Introductory Real Analysis
Introductory Real Analysis

Introductory Real Analysis
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Dover Publications

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978048661226

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Comprehensive, elementary introduction to real and functional analysis. Self-contained, readily accessible to those with background in advanced calculus. Cover basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, much more. 350 problems.
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Introductory Real Analysis Specs:
Product NameIntroductory Real Analysis
ManufacturerDover Publications
Product Number MPN0486612260
Retail Price $15.95
EAN-1409780486612263
UPC978048661226
EAN-1497804866122632
Specifications 
TitleIntroductory Real Analysis
ISBN0486612260
Author(s)A. N. Kolmogorov, S. V. Fomin
Release Date1975-06-01
FormatPaperback
Num of Pages403
Num. of Items1
EAN9780486612263
Deal first added on:22-February-2004

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Latest 6 Reviews
Here is what people are saying about the Introductory Real Analysis
4 Star Rating  "Good intermediate math book"2008-09-24
- Reviewed By Carlos U. from Quito, Ecuador
This is a very good intermediate math book. I used it to write my undergraduate monograph and it actually helped a lot (I'm an economics student). However, it is difficult to understand without the help of other books. In fact, if you want to use this book I recommend to get also: "Topology" by Munkres and "The Way of Analysis" by Robert Strichatz. They all make a very useful math kit and if you are thinking in a Ph.D. in economics they can help you a lot if you read them (not all, buy selected chapters) before you start the math review at the begining of the Ph.D. program.
 
1 Star Rating  "DON'T buy this book!"2008-07-10
- Reviewed By W. Ghost from Brazil
This is not the original work. Just like Emily Dickinson's poems, sometimes you get an "edited" version of a beautiful mathematical work. I am SO sorry that I bought this book. Besides the problem with messing with a finished work, there are serious errors in proofs all over the book.

Get Elements of the Theory of Functions and Functional Analysis instead (also by Dover).
 
4 Star Rating  "Not A Bad Book"2008-05-17
- Reviewed By Patrick from Nassau, Bahamas
I didn't like this book at first because it wasn't what I expected. I think the word "introductory" should be removed from the title. It's actually not an introductory book. I would recommend this book for graduate studies. Most real analysis courses at the graduate level focus on the measure theory and integration. However, I appreciate this book more now.
 
3 Star Rating  "A good read with too many mistakes"2008-03-15
- Reviewed By Jonathan Emberton from Chicago, IL
The advantages of this text have been pointed out by other readers, so I will attempt to exhibit the problems of this book.

There are a lot of mistakes. And by 'a lot', I mean that the careful reader should be able to find at least 5 mathematical mistakes in each chapter. I used this text mainly as a supplement to a fairly advanced analysis course, and we'd often have problems from it used in our problem sets. At first, it appeared as if this were a very well-written text, but once we started with our problem sets, there were at least 2 e-mails sent out per week addressing a concern a student had pointed out. After a while, students stopped e-mailing the professor with their concerns, instead just assuming that they were correct whenever they spotted something weird.

Let's take an example:

Problem 1, pg. 137: Let M be the set of all points x = (x1, x2, ..., xn, ...) in l2 satisfying the condition \sum^{\infty}_{n=1} (n^2) (x_n)^2 \le 1. Prove that M is a convex set, but not a convex body.

The problem with this is that M IS easily a convex body, precisely because x = (0,0,...) is in M.

There are many more big mistakes and little mistakes throughout the exercises, oftentimes destroying the entire POINT of the problem. Take, for example, Problem 1 of pg. 76: Let A be a mapping of a metric space R into itself. Prove that the condition p(Ax,Ay) < p(x,y) (x\ne y) is insufficient for the existence of a fixed point of A.

Now, a counterexample here can be easily produced, even by the most elementary reader. But the exercise quickly becomes worthwhile if we make R complete. It's the little things that count in mathematics, and the small errors like these are clearly detrimental to the student.

But the errors in the text aren't limited to exercises. I was reading independently at the front of the book to get some info on Zorn's Lemma and ordinal numbers, and as I read, I found the following definition:

Let M1 and M2 be two ordered sets of type 01 and 02, respectively. Then we can introduce an ordering in the union M1 U M2 of the two sets by assuming that

1) a and b have the same ordering as in M1 if a,b are in M1
2) a and b have the same ordering as in M2 if a,b are in M2
3) a < b if a in M1, b in M2

The set M1 U M2 ordered in this way is called the ordered sum of M1 and M2, denoted by M1 + M2.

There is a clear problem with this definition pointed out here: http://www.physicsforums.com/showthread.php?t=200985. How is the student expected to learn such important material when even the definitions have loopholes? By the end of our experience with this book, our professor was giving out exercises to correct Kolmogorov/Fomin's incorrect definitions.

Note also that Silverman uses very weird words. For example, 'countably compact' is used instead of 'sequentially compact'.
 
1 Star Rating  "Buy "Elements of the Theory of Functions and Functional Analysis""2007-08-19
- Reviewed By Charles Saunders from Tallahassee, FL United States
I speak Russian and read it so-so - this is not the original work of Kolmogorov and Fomin but is a "freely" translated version. Unfortunately, "free" is not always "correct".
 
5 Star Rating  "95% as good as Big Rudin, but 0.001% of the price"2007-03-08
- Reviewed By Books are more accurate than spoken word. from T.O.

This book is exceptionally well written and planned out. I rate it as around 95% as good as Big Rudin, which means it's probably better than most Real Analysis books out there.

You will actually "understand" the motivation and purpose of the theories as you read through the book. It's rigorous, yet still inspiring and has sufficient examples to hammer ideas home. It's one of those rare books that is rigorous but still captures your interest enough to prevent you from walking away every 10 min. of reading.

For the price Dover charges for this one, I seriously think it's a steal. I'd even buy it for $50, which is still a bargain because the quality of the book is much better than those $100 books table props out there.
 
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