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Real Analysis and Foundations is an advanced undergraduate and first-year graduate textbook that introduces students to introductory topics in real analysis (or real variables), point set topology, and the calculus of variations. This classroom-tested book features over 350 end-of-chapter exercises that clearly develop and reinforce conceptual topics. It also provides an excellent review chapter on math foundations topics, as well as accessible coverage of classical topics, such as Weirstrass Approximation Theorem, Ascoli-Arzela Theorem and Schroeder-Bernstein Theorem. Explanations and discussions of key concepts are so well done that Real Analysis and Foundations will also provide valuable information for professional aerospace and structural engineers.
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The book is recommended as a source for middle-level mathematical courses. It can be used not only at mathematical department, but also by physicists, engineers, economists and other experts in applied sciences who want to understand the main ideas of Analysis in order to use them at the study of mathematical models of different type processes.
The book contains many well-chosen examples and each of the fifteen chapters is followed by almost 500 exercises. ...Illustrative pictures are instructive and the design of the book makes reading it a real pleasure. The book can be recommended for university libraries, teachers, and students.
-EMS Newsletter, Dec. 2005
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