Understanding Real Analysis

Understanding Real Analysis by Zorn, Paul. hardcover edition. ISBN: 9781568814155.

This book is a one-semester text for an introduction to real analysis. The authors primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas, and to see how definitions, proofs, examples, and other forms of mathematical "apparatus" work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques.