A Course in Real Analysis
- 1st Edition - January 12, 1999
- Authors: John N. McDonald, Neil A. Weiss
- Language: English
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 studen… Read more
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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.
@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
* 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
One-year courses in real analysis for undergraduate and first-year graduate courses; primarily for mathematics majors, requires advanced calculus.
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
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
"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
- Edition: 1
- Published: January 12, 1999
- Language: English
JM
John N. McDonald
Affiliations and expertise
Arizona State University, Tempe, U.S.A.NW
Neil A. 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.
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 at [email protected] for more information.