Introduction to Real Analysis

by Michael J. 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.

Genres: Mathematics

384 pages, Paperback

First published August 1, 1995

Reviews

[Darin · Rating 4 out of 5]

If you prefer the theorem-proof approach of most math books, you won't like this book. This book does have theorems and proofs, but most of text consists of the author explaining why things work the way they do. This makes it great for seeing the big picture. I actually enjoyed reading the book.

Note that I believe (and follow) the meanings Goodreads gives for what each number of stars means. Therefore, the majority of my ratings are 3 stars ("liked it").

[Charles Paul · Rating 5 out of 5]

Best textbook I've ever read. Also the only textbook I've ever read that requires a flow chart to communicate what order to read the chapters in.

Really fostered and furthered my love of mathematics.