Understanding Analysis

Front Cover
Springer Science & Business Media, Jan 12, 2001 - Mathematics - 257 pages
11 Reviews
This 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 - 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

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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

XII
42
XIII
48
XIV
53
XV
56
XVI
60
XVII
67
XVIII
71
XIX
73
XXII
76
XXIII
82
XXIV
87
XXV
92
XXVI
94
XXVII
97
XXVIII
101
XXIX
107
XXX
112
XXXI
118
XXXII
123
XLIII
162
XLIV
165
XLV
167
XLVI
174
XLVII
179
XLVIII
181
LI
184
LII
189
LIII
193
LIV
197
LV
201
LVI
208
LVII
211
LVIII
220
LIX
226
LX
241
LXI
249
LXII
251
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