| Softcover ISBN: | 978-1-4704-6904-7 |
| Product Code: | TEXT/10.S |
| List Price: | $75.00 |
| MAA Member Price: | $56.25 |
| AMS Member Price: | $56.25 |
| eBook ISBN: | 978-1-61444-623-1 |
| Product Code: | TEXT/10.E |
| List Price: | $69.00 |
| MAA Member Price: | $51.75 |
| AMS Member Price: | $51.75 |
| Softcover ISBN: | 978-1-4704-6904-7 |
| eBook: ISBN: | 978-1-61444-623-1 |
| Product Code: | TEXT/10.S.B |
| List Price: | $144.00 $109.50 |
| MAA Member Price: | $108.00 $82.13 |
| AMS Member Price: | $108.00 $82.13 |
| Softcover ISBN: | 978-1-4704-6904-7 |
| Product Code: | TEXT/10.S |
| List Price: | $75.00 |
| MAA Member Price: | $56.25 |
| AMS Member Price: | $56.25 |
| eBook ISBN: | 978-1-61444-623-1 |
| Product Code: | TEXT/10.E |
| List Price: | $69.00 |
| MAA Member Price: | $51.75 |
| AMS Member Price: | $51.75 |
| Softcover ISBN: | 978-1-4704-6904-7 |
| eBook ISBN: | 978-1-61444-623-1 |
| Product Code: | TEXT/10.S.B |
| List Price: | $144.00 $109.50 |
| MAA Member Price: | $108.00 $82.13 |
| AMS Member Price: | $108.00 $82.13 |
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Book DetailsAMS/MAA TextbooksVolume: 10; 2007; 339 pp
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.
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Table of Contents
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Chapters
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Chapter 1. Crisis in Mathematics: Fourier’s Series
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Chapter 2. Infinite Summations
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Chapter 3. Differentiability and Continuity
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Chapter 4. The Convergence of Infinite Series
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Chapter 5. Understanding Infinite Series
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Chapter 6. Return to Fourier Series
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Chapter 7. Epilogue
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Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
-
Chapters
-
Chapter 1. Crisis in Mathematics: Fourier’s Series
-
Chapter 2. Infinite Summations
-
Chapter 3. Differentiability and Continuity
-
Chapter 4. The Convergence of Infinite Series
-
Chapter 5. Understanding Infinite Series
-
Chapter 6. Return to Fourier Series
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Chapter 7. Epilogue
