**AMS/MAA Textbooks**

Volume: 10;
2007;
339 pp;
Softcover

**Print ISBN: 978-1-4704-6904-7
Product Code: TEXT/10.S**

List Price: $65.00

AMS Member Price: $48.75

MAA Member Price: $48.75

**Electronic ISBN: 978-1-61444-623-1
Product Code: TEXT/10.E**

List Price: $65.00

AMS Member Price: $48.75

MAA Member Price: $48.75

# A Radical Approach to Real Analysis: Second Edition

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*David Bressoud*

MAA Press: An Imprint of the American Mathematical Society

In this second edition of the 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, 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.

# Table of Contents

## A Radical Approach to Real Analysis: Second Edition

- Cover cover11
- copyright page ii3
- Preface ix10
- Contents xv16
- 1 Crisis in Mathematics: Fourier’s Series 118
- 2 Infinite Summations 926
- 3 Differentiability and Continuity 5774
- 4 The Convergence of Infinite Series 117134
- 5 Understanding Infinite Series 171188
- 6 Return to Fourier Series 217234
- 7 Epilogue 267284
- Appendix A Explorations of the Infinite 271288
- Appendix B Bibliography 303320
- Appendix C Hints to Selected Exercises 305322
- Index 317334
- Back cover 323340