A Course in Real Analysis

by John N. McDonald, Neil A. Weiss

Overview

The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference.

Product Details

ISBN-13:	9780123877741
Publisher:	Elsevier Science
Publication date:	01/13/2012
Edition description:	New Edition
Pages:	688
Product dimensions:	7.60(w) x 9.30(h) x 1.20(d)

About the Author

Neil A. Weiss (deceased) received his Ph.D. from UCLA and subsequently accepted an assistant-professor position at Arizona State University (ASU), where he was ultimately promoted to the rank of full professor. Weiss has taught mathematics, probability, statistics, and operations research from the freshman level to the advanced graduate level.

In recognition of his excellence in teaching, he received the Dean’s Quality Teaching Award from the ASU College of Liberal Arts and Sciences. He has also been runner-up twice for the Charles Wexler Teaching Award in the ASU School of Mathematical and Statistical Sciences. Weiss’s comprehensive knowledge and experience ensures that his texts are mathematically accurate, as well as pedagogically sound.

Weiss has published research papers in both theoretical and applied mathematics, including probability, engineering, operations research, numerical analysis, and psychology. He has also published several teaching-related papers.

In addition to his numerous research publications, Weiss has authored or coauthored books in real analysis, probability, statistics, and finite mathematics. His texts-well known for their precision, readability, and pedagogical excellence-are used worldwide.

Table of Contents

Set Theory.

The Real Numbers and Calculus.

Lebesque Theory on the Real Line.

Measure Theory. Elements of Probability.

Differentiation. Elements of Topological and Metric Spaces.

Completeness, Compactness, and Approximation.

Hilbert Spaces.

Classical Banach Spaces.

Basic Theory of Normed and Locally Convex Spaces.

Elements of Harmonic Analysis. Measurable Dynamical Systems.

Index.

qu:"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."

source:—Bruce A. Barnes, University of Oregon

qu:"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.

source:—Dennis D. Berkey, Boston University

qu:"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."

source:—Peter L. Duren, University of Michigan

What People are Saying About This

From the Publisher

This is a core textbook for a course in real analysis appropriate for students at the upper undergraduate and graduate levels. Sample content available on a companion site, copy and paste this URL into your browser: http://www.elsevierdirect.com/v2/companion.jsp?ISBN=9780123877741Scroll down for more information!

Editorial Reviews

"...truly marvelous...weaves an interesting, lively, and crystal clear sequence of ideas comprising the heart of modern analysis. The order of presentation is so carefully chosen and the exposition is so masterful as to possess the traits of a literary art form." —MAA Reviews, January 2015

"The exposition is very clear and unhurried and the book would be useful both as a text and a book for self-study. The last chapters go beyond what is usually covered in analysis courses and this is all to the good." —Sigurdur Helgason, MIT

"There is a literary quality in the writing that is rare in mathematics texts. It is a pleasure to read this book. The exercises are a strong feature of the book and the examples are well chosen and plentiful." —Peter Duren, University of Michigan

"The outstanding features of the book are the wealth of examples and exercises, the interesting biographical data, and the introduction to wavelets and dynamical systems." —Duong H. Phong, Columbia University

"McDonald and Weiss have crafted a treasure chest of exercises in real analysis. Just an amazing and broad collection. Students and researchers will surely benefit from the enormous amount of superb exercises." —Enno Lenzmann, University of Copenhagen

"I was very impressed by the motivating discussions of a number of difficult concepts, along with their fresh approach to the details following. Their general philosophy of starting with concrete ideas, and slowly abstracting, worked well in communicating even the most difficult concepts in the course." —Todd Kemp, University of California, San Diego

From the Publisher

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)

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