Customer Reviews

Mathematical Analysis: An Introduction (Undergraduate Texts in Mathematics)

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I taught a year analysis with this book. The book contains two semesters at least of undergraduate abstract analysis. The first half or so covers a first semester course with the usual things, metric spaces, continuity, sequences and series, and so forth. The second half or so has Lebesgue integration and multivariable analysis. I found it difficult to find another book having both semesters content in one volume, except for Rudin, which I chose not to use due to its price. So it fits a certain need. But I probably will not use this textbook again in my courses. I found the text to be way to concise, which might have been a result of the effort to fit so much into one volume. This is especially hard for the beginning half of the book, since the transition from calculus to abstract analysis tends to be conceptually challenging for students. Rudin is similar in some respect, since it is also concise. However personally I found it very natural to "fill in the blanks" in sketched proofs in Rudin, whereas in Browder I was more likely to develop a headache doing the same. Also I don't like the problems in the text. There's not really that many, and they tend to be multipart, too difficult and time consuming. The book could be improved by increasing the number of shorter exercises.

This is a very well written book. It is concise, rigorous and contains all the usual material of an undergraduate analysis course. I prefer the treatment of manifolds and differential forms in this book to that given in Rudins' classic book.

(...) First let me remark that talking about content, the book is very good. It contains elegance, rigor and the explanations seem OK. The problem however with the book is the typo density of most of the proofs. Some long proofs are presented as one continuous block without even no linefeed in between the facts. This makes some parts of the book rather uncomfortable to study from. I can 't stop starting to read these beautifull theory, but mostly, after one hour I give up, because "my eyes start dancing" ....
Tip for the author and editor : take exactly the same text, but spread it over 600 pages instead of 350 pages. This will make the book more expensive, but I will definitely buy it..

Browder's book is a great text for serious study of analysis at the beginning level. The coverage is similar to Rudin's "Principles of MA", and it is a worthy successor of it. It is a book for mathematicians, so don't even dare to open it if you are looking for the usual 'calculus for dummies' course. Proofs are usually the most concise and elegant ones, being in the tradition of Rudin again. But the treatment of analysis on manifolds is more standard, just as the construction of Lebesgue measure and integration. Only drawbacks: sticking to real variable and omitting complex numbers on most subjects (even in power series!), and the ominous presence of the usual chapter on Riemann integral. You may buy Rudin or this, and you'll be doing a great investment.

The title says it. The book is great if you're reading it and you already understand the subject matter, for it contains an encyclopedic reference for basic analyis, topology, and manifolds. But, if you've never studied anyone of theese topics, then it flat out sucks. Try doing the chapter on topology just reading the chapter on topology. Its verydifficult, and just makes your eyes water over. It sucks. There exists better books on analysis. I'm not sure about measure theory and other books, for this is the only one i've read. However, if you're looking to learn manifolds, (the last 4 chapters) buy Munkres' Analysis on Manifolds. Its a million times better and with many pictures. Browder has a total of 5 illustrations in the entire book!
Save the headache, get a different book.

This book is for serious students of mathematics. A certain amount of mathematical maturity is needed in order to, fully, appreciate this book. It is also necessary to work through the examples in order to derive the greatest value from this text. Having studied, mathematics, over various years, from texts by Hardy, Rudin, Royden etc., I feel that this book is a worthwhile addition to the armamentarium of a serious student who is interested in learning the tools of rigorous analysis.

The entire book is written in thm. prop. lemma. def. etc... form, with few breaks from this sequence of statements and proofs. While this seems to be the preferred style for a lot of textbooks, frankly I found it boring to read, and difficult to understand. That being said, the book covers a wide variety of topics, and goes into a good level of depth on each. The material is definitely worthwhile, but Browder seems to share the all too common mathematics teachers' curse of poor communications skills.

This book is concise and straightforward. It serves well as a reference when you're trying to solve problems since it follows the definition, theorem, proof, proposition, lemma, example layout. However the block style writing of the proofs is hard to read.

I've read a few books on Real Analysis. Some attempt to cover too much, some don't cover enough. This book seems to include all of the essential topics without going overboard. It is also very easy to navigate.

This is the best book for Stoke's Theorem. The machinery of the Lebesgue integral is used to simplify the integration on manifolds theory. This is very nice and very not ad hoc.

voo de voo de vooooo....I am hypnotizing you......voo de voo......You must buy this book....vooooo.....book good....voo de voo de voo....better than Calculus on Manifolds....voo de voooo....