Understanding Analysis
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This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.
* The Real Numbers • Sequences and Series • Basic Topology of R • Functional Limits and Continuity • The Derivative • Sequences and Series of Functions • The Riemann Integral • Additional Topics
