Inverse Problems

Activities for Undergraduates

Author: C. W. Groetsch

Publisher: Cambridge University Press

ISBN: 9780883857168

Category: Mathematics

Page: 222

View: 301

Problem solving in mathematics is often thought of as a one way process. For example: take two numbers and multiply them together. However for each problem there is also an inverse problem which runs in the opposite direction: now take a number and find a pair of factors. Such problems are considerably more important, in mathematics and throughout science, than they might first appear. This book concentrates on these inverse problems and how they can be usefully introduced to undergraduate students. A historical introduction sets the scene and gives a cultural context for what the rest of the book. Chapters dealing with inverse problems in calculus, differential equations and linear algebra then follow and the book concludes with suggestions for further reading. Whatever their own field of expertise, this will be an essential purchase for anyone interested in the teaching of mathematics.

The Calculus Collection

A Resource for AP and Beyond

Author: Caren L. Diefenderfer,Roger B. Nelsen

Publisher: MAA

ISBN: 9780883857618

Category: Juvenile Nonfiction

Page: 507

View: 6360

The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.The MAA has twice previously issued a calculus reader, collecting articles on calculus from its journals: Selected Papers in Calculus, published in 1969 and reprinted as Part I of A Century of Calculus, and Part II published in 1992. In a sense The Calculus Collection is the third volume in that series, but different in that it is a collection chosen for its usefulness to those who teach first-year calculus in high schools as well as colleges and universities.

Excursions in Classical Analysis

Pathways to Advanced Problem Solving and Undergraduate Research

Author: Hongwei Chen

Publisher: MAA

ISBN: 0883857685

Category: Mathematics

Page: 301

View: 8142

Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof.The author presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that might at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis.The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.

Methods for Euclidean Geometry

Author: Owen Byer,Felix Lazebnik,Deirdre L. Smeltzer

Publisher: MAA

ISBN: 0883857634

Category: Mathematics

Page: 461

View: 1502

Methods for Euclidean Geometry explores one of the oldest and most beautiful of mathematical subjects. The book begins with a thorough presentation of classical solution methods for plane geometry problems, but its distinguishing feature is the subsequent collection of methods which have appeared since 1600. For example, the coordinate method, which is a central part of the book, has been part of mathematics for four centuries. However, it has rarely served as a tool that students consider using when faced with geometry problems. The same holds true regarding the use of trigonometry, vectors, complex numbers, and transformations. The book presents each of these as self-contained topics, providing examples of their applications to geometry problems. Both strengths and weaknesses of various methods, as well as the ranges of their effective applications, are discussed. Importance is placed on the problems and their solutions. The book contains numerous problems of varying difficulty; over a third of its contents are devoted to problem statements, hints, and complete solutions. The book can be used as a textbook for geometry courses; as a source book for geometry and other mathematics courses; for capstone, problem-solving, and enrichment courses; and for independent study courses.

Books in Print

Author: R.R. Bowker Company

Publisher: N.A


Category: American literature

Page: N.A

View: 9489

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Mathematics for Business Decisions: Calculus and optimization

Author: Richard B. Thompson

Publisher: Mathematical Assn of Amer

ISBN: 9780883857311

Category: Business & Economics

Page: N.A

View: 2576

Students are allowed to learn mathematics in a setting that mirrors the professional environment they will encounter after college.

Anschauliche Geometrie

Author: David Hilbert,Stefan Cohn-Vossen

Publisher: Springer-Verlag

ISBN: 3662366851

Category: Mathematics

Page: 312

View: 9525

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Beweise und Widerlegungen

Die Logik mathematischer Entdeckungen

Author: Imre Lakatos

Publisher: Springer-Verlag

ISBN: 3663001962

Category: Mathematics

Page: 163

View: 3556


Enabling Students in Mathematics

A Three-Dimensional Perspective for Teaching Mathematics in Grades 6-12

Author: Gordon Marshall

Publisher: Springer

ISBN: 3319254065

Category: Education

Page: 147

View: 1523

This book addresses the cognitive, social, and psychological dimensions that shape students’ mathematics experience to help students become more capable, cooperative, and confident in the process of engaging mathematics. In these ways they can have a more valuable and enjoyable mathematics experience, and become more valued participants in society. The book focuses on the mathematics classroom for students grades six to twelve and how students can become more successful mathematical thinkers, in addition to how the curriculum could be presented so as to provide a more engaging mathematics experience.

Algebra for College Students

Author: Jerome E. Kaufmann,Karen L. Schwitters

Publisher: Cengage Learning

ISBN: 1285195787

Category: Mathematics

Page: 864

View: 4989

Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics courses. Algebraic ideas are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism. The open and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad range of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. The text's resource package—anchored by Enhanced WebAssign, an online homework management tool—saves instructors time while also providing additional help and skill-building practice for students outside of class. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Research in education

Author: Educational Research Information Center (U.S.)

Publisher: N.A


Category: Education

Page: N.A

View: 354


Lernen sichtbar machen

Author: John Hattie

Publisher: N.A

ISBN: 9783834011909

Category: Effective teaching

Page: 420

View: 5069