Synopsis
A Course in Real Analysis offers more for the student, incorporating sound pedagogical techniques and a breadth of examples and exercises. Professors McDonald and Weiss have written an inspiring text in a contemporary style suitable for graduate or advanced undergraduate course work.
The authors present the elements of measure and integration by first discussing the Lebesgue theory on the line and then the abstract theory. Other chapters include probability theory, differentiation, topological and metric spaces, approximation, and Hilbert, Banach, and locally convex spaces. Application chapters examine harmonic analysis and measurable dynamical systems.
A Course in Real Analysis includes:
• Motivation of Key Concepts—The importance of and rationale behind key ideas are made transparent.
• Illustrative Examples—Roughly 200 examples are presented to illustrate definitions and results.
• Abundant and Varied Exercises—Over 1200 exercises are provided to promote understanding.
• Biographies—Each chapter begins with a brief biography of a famous mathematician.
"This is a beautifully written text. There is an excellent choice of topics and results, topics are well motivated, proofs are precise and very readable, and there are lots of meaningful examples and useful exercises."
—Bruce A. Barnes, University of Oregon
"This text provides the 'between the lines' insight that many students need. The greatest strengths of the text are the order of topics, the inclusion of all major ideas of the theory, the easy readability, and the strong motivation and tight organization of topics.
—Dennis D. Berkey, Boston University
"The authors' exposition is extremely clear. There is literary quality in the writing that is rare in mathematics texts. It is a pleasure to read this text."
—Peter L. Duren, University of Michigan
Booknews
A textbook for a one-year course at the graduate or advanced undergraduate level, incorporating pedagogical techniques not often found in such treatments. Encompasses set theory, real numbers, and calculus; measure, integration, and differentiation; topological, metric, and normed spaces; and harmonic analysis and dynamical systems. Suggests various ways of presenting the material. Includes a biographical sketch of a famous mathematician at the beginning of each chapter. No bibliography. Annotation c. Book News, Inc., Portland, OR (booknews.com)