Introduction to Real Analysis

by Michael Schramm

This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upper-level undergraduates and graduate students of real analysis, it also provides a vital reference book for advanced courses in mathematics.The four-part treatment begins with an introduction to basic logical structures and techniques of proof, including discussions of the cardinality concept and the algebraic and order structures of the real and rational number systems. Part Two presents in-depth examinations of the completeness of the real number system and its topological structure. Part Three reviews and extends the previous explorations of the real number system, and the final part features a selection of topics in real function theory. Numerous and varied exercises range from articulating the steps omitted from examples and observing mechanical results at work to the completion of partial proofs within the text.

386 pages, Kindle Edition

First published May 11, 2012

Reviews

[Greg Tucker-kellogg · Rating 5 out of 5]

I picked up a paperback copy of this Dover book about 10 years ago. Real Analysis had been a conceptually challenging subject for me, and I wanted something to read on a long plane ride. For self-study, this book was exceptional. I worked my way through it, re-learned many things I thought I understood, improved my proof technique, and improved the rigor of my thinking on many mathematical topics.

Some time later (probably on another plane trip) I misplaced my copy, and ended up getting an ebook copy. I can't say I like the ebook nearly as much -- I dislike mathematical texts in ebook format -- but the content, writing, and organisation are still wonderful. Highly recommended.