Basic Real Analysis [Paperback]

Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.

One of the bedrocks of any mathematics education, the study of real analysis introduces students both to mathematical rigor and to the deep theorems and counterexamples that arise from such rigor: for instance, the construction of number systems, the Cantor Set, the Weierstrass nowhere differentiable function, and the Weierstrass approximation theorem. Basic Real Analysis is a modern, systematic text that presents the fundamentals and touchstone results of the subject in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language.

Key features include:

* A broad view of mathematics throughout the book

* Treatment of all concepts for real numbers first, with extensions to metric spaces later, in a separate chapter

* Elegant proofs

* Excellent choice of topics

* Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter

* Emphasis on monotone functions throughout

* Good development of integration theory

* Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis