John M. Erdman
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|License||Creative Commons Attribution-Noncommercial-Share Alike 2.5|
- Current version July 1, 2014
- 29 chapters, 377 pages
- No print version
- Exercises with solutions at the back
- Additional problems without solutions
- For more information and to download
This text is designed for a year long real analysis course at the advanced undergraduate level. It is both a textbook and a well-structured problem set. It is carefully laid out so that nothing has to be relearned in the transition from real valued functions to vector valued functions. It can be used for self-study by an independent student or for review, and it provides an excellent background for the traditional graduate course in real analysis. From the preface:
The proofs of most of the major results are either exercises or problems. The distinction here is that solutions to exercises are written out in a separate chapter in the ProblemText while solutions to problems are not given. I hope that this arrangement will provide flexibility for instructors who wish to use it as a text. For those who prefer a (modified) Moore-style development, where students work out and present most of the material, there is a quite large collection of problems for them to hone their skills on. For instructors who prefer a lecture format, it should be easy to base a coherent series of lectures on the presentation of solutions to thoughtfully chosen problems.
The approach is more sophisticated than the usual text and shows the influence of the now classic textbooks by Dieudonné and Loomis and Sternberg. For example, the sections on integration use the Cauchy integral, which is based on the uniform completion of step functions, rather than the Riemann integral.