Main 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.
- 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
Review quote:
"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
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
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.
- 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
Review quote:
"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
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