Reviews: Bartle and Sherbert, Real Analysis

This is a superb introductory text on real analysis. It is the recommended text for first year undergraduates at the University of Oxford and covers sequences, series, limits, continuity, differentiation, integration, and uniform convergence. There is even a short section on Lebesgue integration.

The book is rigourous yet readable, contains copious exercises and is complemented with short biographies of famous mathematicians, adding a human touch to the proceedings.

The authors eschew the more informal style of some introductory texts and prepare the students for the Definition - Lemma - Theorem technique of higher mathematics. It can be somewhat terse in places, but this has the advantage of focussing the student's mind on the essentials.