A radical approach to real analysis. (English) Zbl 0796.26001

Bressoud, David M.

Classroom Resource Materials. 2. Washington, DC: The Mathematical Association of America. xii, 324 p. (1994).

This book, designed to be a first encounter with real analysis, departs from the standard format. The topics considered revolve around questions raised in 1807 when Fourier astounded some of his contemporaries by asserting that an arbitrary function could be expressed as a linear combination of sines and cosines. Much of the development of modern mathematical analysis has been profoundly influenced by the search for answers to these questions, and the author has carefully structured this book around that search. The author asserts that this is not a history of analysis. But it is a well crafted story about the history of the restructuring of analysis that was influenced by Fourier’s work.
The book can be recommended as a resource for instructors, and as collateral reading for students who may wonder how and why the early pioneers developed concepts such as continuity, differentiability, integrability, and uniform convergence.

Reviewer: T.M.Apostol (Pasadena)

MSC:

26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
01-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography

Keywords:

real analysis; Fourier