The Elements of Real Analysis

by Robert G. Bartle

Presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.

Genres: Mathematics, Textbooks

496 pages, Paperback

Published January 16, 1976

Reviews

[Ryan Wans · Rating 4 out of 5]

Provides an equally rigorous and in-depth introduction of real analysis to Rudin's Principle's of Real Analysis. More emphasis is placed on topological approaches than in other analysis textbooks I've sampled. For example, most theorems and definitions will provide a metric, topological, and sequential approach. Concepts such as cluster points and other topological approaches are favored and in fact this is how Bolzano-Weirestrass is first given. I actually quite liked this aspect, along with the respectable exercises and rigor maintained throughout. One quirk is the emphasis on Jordan content and its usage in integration, but I actually found myself enjoying this section. It connects very nicely to Munkres’ Analysis on Manifolds. Who needs the Lebesgue measure anyway?