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A Course in Real Analysis / Edition 2

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Overview

A Course in Real Analysis provides a firm foundation in real analysis concepts and principles while presenting a

broad range of topics in a clear and concise manner. This student-oriented text balances theory and applications, and contains a

wealth of examples and exercises. Throughout the text, the authors adhere to the idea that most students learn more efficiently

by progressing from the concrete to the abstract. McDonald and Weiss have also created real application chapters on

probability theory, harmonic analysis, and dynamical systems theory. The text offers considerable flexibility in the choice of

material to cover.

Audience: Intended for a one-year course in real analysis for undergraduate and first-year graduate courses. Primarily for mathematics majors and requires advanced calculus.

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Editorial Reviews

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)
From the Publisher

"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."--Zentralblatt MATH 2012-1239-26003 "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

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Product Details

  • ISBN-13: 9780123877741
  • Publisher: Elsevier Science
  • Publication date: 1/27/2012
  • Edition description: New Edition
  • Edition number: 2
  • Pages: 688
  • Product dimensions: 7.60 (w) x 9.30 (h) x 1.20 (d)

Meet the Author

Neil A. Weiss 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.

In his spare time, Weiss enjoys walking and studying and practicing meditation. He is married and has two sons and three grandchildren.

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Table of Contents

Preface
Pt. 1 Set Theory, Real Numbers, and Calculus
1 Set Theory
Biography: Georg Cantor
2 The Real Number System and Calculus
Biography: Georg Friedrich Bernhard Riemann
Pt. 2 Measure, Integration, and Differentiation
3 Lebesgue Theory on the Real Line
Biography: Emile Felix-Edouard-Justin Borel
4 Measure Theory
Biography: Henri Leon Lebesgue
5 Elements of Probability
Biography: Andrei Nikolaevich Kolmogorov
6 Differentiation
Biography: Johann Radon
Pt. 3 Topological, Metric, and Normed Spaces
7 Elements of Topological, Metric, and Normed Spaces
Biography: Pavel Samuilovich Urysohn
8 Complete Spaces, Compact Spaces, and Approximation
Biography: Marshall Harvey Stone
9 Hilbert Spaces and the Classical Banach Spaces
Biography: David Hilbert
10 Basic Theory of Normed and Locally Convex Spaces
Biography: Stefan Banach
Pt. 4 Harmonic Analysis and Dynamical Systems
11 Elements of Harmonic Analysis
Biography: Ingrid Daubechies
12 Measurable Dynamical Systems
Biography: Claude Elwood Shannon
Index
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