Elementary Real and Complex Analysis (Dover Books on Mathematics)

✍ Scribed by Georgi E. Shilov

• Publisher: Dover Publications
• Year: 1996
• Tongue: English
• Leaves: 526
• Series: Dover Books on Mathematics
• Edition: Revised
• Category: Library

✦ Synopsis

Can't beat the price, and the material is well-presented and organized, but it's stripped down to the bare essentials - theorem, proof, lemma, corollary, etc. It's not a book on proof methodology, for sure. I graduated with a degree in computer science, but I haven't done a proof for a while and never took a class beyond linear algebra, and I wanted to teach myself analysis. While I don't find the material too difficult to follow, I really don't find it all that great for self-study. The book yields conclusion after conclusion, but among all the results, I find the text doesn't do a great job of conveying its methodology. In other words, the book spends the vast majority of the time developing new results (the "what" of analysis), but it does little to prepare the reader to understand the "how" of analysis. I feel as though the book is giving me a fish, rather than teaching me to fish.And there are some idiosyncracies. You need to be wary of an occasionally swapped subscript, for instance. And in chapter 1 problem 5: Which is larger, Sqrt(3) + Sqrt(5) or Sqrt(2) + Sqrt(6)? The answer in the back of the book is plain wrong. And the book proves something as fundamental as the uniqueness of 1; and yet it invokes the binomial theorem out of the blue?Anyway, the price is right, but beware that it might make a better reference or a collection of examples than a primary self-study guide. It's not that it's "too easy" as one reader put it; rather, it doesn't integrate the material with exercises and explanations well enough for my liking.

✦ Table of Contents

Title......Page 1
Contents......Page 3
Preface......Page 7
1 Real Numbers......Page 11
2 Sets......Page 37
3 Metric Spaces......Page 63
4 Limits......Page 109
5 Continuous Functions......Page 142
6 Series......Page 196
7 The Derivative......Page 233
8 Higher Derivatives......Page 259
9 The Integral......Page 284
10 Analytic Functions......Page 383
11 Improper Integrals......Page 441
Appendix A Elementary Symbolic Logic......Page 492
Appendix B Measure and Integration on a Compact Metric Space......Page 494
Selected Hints and Answers......Page 499
Index......Page 515