## New MAA Book: A Guide to Real Variables

July 23, 2009

A Guide to Real Variables
Steven G. Krantz
163 pp., hardcover, 2009. Series: MAA Guides #3
ISBN: 978-0-88385-344-3

Dedicated to G.H. Hardy and J. E. Littlewood, "our role models," Steven G. Krantz's A Guide to Real Variables serves as an aid and conceptual support for students studying real analysis. It concentrates on concepts, results, examples, and illustrative figures rather than details of proofs. Core topics are sequences, series, modes of convergence, the derivative, the integral, and metric spaces. Basic examples such as the Cantor set; the Weierstrass nowhere differentiable function; the Weierstrass approximation theorem; the Baire category theorem; and the Ascoli-Arzela theorem are also treated.

Highlights:
• Approaches the subject of real analysis at the introductory level and aims to ground students in concepts central to advanced real analysis.
• Covers the core material for an undergraduate real analysis course.
• Useful to students preparing for qualifying exams.
• Contains a glossary of terms from real variable theory.

Excerpt:
Preface (p. xv). The importance and centrality of real analysis is certainly confirmed by the fact that virtually every graduate program in the country—indeed, in the world—requires its students to take a qualifying exam in the subject. We are exposed to real analysis, both at the undergraduate and graduate levels. Today, analysis has assumed a newly prominent position in the infrastructure because of many new engineering applications such as wavelets, and also new financial applications such as the Black-Scholes theory of option pricing.

Contents:
Preface 1. Basics 2. Sequences 3. Series 4. The Topology of the Real Line 5. Limits and the Continuity of functions 6. The Derivative 7. The Integral 8. Sequences and Series of Functions 9. Advanced Topics Glossary of Terms from Real Variable Theory. Bibliography. Index.