Articles liés à A Radical Approach to Real Analysis

A Radical Approach to Real Analysis - Couverture souple

Bressoud, David

 
9780883857014: A Radical Approach to Real Analysis
Couverture souple
ISBN 10 : 0883857014 ISBN 13 : 9780883857014
Editeur : 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.

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Présentation de l'éditeur

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.

Revue de presse

'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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
The Mathematical Association of America
Date d'édition
1996
Langue
anglais
ISBN 10 
0883857014
ISBN 13 
9780883857014
Reliure
Broché
Nombre de pages
336
Coordonnées du fabricant
non disponible
Personne responsable
non disponible