Customer Reviews

Real Analysis

5 star:		(3)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(2)

 

 

This book is designed to be a one semester book in undergrad analysis.

It covers almost all the material in either Rudin's or Krantz's, which are usually covered in two semesters. however, Prof. Morgan does sacrafice some of the depth that other texts go into (example: theorem a sequence is convegent <=> cauchyis only proved the forward way).

Why I like it:
-This approach is perfect. You get a solid underpinning in the basics and get a taste of many diffrent subjects, (fourier, stirling's formula, Volumes of N-balls etc...). It is perfect for a first class in upper math (beyond linear algebra).

-the problems sets are actual problem sets that should be done on a per lecture basis. other books are filled with extensive problems that usually overwhelm a student with only a linear algebra background.

-all the proofs relating to compactness are written with the three equivilent def. of compactness (closed & bounded in R^N, open covers, sequential compactness). This allows a student to fully appreciate the modern defenition of open covers for compactness.
the same goes for proofs involving continuity (sequential, epsilon-selta, inverse images of opens sets are open).
Both of these techniques makes the transition to general metric spaces, where the open covers and inverse images are primaraly used, smooth.

This book is simply beautiful. It is written as a textbook for just one semester of undergraduate study, and it does the job. It is concise, jet it contains all the main theorems with the proofs rigorous enough. It begins with elementary concepts of numbers and logic, and even topology (so it treats continuity via open sets as well!), compactness is treated in three different ways, Fourier series is explained, and it even touches metric spaces... The book doesn't go very deep, but it talks well about basic issues in analysis and it's rigorous enough for an undergraduate text. The book can even serve well as a manual for those who need to refresh their knowledge about main theorems of analysis while considering other fields of mathematics invoking some analysis issues, because it's concise, rigorous enough and well organized. Very useful.

This is a truly awful textbook. It is written in a patronizing and demeaning tone, suggesting the author does not consider his audience actually capable of learning real analysis. The chapters are brief, often only a single page, and seem to barely scratch the surface of the topic. Many proofs are left out altogether, with occasional suggestions that the reader "find the proof on the internet." Important concepts are also excluded or mentioned only in problems, such as the definition of a Cauchy sequence. The section on Fourier Series includes misprints in two essential definitions. The book is almost entirely void of examples, and often seems to do little more than merely list theorems. Although the price is much less than many other introductory texts, it would be worth your money to look elsewhere.

This book is terrible. It's like an extended contents table, without any deeper explanation. Most of the proofs are left out. Not good for beginners who wants to learn how to write a proof.

It has served its purpose. It seems pretty old but it is in fine condition. you get what you pay for.

This is no conventional Analysis book. It is written to drive the reader's focus to a single topic each time. The chapters are 1-2 pages long and it is useful for what is is thought for. Continuity? You read 1 page, straight to the point. Facts about number sets and infinity? 1 page. Obviously it leaves out many consequences, but the uniqueness of this book is that you will always find the basic facts you need right in the first page you happen to open. It is written so concisely that you will understand everything in the first read. In fact, I like to refer to it as "my first real analysis book". OK, it is true that maybe it is too much to ask $40 for it, but is definitely nice to have it around.