A Radical Approach to Real Analysis - Brossura

Bressoud, David

Brossura

ISBN 10: 0883857014 ISBN 13: 9780883857014

Casa editrice: The Mathematical Association of America, 1996

Riassunto

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.

Su questo libro

Recensione:

'What is radical about this book as real analysis books go, is its stronger historical approach ... The past decade or so has witnessed the appearance of a substantial number of 'bridge the gap' introductions to real analysis which lead the students at a gentler pace through the fundamentals of real analysis according to the traditional syllabus. It is well worth considering whether students in their first undergraduate real analysis course might be better served by a radical approach such as Bressoud's.' Mathematical Reviews

Descrizione del libro:

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.

Su questa edizione

• Editore: The Mathematical Association of America
• Data di pubblicazione: 1996
• ISBN 10: 0883857014
• ISBN 13: 9780883857014
• Rilegatura: Copertina flessibile
• Numero di pagine: 336