A Course in Real Analysis
By- John McDonald, Arizona State University, Tempe, U.S.A.
- Neil Weiss, Areas of Expertise: Analysis, Probability, and Statistics Affiliation: School of Mathematical and Statistical Sciences Arizona State University, Tempe, U.S.A.
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.
Hardbound, 745 Pages
Published: January 1999
Imprint: Academic Press
ISBN: 978-0-12-742830-7
Reviews
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"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
Contents
- Set TheoryThe Real Numbers and CalculusLebesque Theory on the Real LineMeasure TheoryElements of ProbabilityDifferentiationElements of Topological and Metric SpacesCompleteness, Compactness, and ApproximationHilbert SpacesClassical Banach SpacesBasic Theory of Normed and Locally Convex SpacesElements of Harmonic AnalysisMeasurable Dynamical SystemsIndex
