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.
Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.
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.
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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