Description

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.

Key Features

@bul:* 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

Readership

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

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

Details

No. of pages:
745
Language:
English
Copyright:
© 1999
Published:
Imprint:
Academic Press
Print ISBN:
9780127428307
Electronic ISBN:
9780080498461

About the authors

John McDonald

Affiliations and Expertise

Arizona State University, Tempe, U.S.A.

Neil Weiss

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

Affiliations and Expertise

(deceased) - Areas of Expertise: Analysis, Probability, and Statistics.

Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, U.S.A.

Please contact Gerardo Lafferriere (gerardolf@gmail.com) for the solution manual's files.

Reviews

"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