ and n
6.4 Euler Angles and Quaternions
6.5 † Optional Remarks
6.5.1 † Connections to Group Theory
6.5.2 † "Pure" Quaternion Derivation
6.5.3 † Quaternion Exponential Version
6.6 Conclusion
07 VISUALIZING ALGEBRAIC STRUCTURE
7.1 Algebra of Complex Numbers
7.1.1 Complex Numbers
7.1.2 Abstract View of Complex Multiplication
7.1.3 Restriction to Unit-length Case
7.2 Quaternion Algebra
7.2.1 The Multiplication Rule
7.2.2 Scalar Product
7.2.3 Modulus of the Quaternion Product
7.2.4 Preservation of the Unit Quaternions
08 VISUALIZING SPHERES
8.1 2D: Visualizing an Edge-on Circle
8.1.1 Trigonometric Function Method
8.1.2 Complex Variable Method
8.1.3 Square Root Method
8.2 The Square Root Method
8.3 3D: Visualizing a Balloon
8.3.1 Trigonometric Function Method
8.3.2 Square Root Method
8.4 4D: Visualizing Quaternion Geometry on S3
8.4.1 Seeing the Parameters of a Single Quaternion
8.4.2 Hemispheres in S3
09 VISUALIZING LOGARITHMS AND EXPONENTIALS
9.1 Complex Numbers
9.2 Quaternions
10 VISUALIZING INTERPOLATION METHODS
10.1 Basics of Interpolation
10.1.1 Interpolation Issues
10.1.2 Gram-Schmidt Derivation of the SLERP
10.1.3 † Alternative Derivation
10.2 Quaternion Interpolation
10.3 Equivalent 3×3 Matrix Method
11 LOOKING AT ELEMENTARY QUATERNION FRAMES
11.1 A Single Quaternion Frame
11.2 Several Isolated Frames
11.3 A Rotating Frame Sequence
11.4 Synopsis
12 QUATERNIONS AND THE BELT TRICK: CONNECTING TO THE IDENTITY
12.1 Very Interesting, but Why?
12.1.1 The Intuitive Answer
12.1.2 † The Technical Answer
12.2 The Details
12.3 Frame-sequence Visualization Methods
12.3.1 One Rotation
12.3.2 Two Rotations
12.3.3 Synopsis
13 QUATERNIONS AND THE ROLLING BALL: EXPLOITING ORDER DEPENDENCE
13.1 Order Dependence
13.2 The Rolling Ball Controller
13.3 Rolling Ball Quaternions
13.4 † Commutators
13.5 Three Degrees of Freedom From Two
14 QUATERNIONS AND GIMBAL LOCK: LIMITING THE AVAILABLE SPACE
14.1 Guidance System Suspension
14.2 Mathematical Interpolation Singularities
14.3 Quaternion Viewpoint
PART II ADVANCED QUATERNION TOPICS
15 ALTERNATIVE WAYS OF WRITING QUATERNIONS
15.1 Hamilton's Generalization of Complex Numbers
15.2 Pauli Matrices
15.3 Other Matrix Forms
16 EFFICIENCY AND COMPLEXITY ISSUES
16.1 Extracting a Quaternion
16.1.1 Positive Trace R
16.1.2 Nonpositive Trace R
16.2 Efficiency of Vector Operations
17 ADVANCED SPHERE VISUALIZATION
17.1 Projective Method
17.1.1 The Circle S1
17.1.2 General SN Polar Projection
17.2 Distance-preserving Flattening Methods
17.2.1 Unroll-and-Flatten S1
17.2.2 S2 Flattened Equal-area Method
17.2.3 S3 Flattened Equal-volume Method
18 MORE ON LOGARITHMS AND EXPONENTIALS
18.1 2D Rotations
18.2 3D Rotations
18.3 Using Logarithms for Quaternion Calculus
18.4 Quaternion Interpolations Versus Log
19 TWO-DIMENSIONAL CURVES
19.1 Orientation Frames for 2D Space Curves
19.1.1 2D Rotation Matrices
19.1.2 The Frame Matrix in 2D
19.1.3 Frame Evolution in 2D
19.2 What Is a Map?
19.3 Tangent and Normal Maps
19.4 Square Root Form
19.4.1 Frame Evolution in (a, b)
19.4.2 Simplifying the Frame Equations
20 THREE-DIMENSIONAL CURVES
20.1 Introduction to 3D Space Curves
20.2 General Curve Framings in 3D
20.3 Tubing
20.4 Classical Frames
20.4.1 Frenet-Serret Frame
20.4.2 Parallel Transport Frame
20.4.3 Geodesic Reference Frame
20.4.4 General Frames
20.5 Mapping the Curvature and Torsion
20.6 Theory of Quaternion Frames
20.6.1 Generic Quaternion Frame Equations
20.6.2 Quaternion Frenet Frames
20.6.3 Quaternion Parallel Transport Frames
20.7 Assigning Smooth Quaternion Frames
20.7.1 Assigning Quaternions to Frenet Frames
20.7.2 Assigning Quaternions to Parallel Transport Frames
20.8 Examples: Torus Knot and Helix Quaternion Frames
20.9 Comparison of Quaternion Frame Curve Lengths
21 3D SURFACES
21.1 Introduction to 3D Surfaces
21.1.1 Classical Gauss Map
21.1.2 Surface Frame Evolution
21.1.3 Examples of Surface Framings
21.2 Quaternion Weingarten Equations
21.2.1 Quaternion Frame Equations
21.2.2 Quaternion Surface Equations (Weingarten Equations)
21.3 Quaternion Gauss Map
21.4 Example: The Sphere
21.4.1 Quaternion Maps of Alternative Sphere Frames
21.4.2 Covering the Sphere and the Geodesic Reference Frame South Pole Singularity |
More About
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Overview
Presenting a dynamic new historical approach to the study of abstract algebra
Much of modern algebra has its roots in the solvability of equations by radicals. Most introductory modern algebra texts, however, tend to employ an axiomatic strategy, beginning with abstract groups and ending with fields, while ignoring the issue of solvability. This book, by contrast, traces the historical development of modern algebra from the Renaissance solution of the cubic equation to Galois's expositions of his major ideas.
Professor Saul Stahl gives readers a unique opportunity to view the evolution of modern algebra as a consistent movement from concrete problems to abstract principles. By including several pertinent excerpts from the writings of mathematicians whose works kept the movement going, he helps students experience the drama of discovery behind the formulation of pivotal ideas. Students also develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can tell us about multivariate functions and the 15-puzzle. To further this understanding, Dr. Stahl presents abstract groups as unifying principles rather than collections of "interesting" axioms.
This fascinating, highly effective alternative to traditional survey-style expositions sets a new standard for undergraduate mathematics texts and supplies a firm foundation that will continue to support students' understanding of the subject long after the course work is completed.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
Editorial Reviews
Booknews
A textbook for a one-semester introduction for undergraduate mathematics majors and prospective high-school teachers of mathematics. Explains the principles and practices of modern algebra in terms of its historical development from the Renaissance solution to the cubic equation to Galois' exposition of his major ideas. Includes both computer and pencil-and-eraser exercises, the answers to which are in the teacher's manual. Annotation c. by Book News, Inc., Portland, Or.
Related Subjects
Meet the Author
SAUL STAHL, PhD, is Professor of Mathematics at the University of Kansas and a former systems programmer for IBM. He received his MA from the University of California, Berkeley, and his PhD from Western Michigan University. His main field of expertise is combinatorics. In 1986 he received the Carl A. Allendoerfer Award for excellence in expository writing from the Mathematical Association 29, 2000
An Old-New Approach to Mathematics Teaching
Some years ago when I took Introductory Algebra at UCLA I discovered Dr Stahl's book, which presents the subject exactly the way it should be; a clear-cut account of the historical development of Algebra, including translations of the original papers (Abel, Galois) which itself makes this book unique. Exercises are numerous and they actually do provide insight into the subject, also a unique feature among today's 'textbooks'. I recommend this book for those who have a genuine interest in the subject, beyond just earning a good grade in the class. I believe that this book put me on the right course in my understanding of what meaningful Mathematics is, a process which culminated in acceptance into a very prestigious graduate programme in Mathematics.
1 out of 1 people found this review helpful.
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Computing with Mathematica, 2nd edition is engaging and interactive. It is designed to teach readers how to use Mathematica efficiently for solving problems arising in fields such as mathematics, computer science, physics, and engineering. The text moves from simple to complex, often following a specific example on a number of different levels. This gradual increase in complexity allows readers to steadily build their competence without being overwhelmed.
The 2nd edition of this acclaimed book features: * An enclosed CD for Mac and Windows that contains the entire text as a collection of Mathematica notebooks * Substantive real world examples * Challenging exercises, moving from simple to complex * A collection of interactive projects from a variety of applications
"I really think this is an almost perfect text." -Stephen Brick, University of South Alabama
* Substantive real world examples * Challenging exercises, moving from simple to complex examples * Interactive explorations (on the included CD-ROM) from a variety of topics using a multitude of interesting mathematical applications less |
Review of Carnegie Learning's Cognitive Tutor Algebra 1
Carnegie Learning's Algebra 1 curriculum consists of two parts: textbook and software. It is truly a unique curriculum, and unlike anything I've seen before. You can see that a lot of work has gone into creating this product (yet it only costs $99 for home users).
The software is the most innovative part in this curriculum; however the textbook also follows somewhat different ideas and principles than standard algebra textbooks.
The software component is called Cognitive Tutor. It provides the student intelligent practice with everything in Algebra 1 curriculum. The problems that the electronic tutor gives you range from simple simplifying of expressions and equation solvings to modeling of real-world like situations.
It is a "tutor": the software has on-demand hints for all problems that advance from general hints to more specific ones. It is cognitive: the software adapts the problems to the student's performance, and sometimes provides hints for the student ("just-in-time help").
I especially liked the grapher problems in the software. The student is presented with a problem situation from the real world. The questions involve choosing the variables, building an algebraic equation to model the situation, answering questions about specific values of the variables, and making a graph using the Grapher.
The problems require the STUDENT to think what are the quantities that should be chosen as variables, and those are linked to each other (via an algebraic expression). The situations were from the real world, such as work hours/pay or time/distance or packages/price. In each case, the student then makes a graph, thus building his understanding of linear equations and graphs even before the formal chapter about them.
Screenshots from the program
The student either fills in empty boxes, chooses from multiple possible choices, or makes graphs etc. The problems are quite varied. The problems advance step-by-step towards more open-ended ones. For example, when learning equation solving, at first the student only chooses which transformation to do, and the program does it. Then in later problems, the student has to choose the transformation, and do it (type in the transformed equation).
The problems in the software cover the whole scope of an algebra 1 curriculum. See below a few examples. Click the images to enlarge them.
The student chooses which transformation or simplification to apply to the equation. The first step was to use distributive property, which is under "Simplification" menu.
The student first chooses which graphing method to use for the boundary lines of each inequality, and the grapher program allows him to graph the lines. That is already done here. Then, the student chooses how the shading is done.
The student fills in the boxes to build the proportion from the word problem.
The student chooses a graphing method and graphs the two lines, then the intersection is found.
The student finds and models squares and square roots.
This is a real-life situation about shooting a bottle rocket up, but it is a dud and falls back to the ground. The height versus time graph is a parabola.
The student carefully fills in the table the parts of the triangle to study Pythagorean theorem.
A scenario of exponential growth - lilies in a pond that double in area very day.
The textbook
The student is supposed to spend about 40% of learning time with the software, and the rest with problem-solving activities from the textbook, so while reading all the above it might appear to you that the software is the most important part, it is just about equally important with the textbook.
I only saw the first chapter of the printed textbook. It contains extended investigations or problem situations in which the student learns by guided exploration. The problems use real-world situations and they are designed so as to emphasize connections between verbal, numeric, graphic and algebraic representations.
The textbook would be better described as a worktext. It presents you with a scenario, and then problems and questions follow. In between all that are short teaching boxes that explain terms, notation, or concepts. In fact, the explanations may even be in the end of the lesson. In short, all learning is occurring within a context of a real-life problem.
While the program is excellent, I am a bit hesitant to recommend it if the parent does not already know some algebra.
It is different from your "standard" algebra curriculum in two main aspects: because of the software, and because the textbook is based upon investigations instead of plain "lecturing".
These features do make the curriculum excellent and highly commendable! In fact, a parent and a homeschooled student can probably study together and the parent is likely to learn a bunch as well.
However, a parent with weak math background might not be able to guide the student through the explorations. When using open-ended investigations in teaching, the teacher needs to understand beforehand what the investigation is coming to and what are the goals of such instruction. School teachers using this receive several days of training so they understand how to best implement this curriculum.
If you feel you need help in these aspects, consider buying the teacher's guide as well.
What I didn't like
The program makes the student to go through the problems in order, and automatically advances him to the next level when the software determines he is ready. This is good for most students, but can be a constraint as well. However, the teacher can change the student placement manually.
Sometimes I had to stop and think to figure out what the program wanted in which box, or in which order I needed to do things before the program would let me proceed.
In one instance I did not like the mathematical approach: the chapter about proportions. In another place (simplifying rational expressions), I thought the placing of text and of the empty boxes to fill made the whole problem to look very confusing. But the program is in constant development, and little things like that are likely to be changed based on user feedback. |
...
More About
This Book
problems, and practice exercises to test your skills.
This Schaum's Outline gives you
1,000 fully solved problems
Complete review of all course fundamentals
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time—and get your best test scores!
Topics include: Number Systems; The Earliest Mathematics;
Additive Systems;
The Egyptian Number System;
Alphabetic Systems;
Positional Systems on a Fixed Base;
Historical Examples of Positional Systems with a Base Different from Ten;
The Babylonian Number System;
The Mayan Number System;
Method for Translating Base Ten into Base Two;
The Algebra of Sets;
Set Theoretic Exponentiation;
Cardinal Numbers;
Theory of Numbers;
Mathematical Induction;
Complete Induction;
Prime Numbers;
The Division Theorem;
Testing for Primality;
The Greatest Common Divisor;
Irrational Numbers;
Factorization into Primes;
The Least Common Multiple;
The Euclidean Algorithm;
Some Famous Unsolved Problems (Perfect numbers,
Fermat primes, The Goldbach Conjecture);
Linear Diophantine Equations;
Fractions (How is a fraction represented in diagrams?
How are fractions represented on a number line?
What is the "unit"?
What is the "shifting unit"?
What is the multiplicative identity element for fractions?
What is a proper fraction?
What is an improper fraction?
When is a fraction larger than one whole?
What is a unit fraction?
How are fractions "simplified" (or "reduced")?
When is a fraction in "simplest form" (or "lowest terms")?
How are mixed numbers changed to improper fractions?
What are equivalent fractions?
How can we determine when fractions are equivalent?
How are fractions ordered from largest to smallest or from smallest to largest? How are fractions compared to find the largest or smallest value?
How is the least common denominator (LCD) determined?
How is the numerator determined once the LCD or common denominator is known?
How are fractions added and subtracted?
What are the properties of fraction addition?
How are fractions multiplied?
What are the properties of fraction multiplication?
Why is the product of two proper fractions smaller in value than either fraction factor?
What is the "multiplicative inverse," or "reciprocal" of a fraction?
How are fractions divided?
Why does the "invert-and-multiply" rule "work" when dividing fractions?
What are complex fractions?
How are complex fractions simplified?);
Decimals, Ratios, Proportions, and Percents (
What is a decimal fraction?
What is a mixed decimal?
What are the place values for decimals?
How are decimals written in expanded form?
What are terminating decimals?
What are equivalent decimals?
What are repeating (or recurring) nonterminating decimals?
What are nonepeating, nonterminating decimals?
How can common fractions be written as decimals?
How can decimals be written as common fractions?
How are mixed numbers written as decimals?
How are decimals ordered and compared?
How are decimals rounded?
How are decimals added and subtracted?
How are decimals multiplied?
Why is the placement of the decimal point in the product of two decimals determined by counting the number of decimal places in the factors?
How is decimal multiplication the same as whole number multiplication? How is decimal multiplication different from whole number multiplication?
How are decimals divided?
How is decimal division different from whole number division? How is decimal division the same as whole number division?
What does it mean to "add a zero" to the end of a decimal fraction?
What is scientific notation and how is it used?
What is a ratio?
What is a rate?
How are ratios and rates the same? How are they different?
How are ratios expressed as decimals? As percents?
When are two ratios equal?
What is a proportion?
What is a scaled drawing?
How are scales used to calculate actual quantities?
What does percent mean?
How are percents changed to decimals?
How are decimals changed to percents?
How are percents changed to common fractions?
How are common fractions changed to percents?
What does a percent greater than 100% mean?
What does a percent less than 1% mean?
How is a percent of a number calculated and what does it mean?
What are the aliquot parts of 100?
How is the percent of a number calculated?
When finding the percent of a number, when is it appropriate to use the fraction form of a rational number and when is it appropriate to use a decimal form of a rational number?
How can we find a number when a percent of it is known?
How is the percent of increase or decrease found?);
Algebra, Patterns, and Functions (What is a variable?
How are a "variable" and an "unknown" the same? How are they different?
What does the equal sign mean?
What is an algebraic expression?
What is an equation?
What is a linear equation?
How are linear equations solved?
What is an inequality?
How are linear inequalities solved?
What is the absolute value of a number?
What is a pattern? How are patterns used to solve problems?
What is a function?
What is the slope of a line?
What is the y-intercept of a line?
How is a linear equation graphed?
What is factoring?
How are algebraic expressions factored?
What is the Pythagorean Theorem?
What are Pythagorean triples?
What is a quadratic equation?
What is covariation?
What is direct variation?
What is inverse variation?);
Geometry and Measurement; Combinatorics and Probability; The Multiplication Principle; Terminology of Sets;
Probability; The Meaning of Probability;
Basic Ideas of Probability Theory: Probability Spaces
Events;
Conditional Probability;
Independent Events;
Random Variables and Expected Values;
; Statistics; Distributions and Types of Data
(What is a distribution?
What is a normal distribution?
What is a skewed distribution?
What are discrete data (also known as "categorical data") and how are they analyzed?
What are continuous data (sometimes also called, numerical data) and how are they analyzed?);
Populations and Samples (
What is the difference between a population and a sample?
What is convenience sampling?
What is systematic sampling?
What is voluntary-response sampling?
What is random sampling?
What is a biased sample?
What is a simulation?
What are frequency tables and how are they constructed?
What is relative frequency?
What is a picture graph (also known as a pictograph, pictogram, or pictorial graph) and how is it constructed?
What is a bar graph (also known as a bar chart) and how is it constructed?
What is a double or multiple bar graph and how is it constructed?
What is a stacked bar graph and how is it constructed?
What is a histogram and how is it constructed?
How are bar graphs and histograms the same? How are they different?
What is a line graph (also known as a broken line graph) and how is it constructed?
What is a double line graph and how is it constructed?
What is a circle graph (also known as a pie graph, pie chart, pie diagram, area graph) and how is it constructed?
What is a line plot?
What is a stemplot (also known as a stem-and-leaf plot) and how is it constructed?
What is a back-to-back stem-and-leaf plot and how is it constructed?
What is a scatterplot and how is it constructed?
What is correlation?
What is a line of best fit and how can it be found?);
Measures of Center (What are measures of central tendency?
What is the mean of a set of data (also known as the arithmetic mean or arithmetic average) and how is it determined?
What is the median of a set of data and how is it found?
What is the mode of a set of data?);
Measures of Spread (What are measures of dispersion?
What is the range of a set of data and how is it calculated?
What is the variance of a set of data and how is it calculated?
What is the standard deviation of a set of data and how is it calculated?
What are percentiles?
What are quartiles and how are they determined?
What is the interquartile range?
What is a boxplot (also known as a box-and-whisker plot) and how is it constructed?
Table of Contents
Chapter 1: Number Systems
The Earliest Mathematics
Additive Systems
The Egyptian Number System
Alphabetic Systems
Positional Systems on a Fixed Base
Historical Examples of Positional Systems with a Base Different from Ten
The Babylonian Number System
The Mayan Number System
Method for Translating Base Ten into Base Two
Chapter 2: Sets
The Algebra of Sets
Set Theoretic Exponentiation
Cardinal Numbers
Chapter 3: Theory of Numbers
Mathematical Induction
Complete Induction
Prime Numbers
The Division Theorem
Testing for Primality
The Greatest Common Divisor
Irrational Numbers
Factorization into Primes
The Least Common Multiple
The Euclidean Algorithm
Some Famous Unsolved Problems (Perfect numbers, Fermat primes, The Goldbach Conjecture)
Linear Diophantine Equations
Chapter 4: Fractions
Introduction
Try These First
4.1 What is a "fraction"?
4.2 How is a fraction represented in diagrams?
4.3 How are fractions represented on a number line?
4.4 What is the "unit"?
4.5 What is the "shifting unit"?
4.6 What is the multiplicative identity element for fractions?
4.7 What is a proper fraction?
4.8 What is an improper fraction?
4.9 When is a fraction larger than one whole?
4.10 What is a unit fraction?
4.11 How are fractions "simplified" (or "reduced")?
4.12 When is a fraction in "simplest form" (or "lowest terms")?
4.13 How are mixed numbers changed to improper fractions?
4.14 What are equivalent fractions?
4.15 How can we determine when fractions are equivalent?
4.16 How are fractions ordered from largest to smallest or from smallest to largest? How are fractions compared to find the largest or smallest value?
4.17 How is the least common denominator (LCD) determined?
4.18 How is the numerator determined once the LCD or common denominator is known?
4.19 How are fractions added and subtracted?
4.20 What are the properties of fraction addition?
4.21 How are fractions multiplied?
4.22 What are the properties of fraction multiplication?
4.23 Why is the product of two proper fractions smaller in value than either fraction factor?
4.24 What is the "multiplicative inverse," or "reciprocal" of a fraction?
4.25 How are fractions divided?
4.26 Why does the "invert-and-multiply" rule "work" when dividing fractions?
4.27 What are complex fractions?
4.28 How are complex fractions simplified?
End of Chapter Exercises
Sample Certification Test Items
Chapter 5: Decimals, Ratios, Proportions, and Percents
Introduction
Try These First
5.1 What is a decimal fraction?
5.2 What is a mixed decimal?
5.3 What are the place values for decimals?
5.4 How are decimals written in expanded form?
5.5 What are terminating decimals?
5.6 What are equivalent decimals?
5.7 What are repeating (or recurring) nonterminating decimals?
5.8 What are nonepeating, nonterminating decimals?
5.9 How can common fractions be written as decimals?
5.10 How can decimals be written as common fractions?
5.11 How are mixed numbers written as decimals?
5.12 How are decimals ordered and compared?
5.13 How are decimals rounded?
5.14 How are decimals added and subtracted?
5.15 How are decimals multiplied?
5.16 Why is the placement of the decimal point in the product of two decimals determined by counting the number of decimal places in the factors?
5.17 How is decimal multiplication the same as whole number multiplication? How is decimal multiplication different from whole number multiplication?
5.18 How are decimals divided?
5.19 How is decimal division different from whole number division? How is decimal division the same as whole number division?
5.20 What does it mean to "add a zero" to the end of a decimal fraction?
5.21 What is scientific notation and how is it used?
5.22 What is a ratio?
5.23 What is a rate?
5.24 How are ratios and rates the same? How are they different?
5.25 How are ratios expressed as decimals? As percents?
5.26 When are two ratios equal?
5.27 What is a proportion?
5.28 What is a scaled drawing?
5.29 How are scales used to calculate actual quantities?
5.30 What does percent mean?
5.31 How are percents changed to decimals?
5.32 How are decimals changed to percents?
5.33 How are percents changed to common fractions?
5.34 How are common fractions changed to percents?
5.35 What does a percent greater than 100% mean?
5.36 What does a percent less than 1% mean?
5.37 How is a percent of a number calculated and what does it mean?
5.38 What are the aliquot parts of 100?
5.39 How is the percent of a number calculated?
5.40 When finding the percent of a number, when is it appropriate to use the fraction form of a rational number and when is it appropriate to use a decimal form of a rational number?
5.41 How can we find a number when a percent of it is known?
5.42 How is the percent of increase or decrease found?
End of Chapter Exercises
Sample Certification Test Items
Chapter 6: Algebra, Patterns, and Functions
Introduction
Try These First
6.1 What is algebra?
6.2 What is a variable?
6.3 How are a "variable" and an "unknown" the same? How are they different?
6.4 What does the equal sign mean?
6.5 What is an algebraic expression?
6.6 What is an equation?
6.7 What is a linear equation?
6.8 How are linear equations solved?
6.9 What is an inequality?
6.10 How are linear inequalities solved?
6.11 What is the absolute value of a number?
6.12 What is a pattern? How are patterns used to solve problems?
6.13 What is a function?
6.14 What is the slope of a line?
6.15 What is the y-intercept of a line?
6.16 How is a linear equation graphed?
6.17 What is factoring?
6.18 How are algebraic expressions factored?
6.19 What is the Pythagorean Theorem?
6.20 What are Pythagorean triples?
6.21 What is a quadratic equation?
6.22 What is covariation?
6.23 What is direct variation?
6.24 What is inverse variation?
End of Chapter Exercises
Sample Certification Test Items
Chapter 7: Geometry and Measurement
Chapter 8: Combinatorics and Probability
Let Us Count the Ways
The Multiplication Principle
Terminology of Sets
Probability
The Meaning of Probability
Basic Ideas of Probability Theory: Probability Spaces Events
Conditional Probability
Independent Events
Random Variables and Expected Values
Chapter 9: Statistics
Introduction
Try These First
Distributions and Types of Data
9.1 What is a distribution?
9.2 What is a normal distribution?
9.3 What is a skewed distribution?
9.4 What are discrete data (also known as "categorical data") and how are they analyzed?
9.5 What are continuous data (sometimes also called, numerical data) and how are they analyzed?
Populations and Samples
9.6 What is the difference between a population and a sample?
9.7 What is convenience sampling?
9.8 What is systematic sampling?
9.9 What is voluntary-response sampling?
9.10 What is random sampling?
9.11 What is a biased sample?
9.12 What is a simulation?
9.13 What are frequency tables and how are they constructed?
9.14 What is relative frequency?
9.15 What is a picture graph (also known as a pictograph, pictogram, or pictorial graph) and how is it constructed?
9.16 What is a bar graph (also known as a bar chart) and how is it constructed?
9.17 What is a double or multiple bar graph and how is it constructed?
9.18 What is a stacked bar graph and how is it constructed?
9.19 What is a histogram and how is it constructed?
9.20 How are bar graphs and histograms the same? How are they different?
9.21 What is a line graph (also known as a broken line graph) and how is it constructed?
9.22 What is a double line graph and how is it constructed?
9.23 What is a circle graph (also known as a pie graph, pie chart, pie diagram, area graph) and how is it constructed?
9.24 What is a line plot?
9.25 What is a stemplot (also known as a stem-and-leaf plot) and how is it constructed?
9.26 What is a back-to-back stem-and-leaf plot and how is it constructed?
9.27 What is a scatterplot and how is it constructed?
9.28 What is correlation?
9.29 What is a line of best fit and how can it be found?
Measures of Center
9.30 What are measures of central tendency?
9.31 What is the mean of a set of data (also known as the arithmetic mean or arithmetic average) and how is it determined?
9.32 What is the median of a set of data and how is it found?
9.33 What is the mode of a set of data?
Measures of Spread
9.34 What are measures of dispersion?
9.35 What is the range of a set of data and how is it calculated?
9.36 What is the variance of a set of data and how is it calculated?
9.37 What is the standard deviation of a set of data and how is it calculated?
9.38 What are percentiles?
9.39 What are quartiles and how are they determined?
9.40 What is the interquartile range?
9.41 What is a boxplot (also known as a box-and-whisker plot) and how is it constructed?
9.42 What is an outlier and how is it determined?
9.43 What is a cluster?
9.44 What is a gap?
9.45 What is a z-score (also standard score) and how is it calculated?
End of Chapter Exercises
Sample Certification Test Items
Bibliography
Answer KeyIndex |
More About
This Textbook
Overview
The Heart of Mathematics: An invitation to effective thinking --now in its second edition--succeeds at reaching non-math, non-science-oriented readers and encourages them to discover the mathematics inherent in the world around them. Infused throughout with the authors' humor and enthusiasm, The Heart of Mathematics introduces readers to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.
Related Subjects
Meet the Author
Edward B. Burger is professor of mathematics in the Department of Mathematics and Statistics at Williams College. He graduated from Connecticut College in 1985, where he earned B.A. Summa Cum Laude with Distinction in Mathematics, and received his Ph.D. in mathematics from the University of Texas at Austin. He did his postdoctoral work at the University of Waterloo in Canada. Dr. Burger has received numerous awards including: the Award of Excellence, for "educational mathematics videos that break new ground from the Technology & Learning magazine, and the Distinguished Achievement Award, for Educational Video Technology from The Association of Educational Publishers. He was honored as one of the "100 Best of America", Listed in Reader's Digest's Annual Special Issue as Best Math Teacher. He also received the Residence Life Academic Teaching Award, University of Colorado at Boulder and the Robert W. Hamilton Book Award, for "The Heart of Mathematics".
Michael Starbird Michael Starbird is a University Distinguished Teaching Professor of Mathematics at The University of Texas at Austin. He has received more than a dozen teaching awards including the Mathematical Association of America's 2007 national teaching award and several university-wide teaching awards based largely on his course in mathematics for liberal arts students. Starbird brings intriguing mathematics to general audiences through his classes, lectures, books, and video courses. In 1989, Starbird was UT's Recreational Sports Super Racquets Champion.
Table of Contents
But First, a Word from our Sponsors ix
Welcome! xi
Surfing the Book xv
Chapter One: Fun and Games: An Introduction to Rigorous Thought 2
1.1 Silly Stories Each with a Moral 4
Conundrums that Evoke Techniques of Effective Thinking
1.2 Nudges 4
Leading Questions and Hints for Resolving the Stories
1.3 The Punch Lines 18
Solutions and Further Commentary
1.4 From Play to Power 27
Discovering Strategies of Thought for Life
Chapter Two: Number Contemplation 38
2.1 Counting 40
How the Pigeonhole Principle Leads to Precision Through Estimation
2.2 Numberical Patterns in Nature 49
Discovering the Beauty of the Fibonacci Numbers
2.3 Prime Cuts of Numbers 64
How the Primes Numbers are the Building Blocks of All Natural Numbers
2.4 Crazy Clocks and Checking Out Bars 82
Cyclical Clock Arithmetic and Bar Codes
2.5 Public Secret Codes adn How to Become a Spy 95
Encrypting Information Using Modula Arithmetic and Primes
2.6 The Irrational Side of Numbers 110
Are There Numbers Beyond Fractions?
2.7 Get Real 121
The Point of Decimals and Pinpointing Numbers on the Real Line
Chapter Three: Infinity 136
3.1 Beyond Numbers 138
What Does Infinity Mean?
3.2 Comparing the Infinite 145
Pairing Up Collections via a One-to-One Corerspondence
3.3 The Missing Member 162
Georg Cantor Answers: Are Some Infinities Larger Than Others?
Chapter Four: Geometric Gems 206
4.1 Pythagoras and His Hypotenuse 208
How a Puzzle Leads to the Proof of one of the Gems of Mathematics
4.2 A View of an Art Gallery 218
Using Computational Geometry to Place Security Cameras in Musuems
4.3 The Sexiest Rectangle 232
Finding Aesthetics in Life, Art, and Math Through the Golden Rectangle
4.4 Soothing Symmetry and Spinning Pinwheels 249
Can a Floor be Tiled without any Repeating Pattern?
4.5 The Platonic Solids Turn Amorous 269
Discovering the Symmetry and Interconnections Among the Platonic Solds
4.6 The Shape of Reality? 289
How Straight Lines Can Bend in Non-Euclidean Geometries
4.7 The Fouther Dimension 307
Can You See It?
Chapter Five: Contortions of Space 326
5.1 Rubger Sheet Geometry 328
Discovering the Topological Idea of Equivalence by Distortion
5.2 The Band That Wouldn't Stop Playing 46
Experimenting with the Mobius Band and Klein Bottle
5.3 Feeling Edgy? 359
Exploring Relationships Among Vertices, Edges, and Faces
5.4 Knots and Links 374
Untangling Ropes and Rings
5.5 Fixed Points, Hot Loops, and Rainy Days 389
How the Certainty of Fixed Points Implies Certain Weather Phenomena
Chapter Six: Chaos and Fractals 402
6.1 Images 404
Viewing a Gallery of Fractals
6.2 The Dynamics of Change 412
Can Change be Modeled by Repeated Applications of Simple Processes?
6.3 The Infinitely Detailed Beuty of Fractals 430
How to Create Workds of Ifinite Intricacy THrough Repeated PRocesses
6.4 The Mysterious Art of Imaginary Fractals 458
Creating Juila and Mandelbrot Sets by Stepping Out in the Complex Plane
6.5 Predetermined Chase 482
How Repeated SImple Processes Result in Utter Chaos
6.6 Between Dimnsions 503
Can the Dimensions of Fractals Fall Through the Cracks?
Chapter Seven: Taming Uncertainty 514
7.1 Chance Surprises 516
Some Scenarioos Involving Chance that Confound our Intuition
7.2 Predicting the Future in an Uncertain World 523
How to MEasure Uncertainty Using the Idea of Probability
7.3 Random Thoughtss 541
Are Coincidences as Truly Amazing as They First Appear?
7.4 Down for the Count 554
Systematically Counting all Possible Outcomes
7.5 Collecting Data Rather than Dust 571
The Power and Pitfalls fo Statistics
7.6 What the Average American Has 585
Different Means of Describing Data
7.7 Parenting Peas, Twins, and Hypotheses 610
Making Inferences from Data
Chapter Eight: Deciding Wisely 628
Applications of Rigorous THinking
8.1 Great Expectations 630
Deciding How to Weigh the Unknown Future
8.2 Risk 645
Deciding Personal and PUblic Policy
8.3 Money matters 663
Deciding Between Faring Well and Welfare
8.4 Peril at the Polls 682
Deciding Who Actually Wins an Election
8.5
Cutting Cake for Greedy People 700
Deciding How to Slice Up Scarce Resources
Farewell 716
Acknowledgements: Second Edition 719
Acknowledgements: First Edition 722
Hints and Solutions 725
Index 747
Credits 7 |
Summary: 95% of Introductory Statistics students will never take another Statistics course. What do you want your students to learn?Discover the Power of Real DataMario Triola remains the market-leading statistics author by engaging students each edition with an abundance of real data in the examples, applications, and exercises. Statistics is all around us, and Triola helps students understand how this course will impact their lives beyondthe classroomndash;as consumers, citizens, and profes...show moresionals.Elementary Statistics Using the TI-83/84 Plus Calculator, Third Edition provides extensive instruction for using the TI-83 and TI-84 Plus (and Silver Edition) calculators for statistics, with information on calculator functions, images of screen displays, and projects designed exclusively for the graphing calculator. Drawn from Triola's Elementary Statistics, Eleventh Edition, this text provides the same student-friendly approach with material presented in a real-world context.The Third Edition contains more than 2,000 exercises, 87% are new, and 82% use real data. It also contains hundreds of examples; 86% are new and 94% use real data. By analyzing real data, students are able to connect abstract concepts to the world at large, learning to think statistically and apply conceptual understanding using the same methods that professional statisticians employ.Datasets and other resources (where applicable) for this book are available here . ...show less
Hardcover Fine 0321641485 covers and corners may show shelf wear used books may be missing software and or codes. spirals will show more wear because of nature of book.
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Please read before purchase>> annotated teacher edition New no writing or marks includes all Students content and all answers. Includes sealed Cd and formulas charts no access code or other supplemen...show morets. ship immediately - Expedited shipping available ...show less
$98148.80 |
Wavelet Theory. An Elementary Approach with Applications
A self-contained, elementary introduction to wavelet theory and applications
Exploring the growing relevance of wavelets in the field of mathematics, Wavelet Theory: An Elementary Approach with Applications provides an introduction to the topic, detailing the fundamental concepts and presenting its major impacts in the world beyond academia. Drawing on concepts from calculus and linear algebra, this book helps readers sharpen their mathematical proof writing and reading skills through interesting, real-world applications.
The book begins with a brief introduction to the fundamentals of complex numbers and the space of square-integrable functions. Next, Fourier series and the Fourier transform are presented as tools for understanding wavelet analysis and the study of wavelets in the transform domain. Subsequent chapters provide a comprehensive treatment of various types of wavelets and their related concepts, such as Haar spaces, multiresolution analysis, Daubechies wavelets, and biorthogonal wavelets. In addition, the authors include two chapters that carefully detail the transition from wavelet theory to the discrete wavelet transformations. To illustrate the relevance
of wavelet theory in the digital age, the book includes two in-depth sections on current applications: the FBI Wavelet Scalar Quantization Standard and image segmentation.
In order to facilitate mastery of the content, the book features more than 400 exercises that range from theoretical to computational in nature and are structured in a multi-part format in order to assist readers with the correct proof or solution. These problems provide an opportunity for readers to further investigate various applications of wavelets. All problems are compatible with software packages and computer labs that are available on the book's related Web site, allowing readers to perform various imaging/audio tasks, explore computer wavelet transformations and their inverses, and visualize the applications discussed throughout the book.
Requiring only a prerequisite knowledge of linear algebra and calculus, Wavelet Theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level.
SHOW LESS
READ MORE >
Preface.
Acknowledgments.
1 The Complex Plane and the Space L2(R).
1.1 Complex Numbers and Basic Operations.
Problems.
1.2 The Space L2(R).
Problems.
1.3 Inner Products.
Problems.
1.4 Bases and Projections.
Problems.
2 Fourier Series and Fourier Transformations.
2.1 Euler's Formula and the Complex Exponential Function.
Problems.
2.2 Fourier Series.
Problems.
2.3 The Fourier Transform.
Problems.
2.4 Convolution and B-Splines.
Problems.
3 Haar Spaces.
3.1 The Haar Space V0.
Problems.
3.2 The General Haar Space Vj.
Problems.
3.3 The Haar Wavelet Space W0.
Problems.
3.4 The General Haar Wavelet Space Wj.
Problems.
3.5 Decomposition and Reconstruction.
Problems.
3.6 Summary.
4 The Discrete Haar Wavelet Transform and Applications.
4.1 The One-Dimensional Transformation.
Problems.
4.2 The Two-Dimensional Transformation.
Problems.
4.3 Edge Detection and Naive Image Compression.
5 Multiresolution Analysis.
5.1 Multiresolution Analysis.
Problems.
5.2 The View from the Transform Domain.
Problems.
5.3 Examples of Multiresolution Analyses.
Problems.
5.4 Summary.
6 Daubechies Scaling Functions and Wavelets.
6.1 Constructing the Daubechies Scaling Functions.
Problems.
6.2 The Cascade Algorithm.
Problems.
6.3 Orthogonal Translates, Coding and Projections.
Problems.
7 The Discrete Daubechies Transformation and Applications.
7.1 The Discrete Daubechies Wavelet Transform.
Problems.
7.2 Projections and Signal and Image Compression.
Problems.
7.3 Naive Image Segmentation.
Problems.
8 Biorthogonal Scaling Functions and Wavelets.
8.1 A Biorthogonal Example and Duality.
Problems.
8.2 Biorthogonality Conditions for Symbols and Wavelet Spaces.
Problems.
8.3 Biorthogonal Spline Filter Pairs and the CDF97 Filter Pair.
Problems.
8.4 Decomposition and Reconstruction.
Problems.
8.5 The Discrete Biorthogonal Wavelet Transformation.
Problems.
8.6 Riesz Basis Theory.
Problems.
9 Wavelet Packets.
9.1 Constructing Wavelet Packet Functions.
Problems.
9.2 Wavelet Packet Spaces.
Problems.
9.3 The Discrete Packet Transform and Best Basis Algorithm.
Problems.
9.4 The FBI Fingerprint Compression Standard.
Appendix A: Huffman Coding.
Problems.
References.
Topic Index.
Author Index.
"The book, putting emphasize on an analytic facet of wavelets, can be seen as complementary. to the previous Patrick J. Van Fleet's book, DiscreteWavelet Transformations: An Elementary. Approach with Applications, focused on their algebraic properties." (Zentralblatt MATH, 2011)
"Requiring only a prerequisite knowledge of calculus and linear algebra, Wavelet theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level." (Mathematical Reviews, 2011 |
College Algebra and Trigonometry: A Graphing Approach
Intended to provide a flexible approach to the college algebra and trigonometry curriculum that emphasizes real-world applications, this text ...Show synopsisIntended to provide a flexible approach to the college algebra and trigonometry curriculum that emphasizes real-world applications, this text integrates technology into the presentation without making it an end in itself, and is suitable for a variety of audiences. Mathematical concepts are presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving. Pedagogical elements including chapter opening applications, graphing explorations, technology tips, calculator investigations, and discovery projects are some of the tools students will use to master the material and begin applying the mathematics to solve real-world problems. CONTEMPORARY COLLEGE ALGEBRA AND TRIGONOMETRY includes a full review of basic algebra in Chapter 0 and full coverage of trigonometry to prepare students for the standard science/engineering calculus sequence. (The companion volume, CONTEMPORARY COLLEGE ALGEBRA includes all of the non-trigonometry topics, covered in sufficient detail to prepare a student for a business/social science calculus course.) Those who are familiar with the author's CONTEMPORARY PRECALCULUS should note that this book covers topics in a different order, and with a slower, gentle approach. Also, more drill exercises are included |
Contact Us
What Class should you take?
Be sure to first check with your major advisor(s) to determine your first mathematics course.
One way to determine which course you are qualified to take is by ACT Math, SAT Math or COMPASS Math scores. See the chart below to determine which course you are eligible to take.
Group
ACT Math
SAT Math
Compass
You can take:
Mth1
0 - 18
or
200 - 460
or
Algebra < 36
Math 108, 123*
Mth2
19 - 21
or
470 - 510
or
36 ≤ Algebra < 61 OR
College Algebra < 45
Math 108, 123*, 130*
Mth3
22 - 26
or
520 - 600
or
Algebra ≥ 61 OR
45 ≤ College Algebra < 49
Math 108, 123*, 130*, 143, 144
Mth4
27 - 28
or
610 - 640
or
49 ≤ College Algebra < 51
Math 108, 123*, 130*, 143, 144, 160*
Mth5
29 - 36
or
650 - 800
or
College Algebra ≥ 51 AND
Trigonometry ≥ 51
Math 108, 123*, 130*, 143, 160*,144, 170, 176*
*WARNING: Do not automatically enroll in the "highest" math course available based on your exam scores.
Many courses (including Math 123, Math 130, Math 160, and Math 176) are terminal courses and do not
provide the prerequisite preparation needed for other required courses. Check with your adviser and/or the
Math department to determine which course is best for you.
In order to support and improve the success of our students the Mathematics Department has updated its override policy. Effective immediately the Mathematics Department will be following pre-requisite requirements as described in the course catalog without exception.
Overrides will be provided only to those students who have satisfied the prerequisites either by having completed the prerequisite course or having sufficient exam scores. If the student has documentation showing updated exam scores or unofficial transcripts they should come to the mathematics main office or submit transcript or scores by fax/email for the override. We must see the updated scores to provide the override. We will no longer be able to give overrides to students who are "on track" to complete the prerequisites for a course. Please send email messages requesting overrides to math@uidaho.edu with official scores or transcripts.
If a student does not feel their exam scores accurately portray their mathematical experience they will need to take a compass math test to be re-evaluated.
If a student believes he or she would test into a course higher than Math 170 they will need to contact the mathematics main office to be evaluated. To place into a course above Math 170, a student will need to have proof of successful completion of prerequisite courses on an official or unofficial transcript.
If you are not satisfied with your ACT or SAT placement, you are strongly encouraged to CHALLENGE YOUR PLACEMENT by scoring high enough on the computerized COMPASS math test.
To take the Compass Placement Exams at UI go to the UI Counseling and Testing Center, 306 Continuing Education Building, 885-6716. The exam is also given at all universities and colleges in Idaho, and at many throughout the U.S. Ask them to forward your results to the UI Admissions Office and the Mathematics Department.
If you have any questions, please contact the Mathematics Office at 208-885-6742. |
More About
This Textbook
Overview
Succeed in statistics with ELEMENTARY STATISTICS! Including relevant examples, exercises, and applications, this textbook gives you the tools you need to get a good grade in your statistics course. Struggling with a specific concept' Log onto vMentor' to get live, one-on-one online tutoring from a statistician who has a copy of the textbook. Video Skillbuilders and StatisticsNow (an online learning tool built around your individual progress that gives you a simple pre-test, and then focuses your learning experience on your studying needs) provide additional online support. Learning to use MINITAB, Excel, and the TI-83/84 graphing calculator is made easy with instructions included in relevant sections throughout the text.
Editorial Reviews
Booknews
A textbook for an introductory course for students who need a working knowledge of statistics but do not have a strong mathematical background. Johnson and Kuby (both Monroe Community College) suggest at least one semester of college mathematics for students who have not completed intermediate algebra. They strive to present the concepts and methods in a context familiar and useful to students, and focus on using computers and interpreting the outcome. The CD contains data sets, concept links, short videos, longer tutorials, and lectures for lecture presentation or notes. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Product Details
ISBN-13: 9780495188414
Publisher: Cengage Learning
Publication date: 1/1/2007
Edition description: Enhanced Review Edition
Edition number: 10
Meet the Author
Robert R. Johnson is Professor of Mathematics Emeritus and a former chair of the Mathematics Department at Monroe Community College. He received his B.S. from SUNY Cortland and his M.A. from University of Northern Iowa, both in mathematics; and has studied statistics at University of Iowa and Rochester Institute of Technology. He is the co-author of JUST THE ESSENTIALS OF ELEMENTARY STATISTICS, Ninth Edition. Professor Johnson has given several presentations about the "teaching of statistics" and the use of MINITAB® in teaching statistics at various conferences and workshops. He has been using computers and MINITAB for over 30 years to aid in teaching statistics. He is also an active advocate for writing across the curriculum. Organizing the Beyond the Formula Statistics Conferences for teachers of Introductory Statistics has been a passion since |
Prealgebra - 7th edition
Summary: For the modern student like you--Pat McKeague's PREALGEBRA, 7E--offers concise writing, continuous review, and contemporary applications to show you how mathematics connects to your modern world. The new edition continues to reflect the author's passion for teaching mathematics by offering guided practice, review, and reinforcement to help you build skills through hundreds of new examples and applications. Use the examples, practice exercises, tutorials, videos, and e-Book sections i...show moren Enhanced WebAssign to practice your skills and demonstrate your knowledge. ...show less
New Book. Shipped from US within 4 to 14 business days. Established seller since 2000
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Brand New Title. We're a Power Distributor; Your satisfaction is our guarantee!
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PROFESSIONAL & ACADEMIC BOOKSTORE Dundee, MI
111198686 |
More About
This Textbook
Overview
Introductory Algebra and Trignometry with Applications by Paul Calter and Carol Felsinger Rogers This textbook introduces all the important topics for a student who needs preparatory, review, or remedial work in mathematics. Adapted from Calter's Technical Mathematics, it uses an intuitive approach and gives information in very small-segments. Careful page layout and numerous illustrations make the material easy to follow. Features of Introductory Algebra and Trigonometry with Applications include the following.*Graphing Calculator: The graphing calculator has been fully integrated throughout the text, and calculator problems are given in the exercises. The book does not present any particular calculator. Keystrokes are shown in the early chapters, with verbal descriptions given thereafter.*Common Error Boxes: Many of the mistakes that students repeatedly make have been identified and are presented in the text as Common Error boxes.*Summary of Facts and Formulas: All important formulas are boxed and numbered in the text and are listed in the Summary of Facts and Formulas at the end of the book.*Examples: The many fully worked examples are specifically chosen to help the student do the exercises.*Exercises: A large number of exercises is given after each section, graded by difficulty and grouped by type.*Chapter Review Exercises: Every chapter ends with a set of Chapter Review Exercises. In contrast to the exercises, most are scrambled as to type and difficulty, requiring the student to be able to identify type.*Applications: Applications drawn from many fields are included in the examples, the exercises, and the Chapter Review.*Writing Questions:The "writing-across-the-curriculum" movement urges writing in every course as an aid to learning. In response, this text provides a writing question at the end of every chapter.*Team Projects: As an aid to collaborative learning, a team project is included at the end of most chapters.*Thorough Support Material: Among valuable components found at the end of the book are the Summary of Facts and Formulas, Conversion Factors, Answers to Selected Exercises, Index to Applications, Index to Writing Questions, Index to Team Projects, and General Index.*For the Instructor: An Instructor's Manual contains worked-out solutions to every even-numbered problem in the text. This most valuable supplement is available to any instructor using the textbook |
This geometry lesson from Illuminations uses the model of the orbits of Mars and Earth relative to the sun to illustrate parametric equations. As an interdisciplinary learning activity, the material may be used in...
Based at the University of Plymouth, the Centre for Innovation in Mathematics Teaching has developed many instructional materials designed to help both novice and experienced math teachers. This particular area of the...
This document from SpaceTEC National Aerospace Technical Education Center is one of three handbooks for people preparing for mechanic certification with airframe or powerplant ratings, or both. This particular volume...
This site uses the example of Native American building design to demonstrate the mathematical concepts of angles, coordinates and parabolas. Tutorials on arc geometry and arc coordinates are included. This...
The Center for Cultural Design presents this site on breakdancing as a way of teaching mathematical concepts. Specifically, rotation and sine function are demonstrated. The cultural and social background of breakdance... |
Conic
Sections Movie - Animated moved
shows how slicing through a cone with a plane produces the various
conic sections. The movie goes a bit too fast to follow both the left
and right images and see their relationship. Try advancing it a frame
at a time.
Conics
- Some interesting interactive demonstrations of drawing conics and
their reflective properties.
Financial
Calculator -- The site will
perform a variety of mortgage-related
calculations including how much house you can afford and amortization
schedules. It will even show you how much can be saved by making
biweekly payments or extra payments toward principal.
KnotPlot Site
- Here you
will find a collection of knots and links, viewed from a (mostly)
mathematical perspective. Nearly all of the images here were created
with KnotPlot, a fairly elaborate program to visualize and manipulate
mathematical knots in three and four dimensions. You can download
KnotPlot and try it on your computer.
"Magic" Tricks
- With a
little logic you can figure out how it's done. It the meantime, it's
intriguing fun.
Math
Dictionary for Kids - Contains a
clickable alphabetical listing
of over 400 mathematical terms beginning with abacus and ending with
zero.
Math
Help -
links to a variety of online resources compiled by students at Chalmers
University of Technology in Sweden.
Math is
Power is the theme of the public service
advertising campaign of NACME, The National Action Council for
Minorities in Engineering, Inc. If no one has told you how math
classes can improve your future, call NACME at 1-800-97NACME. They
will tell you.
MathNerds
- A free service providing hints, direction, references, or guidance
(not necessarily answers) in many areas of mathematics. The MathNerds
team members are unpaid volunteers whose only compensation for their
efforts are the "Thank You" messages from our clients.
3DXplorMath
This is a Mac OS X program for creating all sorts of math graphs. This
program is very versatile (and a little overwhelming). It can graph 2D
(including polar, parametric, and implicitly defined funcions) and 3D.
Click on all the pull-down menus to see what your options are, or even
better if you have the time, read the manual. |
Find a Littleton City Offices as general hardware and software...
...However, you often use the same techniques you're already familiar with to solve algebra 2 problems! So really, algebra 2 is a lot like the kinds of things you have already worked with - it just "looks" harder. Algebra 2 topics include setting up and solving word problems, working with absolute |
Main navigation
This book is an informal guide to Intermediate Olympiads, not only for potential candidates, but for anyone wishing to tackle more challenging problems. The discussions of sample questions aim to show how to attack a problem which may be quite unlike anything seen before.
Includes 10 years' IMOK Olympiad papers (Cayley, Hamilton, Maclaurin) and their solutions.
For ages 13-16.
Latest News
We are now taking bookings for our 2014 one-day CPD seminars in Edinburgh, Leicester, London, Bristol and Brighton. Click here for dates, agendas and application form.
The UKMT Primary Team Maths Resources are free and can be used as you wish e.g. with feeder schools, or as a Year 7 end of term activity. See this page for previous years' materials and how to obtain the 2014 materials.
About the Trust We were established in 1996 and last academic year over 600,000 pupils from 4,000 schools took part in the three individual challenges, the UK's biggest national maths competitions. Each challenge leads into a follow-on Olympiad round and we run mentoring schemes and summer schools for high performing students as well as training the team of six to represent the UK in the International Mathematical Olympiad. We also run team maths competitions for two age ranges, publish books and organise enrichment seminars for teachers. |
* Be able to use graphical and algebraic properties of families of functions both with and without graphing calculators to generate solutions to conceptual and applied problems * Develop more mature mathematical thinking * Use functions to model real world situations * Develop the skills, strategies, and knowledge to be able to use all the problem solving techniques and mathematical concepts that were taught in algebra I, geometry, algebra 2. * Apply the concepts of right triangle trigonometry to the concepts of imaginary numbers. |
12 consumable spiral-bound text-workbook contains 34 lessons in six sections that teach students how to use the efficient 10-key touch method to solve business problems on a calculator.
Table of Contents
Section 1 10-Key Touch Method
Lesson 1 Touch Addition of Whole Numbers
Lesson 2 Touch Addition and Subtraction of Whole Numbers
Lesson 3 Crossfooting
Lesson 4 Touch Addition and Subtraction of Dollars and Cents
Lesson 5 Rounding and Estimating Without a Calculator
Lesson 6 Multiplication
Lesson 7 Division
Business Calculator Applications 1: Keypad Introduction
Practice Test 1
Section 2 Multiplication and Division
Lesson 8 Constant Multiplication and Division
Lesson 9 Multiplying Three or More Factors
Lesson 10 Mixed Operations
Lesson 11 Accumulative Multiplication
Lesson 12 Negative Multiplication
Business Calculator Applications 2: Using Memory Keys for Repeated Operations
Practice Test 2
Section 3 Percents and Discounts
Lesson 13 Fractions and Decimals
Lesson 14 Percents
Lesson 15 Finding Percentage, Rate, and Base
Lesson 16 Amounts and Percents of Increase or Decrease
Lesson 17 Single Discounts
Lesson 18 Series Discounts
Lesson 19 Extending Invoices and Quantity Pricing
Lesson 20 Auditing Invoices
Business Calculator Applications 3: Percent of Change, The Percentage Formula, and Discounts
Practice Test 3
Section 4 Retail Calculations and Payroll
Lesson 22 Markdown
Lesson 23 Monthly and Semimonthly Payrolls
Lesson 24 Payrolls for Hourly Workers
Lesson 25 Commission Payroll Plans
Business Calculator Applications 4: Retail Calculations
Practice Test 4
Section 5 Stocks and Bonds
Lesson 27 Investments in Bonds
Lesson 28 Yields on Investments
Lesson 29 Selling Price of Stocks
Business Calculator Applications 5: Prices of Treasury Bonds and Notes |
Measures and Units - Involves properties of the physical world that can be measured, the units used to measure them and the process of measurement.
Number and Arithmetic - Involves types of numbers, their properties and number operations. The strand has strong links with Measures and Units, Algebra and Patterns and Chance and Data. It also has some links with Space and Geometry.
Space and Geometry - Involves the properties of two-dimensional and three-dimensional space.
There are differences in content across papers to ensure they are appropriate for year levels.
Papers A, B, C, D and E
Calculators are not permitted.
Formal algebra is not tested. The emphasis is put on pattern, structure and puzzles.
Formal geometry is not tested (except for a few items in Paper E). The emphasis is put on spatial skills.
Papers F, G, H, I and J
Calculators are required.
Formal algebra is tested. Students are expected to be familiar with some conventions of algebra.
Formal geometry is tested. Students are expected to be familiar with some conventions of geometry. |
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ConAdvanced Algebra II: Activities and Homework
Collection Properties
Summary: This is the main text of Kenny Felder's course in Advanced Algebra II. It consists of a series of worksheets, some intended to be used in class as group activities, and some intended to be used as homework assignments. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" ( and the "Advanced Algebra II: Teacher's Guide" ( collections to make up the entire course |
Chattahoochee Hills, GA Algebra working with you!The first part of Algebra, Algebra 1, is a summary of the ideas learned in the preliminary classes leading up Algebra 1. Depending on the curriculum, this may include the subjects I mentioned in prealgebra and precalculus and beyond that: exponential functions... |
College Algebra - 4th edition
Summary: Providing Strategies for Success: This text provides numerous strategies for success for both students and instructors. Instructors will find the book easier to use with such additions as an Annotated Instructor's Edition, instructor notes within the exercise sets, and an Insider's Guide. Students will find success through features including highlights, exercise hints, art annotations, critical thinking exercises, and pop quizzes, as well as procedures, strategies, a...show morend summaries. ...show less
Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Nonlinear Systems of Equations. Partial Fractions. Inequalities and Systems of Inequalities in Two Variables. Linear Programming.
6. Matrices and Determinants.
Solving Linear Systems Using Matrices. Operations with Matrices. Multiplication of Matrices. Inverses of Matrices. Solution of Linear Systems in Two Variables. Using Determinants. Solution of Linear Systems in Three Variables Using Determinants.
Nice condition with minor indications of previous handling2005 Hardcover Fair Acceptable condition and jacket is worn and taped on corners. Same day shipping. Thank you.
$9.45 +$3.99 s/h
Good
Quality School Texts OH Coshocton, OH
2005-12-29 Hardcover Good Names on inside cover and numbers on bookedge; no other internal marking/highlighting.
$14.97 |
is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow. |
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