A Radical Approach to Real Analysis
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A Radical Approach to Real Analysis: (MAA Textbooks)

A Radical Approach to Real Analysis: (MAA Textbooks)


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About the Book

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:
Preface; 1. Crisis in mathematics: Fourier's series; 2. Infinite summations; 3. Differentiability and continuity; 4. The convergence of infinite series; 5. Understanding infinite series; 6. Return to Fourier series; 7. Epilogue; A. Explorations of the infinite; B. Bibliography; C. Hints to selected exercises.

About the Author :
David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College, Minnesota. He is Chair of the MAA Committee on the Undergraduate Program in Mathematics and Chair-Elect of the MAA Special Interest Group on Teaching Advanced High School Mathematics.

Review :
1st edition: '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 undergraduate real analysis course might be better served by a radical approach such as Bressoud's.' G. A. Heuer, Mathematical Reviews 1st edition: 'It will appeal as a text; it should be in every library as a reference.' Wayne Roberts, Choice


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Product Details
  • ISBN-13: 9780883857472
  • Publisher: Mathematical Association of America
  • Publisher Imprint: Mathematical Association of America
  • Edition: New edition
  • Language: English
  • Returnable: Y
  • Spine Width: 23 mm
  • Width: 152 mm
  • ISBN-10: 0883857472
  • Publisher Date: 30 Mar 2018
  • Binding: Hardback
  • Height: 229 mm
  • No of Pages: 339
  • Series Title: MAA Textbooks
  • Weight: 740 gr


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