Understanding AnalysisThis elementary presentation exposes readers 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 is 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. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions. 
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LibraryThing Review
User Review  aethercowboy  LibraryThingIf 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.
Contents
II  xi 
IV  2 
V  11 
VI  16 
VII  27 
VIII  31 
IX  33 
XI  36 
XXXIII  125 
XXXIV  127 
XXXVII  129 
XXXVIII  135 
XXXIX  142 
XL  146 
XLI  149 
XLII  152 
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References to this book
Capture Dynamics and Chaotic Motions in Celestial Mechanics: With ... Edward Belbruno Limited preview  2004 