Mathematical Analysis, Second Edition
by Tom M. Apostol
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Book Summary Information
Author: Tom M. ApostolEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1974-01-11
ISBN: 0201002884
Number of pages: 492
Publisher: Addison Wesley
Book Reviews of Mathematical Analysis, Second Edition
Book Review: One of the best I own...
Summary: 5 Stars
I own books on mathematical analysis by Browder (0387946144), Douglas S Bridges (0387982396
), Haaser Sullivan (0486665097), Pfaffenberger(0486421740), Dudley (0521007542),Abbot(0387950605) and Apostol.
All books cover abstract multivariable spaces, except Abbott who limits himself to the real line.
None of these books are perfect, but of all these books Apostol is the one I prefer for the following reasons :
1. The contents : I think a beginning analysis course should serve two aims :
a. teach basic techniques that can be used in other theoretical oriented courses like physics,economics,...
b. at the same time let the students discover the beauty of abstract and rigorous math.
In this context Apostol has reached the ideal mix between abstraction and usability. He covers practical topics , used as a basis in a lot of other courses, but he does this by making the needed level of abstraction in order to proof everything in a rigorous way.
Each book is self contained, though none of these books give a good introduction into basic mathematical logic. However an introduction to set theory is explained well in all books.
Dudley 's beautifull book is the most abstract but requires the highest level of mathematical maturity.
2 Layout : The books of Haaser Sullivan , Pfaffenberger cover excellent material in a very clear way but they are cheap Dover editions, putting as much text as possible on one page. Browder 's contents I like most (and contains really excellent explanations), but his layout is also very dense and not always comfortable to read. The layout of Apostol is the best of all these books, its pages are well filled, but the difficult proofs contain enough whitspace for a confortable read.
3.Completeness and rigor : Apostol and all these books, except Abbott and Douglas S Bridges, proof everything they mention (exceptionally, they leaf a proof as an exercise, but then the proof is relatively easy enough if you understand the material). This is an approach I like : present the complete theory and then (like all of them do) create challenging exercises seperate from the basic theory.
In contrast, the book of Douglas S Bridges represents all material as one big exercise.This is nice if you have anough time, but most of us do not have that much time,I am afraid. Also Abbott has a lot of difficult proofs left as an exercise to the reader. But at the same time, Abbott is the best in motivating the reader. Abbott often provides excellent background in order to motivate the reader and sharpen the readers mathematical intuition.
While Apostol is not best on all the criteria mentioned above, Apostol scores good on all off them and as a consequence he has the best total average. This being said, I must omit that reading Apostol requires patience. Yes his explanations are clear, but can be very terse (especially his examples). Though, in principle everything is explained without gaps. This book requires reading every word carefully and take the time to reflect, but maybe that is the only way to learn advanced math.
Finally a remark about the price, I bought this book in Europe where it is much cheaper (check amazon.co.uk)
So compared with the others this a very good book.
Summary of Mathematical Analysis, Second Edition
| It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis. |
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