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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
* Solid preparation for deeper study of functional analysis
* Chapter on elementary probability
* Comprehensive bibliography and index
* Solutions manual available to instructors upon request
By covering all the basics and developing rigor simultaneously, this introduction to real analysis is ideal for senior undergraduates and beginning graduate students, both as a classroom text or for self-study. With its wide range of topics and its view of real analysis in a larger context, the book will be appropriate for more advanced readers as well.
