A Radical Approach to Real Analysis (Classroom Resource Materials) - Softcover

David Bressoud

Softcover

ISBN 10: 0883857014 ISBN 13: 9780883857014

Publisher: The Mathematical Association of America, 1996

Synopsis

This book is an undergraduate introduction to real analysis. Teachers can use it as a textbook for an innovative course, or as a resource for a traditional course. Students who have been through a traditional course, but do not understand what real analysis is about and why it was created, will find answers to many of their questions in this book. Although this is not a history of analysis, the author returns to the roots of the subject to make it more comprehensible. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early nineteenth century. Cauchy's attempts to establish a firm foundation for calculus follow, and the author considers his failures and his successes. The book culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof. Mathematica ® commands and programs are included in the exercises. However, the reader may use any mathematical tool that has graphing capabilities, including the graphing calculator.

About this title

Book Description

This book is an undergraduate introduction to real analysis. Teachers can use it as a textbook for an innovative course, or as a resource for a traditional course. Students who have been through a traditional course, but do not understand what real analysis is about and why it was created, will find answers to many of their questions in this book.

From the Inside Flap

In the second edition of this MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, or as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier’s introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy’s attempts to establish a firm foundation for calculus, and considers his failures as well as his successes. It culminates with Dirichlet’s proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet’s proof.

Edition details

• Publisher: The Mathematical Association of America
• Publication date: 1996
• ISBN 10: 0883857014
• ISBN 13: 9780883857014
• Binding: Paperback
• Language: English
• Number of pages: 336