New MAA Book: A Guide to Advanced Real Analysis

July 23, 2009

A Guide to Advanced Real Analysis
Gerald B. Folland
117 pp., hardcover, 2009. Series: MAA Guides #2; Doliciani Mathematical Expositions #37
ISBN: 978-0-88385-343-6

The second publication in the MAA Guides series, this book is a concise introduction to real analysis, covering the core material of a graduate-level real analysis course. On an abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On a more concrete level, it deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions.

Highlights:

• Covers the core material found in a graduate course on real analysis.
• Gives an overview of the subject so that it can be used as a guide for a beginner or as a refresher for those who have previously studied the subject.
• Provides essential definitions, major theorems, and key ideas of proofs without the technical details.

Excerpt:

Metric Spaces (p. 5). The early years of the twentieth century witnessed a great increase in the level of abstraction and generality in mathematical thinking. In particular, mathematicians at that time developed theories that provide a very general setting for studying the circle of ideas related to limits and continuity, which previously had been considered in the context of subsets of Euclidean space or functions of one or several real or complex variables.

The most straightforward generalizations of Euclidean space for this purpose is the notion of metric space.

Contents:
Preface. Prologue: Notation, Terminology, and Set Theory. 1. Topology 2. Measure and Integration: General Theory 3. Measure and Integration: Constructions and Special Examples 4. Rudiments of Functional Analysis 5. Function Spaces 6. Topics in Analysis on Euclidean Space. Bibliography. Index.

About the Author:
Gerald B. Folland (University of Washington) has written textbooks and monographs in the areas of real analysis, harmonic analysis, partial differential equations, and mathematical physics.

Order A Guide to Advanced Real Analysis from the MAA Bookstore or call 1.800.331.1622.
List: $49.95
MAA Member Price: $39.95