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.
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LibraryThing ReviewUser Review - aethercowboy - LibraryThing
If you have ever wanted to push the envelope for your mathematical learning, I suggest reading this book. It is an overview of mathematical analysis, involving rigorous proofs. The book is small, but it is filled to the brim with knowledge. A must for any serious student of mathematics. Read full review
This book has a very clear writing style, and the exercises are illustrative of the concepts discussed. I also like that the author grounds the math in a historical context-- it makes the material richer for the reader.
I have looked at a lot of analysis books, and this is among the best. Another I really like is The Way of Analysis. I think these two are some of the best for understanding the material.
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Limited preview - 2004