Customer Reviews

Introduction to Analysis (2nd Edition)

5 star:		(4)
4 star:		(2)
3 star:		(3)
2 star:		(4)
1 star:		(8)

 

 

The strongest point of the book is the exercises. They force you to reread and understand the proofs and they build a foundation for material that is to come.

Chapter 1 (2nd edition) need a complete rewrite. How can you obfuscate something as simple as the Archimedean property in all its forms? Chapter 8 on Euclidean spaces needs to be better integrated with what the student should know from the first linear algebra course.

The author's proofs are not clear and I found myself rewriting many of them in my own words or turning to other references.

The core chapters 2-7 and 11-13 are fine - especially if you buy the approach of doing analysis first in R and then doing it a second time in R^n. This may be especially appropriate in an environment where most of the students are future high school teachers and will only take 1 advanced calculus course.

There are an unusual number of typos in the second edition. They are no longer accessible on the author's website. But hey, the 3rd edition is available, just throw out the 2nd and get the latest.

This book was used in my Analysis I class. I later had to prepare again for my masters certifying exam on Analysis and the primary reason I didn't use this book, even though I owned it, was the binding. By the end of my analysis course, it was practically in individual pages. The binding is atrocious - how can a $100+ book just be sort of glued together weakly that it falls apart after 1 semester of use.

The other reason I didn't use this book was that it goes through the 1-dimensional analysis pretty fast. My chosen analysis preparation book was also supposed to be my preparation for Royden's Real Analysis but I choose a book that covers the 1-dimensional analysis in twice the amount of pages and exercises taking a more detailed topology route. So, I'd advise a little bit of caution there if this is your path to graduate level Real Analysis.

However, with the 3rd edition out, our department threw out all the old 2nd edition books. I needed a multi-dimensional analysis text to prepare for my graduate PDE course and took 3 copies of the thrown ones out.

The reason I took 3 copies was that I knew the binding was going to fall apart and sure enough it did. It sort of breaks down into little booklets each that is glued to the spine. The pages on booklet peel off real easy and soon you have just pages instead of a book.

As for the multidimensional analysis it covers, it was very entertaining and fun to do. Chapter 13 becomes a little bit in the air as the exercises get a little tedious with calculate this integral with all sorts of surfaces enclosing it and not really much exercises requring a lot of threading of analysis ideas. I don't as of yet know if it has me prepared enough for Evan's PDE book but this was the only text conviniently showed up in the "free books" bin. But, I did have a nice linear and fun writing to it and I enjoyed it. Though not much as some of my other books.

There HAS to be better texts out there in analysis. This book obscures simple concepts and neglects vital information for an introduction to analysis. I have suffered through this book, working VERY hard for three semesters. Nevertheless there are still concepts that I don't TRULY understand, which is largely attributable Wade's poor exposition of the topic. For example, the entire treatment of differentiability in Euclidean n-space, including the manner in which Wade introduces the definition, is pathetically motivated/explained. This makes it difficult to understand and convince yourself of other proofs/concepts which rely on a firm understanding of the previously studied material.

For a truly comprehensive introduction, I'd suggest Introduction to Analysis by Maxwell Rosenlicht. I bought this as a supplementary text to the courses I have taken, largely due to positive reviews, and was very pleased. I gained significant insight due to the presence of discussions spanning more than three sentences between each lemma, theorem, corollary, or remark, in complete contrast to Wade's book. Another plus is that it's around 10% of the cost.

[A review of the 3rd EDITION.]

I would compare Wade's book with Jerrold Marsden's "Elementary Classical Analysis". Both cover roughly the same material. Essentially directed at maths majors, and possibly majors in theoretical physics. The level of rigour in the proofs that Wade gives is really unlikely to be needed in other fields. Wade's text does start right at the beginning of calculus, unlike Marsden. Also, Marsden's book is sometimes a little terse. Wade can give more explanatory details, which may help some readers.

Wade also furnishes many exercises, with answers to a few. The exercises do a good job of expanding on the chapters' ideas. Which of course has the corollary that you'd benefit by doing as many as you can.

Analysis: once in R, then again in R^n? No thanks. This book is verbose when a theorem is obvious, and too brief when a big proof has just been dropped. The exercises have nothing on Kolmogorov & Fomin.

Long live Rudin!

First of all the binding of the 3rd edition is horrible, and I barely used it. My class used this book for analysis 2, basically just using the second half of the book. The notation is horrible, there is almost no expository writing between the proofs and theorems. Often proofs are longer than they need to be, but others are extremely terse and skip key pieces of logic. For analysis 1 I loved Ross's Book "Elementary analysis: the theory of calculus", and I think analysis 2 would have been better off transitioning to Rudin as opposed to this book.

This is the worst analysis book ever. Short, unclear proofs. It takes forever to fill in what the author omits. Sections include no examples, or one of them if you're lucky. Pathetic textbook, I have no idea why professors keep assigning it. It should go extinct.

Case study: why did my department adopt this text?

This was an assigned text for my masters-level two-semester intro analysis course, with students' prior exposure ranging from no undergrad mathematics, to engineers, to a couple with math undergrads. Well-prepared students skipped this course and took a higher-level course using Royden. I suspect the Wade text was adopted because it is supposed to be versatile enough for the wide range of students in this course.

I agree with most other reviewers' complaints -- my list is as follows: needlessly expensive, poor binding, inelegant style, exercises annoyingly shuffled around so you have to buy the latest edition, a good number of errors (some obviously introduced during the aforementioned shuffle -- but why bother submitting them to the publisher since they will just remix it and cash in again in a couple years?). Actually, who cares if the binding falls apart -- this is probably not the text one will lovingly store on the shelf forever, and will have negligible resale value as soon as the new edition is out.

However, despite the fact that most students in my course disliked the text, it isn't uniformly atrocious. This was over a year ago but I remember some decent exercises which would lead you to derive seemingly useful results, mixed in with many drill exercises (which I admit we needed). I can attest that it is possible to learn analysis from this book, which most of us did after we stopped complaining about the book -- two stars for that.

If the students were stronger and more uniform, maybe the dept should have adopted Rudin or Pugh instead. Rosenlicht is cleaner, but intended for a one-semester course. Courant/John is very nice, but old enough that e.g. there seem to be no metric spaces. Perhaps it is a hopeless/thankless task to write analysis books for this hodgepodge of an audience, some of whom are ill-prepared, some of whom need preparation for applied courses, some of whom will need a theoretical foundation for more sophisticated analysis.

It still seems that a better text must exist for this (obviously rather profitable) niche, but I can't quite say which one.

I used this book for my first analysis course. Over all, I think it does a nice job, but it could use a little tweeking. Let's start with the good...

First off, Wade understands the difficult time most students have with the transition from the early calculus courses to the higher, more abstract classes. Several proofs in this text are a little more drawn out than in others, and this is to aid the in the understaning of the art of proof writing (and it really is an art).

Another think I liked is the variety of exercises. They range from relatively easy to rather difficult (I was unable to solve some...).

Now for the bad...

I really didn't like the layout of some of the material. Especially in chapter 1. He states a definition, and then it's results. Another definiton will be thrown in along with more results. Especially in chapter 1, it would be nice if all the definitions and axioms are put into one place, and the results to follow in a later section (Shilov does this, and I used his book a lot as well during the course). I find that referencing definitions that are organized in such a fashion much nicer.

If you're a budding mathematician, and would like to get a better understanding of analysis, I'd feel confident about adding this one to your collection.

I am really sorry if your instructor has forced you to buy this book. Buy Mary Hart's Guide to Analysis in order to understand the material Guide to Analysis (Macmillan Mathematical Guides). It will get you through the first half of Wade, but sadly ends before the second half of Wade. Only use wade so that you have the assignment questions.

The author skips major sections of proofs necessary to understanding the material with a snide arrogance that is downright insulting to the student. It is astounding what tenured professors and coddled publishers can get away with these days.