Customer Reviews

Introduction to Real Analysis, 3rd Edition

5 star:		(18)
4 star:		(8)
3 star:		(4)
2 star:		(3)
1 star:		(2)

 

 

At first, I hated this textbook. New to Analysis, I couldn't make any sense of it. But, I was trying do accomplish too much on my own without the help of the instructor. This textbook is terrible for self-study. A poor course instructor (you know the kind - the ones who read the book to you) can make learning Analysis a singularly miserable experience. However, if you're lucky enough to have an instructor that's willing to supplement and clarify the material in class (i.e. get you over the hump), you'll find this textbook quite adequate and worthy of keeping for reference. To get the most out of it, however, you'll need to be prepared to work much harder than you have in your previous math courses.

I know that there are two camps of reviewers of analysis books. There are those who complain that a text is too terse and those who say it's too wordy. This book finds a nice balance. It can be very frustrating at times...but, such is analysis. (Note that the authors warn you of this in the first paragraph of the Preface.) Mastery of the first two chapters is essential for one to succeed in the rest of the book.

I have given this textbook three stars because it let's the reader down on some topics. A couple of the proofs (L'Hospital's Rule is an example) are a bit too sparse in explanation for the beginner who must fill in the missing steps as part of his study. Also, a few topics are more notationally cumbersome than necessary, requiring the reader to be very adept with indexed summations. The chapter on Riemann integration is understandable, but falls short of most other texts in this area. (In my class, we used a different text for the Riemann Integral.)

If this is the required textbook for your upcoming Analysis course, I recommend that you read every section VERY carefully many, many times. Physically work through the examples and given proofs with pencil and paper. Many times the example proofs provide a model for the student that he/she can apply to the problems. If you still find it tough, make a separate notebook in which to write the definitions, thereoms, and even examples. Try diagramming the definitions and theroems, separating the conditions from the conclusions that they imply (don't forget what "if and only if" means).

The authors have included some very helpful appendices that should be treated with the same careful study as the rest of the book. Analysis is not a subject where one can pick up on a proceedure and calculate an outcome as one might do in Algebra or regular Calculus. One must learn to know and apply the definitions and thereoms logically. Well-known problem solving strategies still work here, but the method in which a student may be accustomed is entirely different (see How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) or, for proofs How to Prove It: A Structured Approach). Above all, rise to the challenge and don't get discouraged. All but the most gifted will find this subject difficult. Find help if you need it.

I recommend reading the linked books above before entering into analysis. Another really good book in the subject that will immensely help you is Yet Another Introduction to Analysis.

Honestly this is a 4 star book, but like many of the advanced math textbooks the average score is too low, because of reviewers who clearly did not understand what they were getting into.

Probably the best piece of advice with regards to advanced math books like this is given in the "Preface to the Student" in Sheldon Axler's Linear Algebra Done Right, he states: "You cannot expect to read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast."

If you study from this book from that standpoint, you will get a lot out of it. But its a serious commitment.

I'm using this book for my real analysis course at University of Illinois and I love it. Most readers seem to be upset that some of the material isn't presented as easily as it could be, but this book is an introduction to real analysis, not to math. This is not a good book for people who have never written or read formal proofs or who are not familiar with concepts like the triangle inequality. This is a good book if you are familiar with formal mathematics and have interest in real analysis.

I have read this whole book for a Phd qualifying exam, mastering all the proofs and solving almost all the excercises, excep for the sections on numerical methods. I can say that this book is a masterpiece.
The proofs are clear and easy to follow, and the book flowes smoothly. I can say that it is a classic in its filed as Royden's Real Analysis (3rd Edition), Churchill's Complex Variables and Applications, Fraleigh's First Course in Abstract Algebra, A (7th Edition) and so on.

In Analysis I, we used the first 6 chapters of this book and now in Analysis II, we're covering most of the rest. This book is quite good. When I use this book, I often sit in front of a computer so that I can look up anything I don't understand. Basically, I study Analysis all from this book, Wikipedia, and random sites. I do agree that if you don't have access to full solutions to some problems at first, it's not easy to imitate the proofs in the book.

One thing to point out is the exercises are quite crucial. If you don't do most, you will miss many subtleties that are not explicitly mentioned. For example, a function that is continuous except for countably many (maybe infinite) discontinuities is integrable. Another thing to note is for Chapter 7 which is more succint and to the point in 2nd ed. than in the 3rd.

If you want solutions, with a bit of search on google you can find quite many. The key is to search for Universities that use this book and check out the course webpage.

In Analysis III and IV, we use Rudin.

I used this book all through my freshman and sophomore years. I struggled with it and really tried hard to solve the problems. I mulled over every word and every proof in the first few chapters for days. However at the end of this rather trying exercise, I had a real sense of satisfaction and thought I had a firm grasp of the basics of real analysis. This is not one of those volumes that will instantly get you hooked but it's a volume that rewards patience like few other math books do. If you master the first few chapters of the book including those on series and sequences, you should have as good a grasp of "elementary" real analysis as anyone else. The book is for the serious student of mathematics and it provides a rigorous and comprehensive introduction to real analysis. To master it you will have to read and understand the proofs as carefully as possible; don't be discouraged and become impatient if you cannot do this easily, since the time spent on doing it is worth it. However, having a good instructor to help out will be enormously useful.

"Introduction to Real Analysis" by R. G. Bartle and D. R. Sherbert gives an excellent introduction to the topic of real analysis. The chapters are presented in a logical order, such that one topic flows seamlessly into the next. The authors explain the concepts of real analysis very clearly and succinctly. This book would be an excellent reference for those currently enroled in a real analysis course, or for those that simply need to brush up on the concepts and ideas of the subject.

A good introduction to real analysis. Proofs are detailed. This book is definitely for anyone who loves real analysis.

This book is very helpful to those student who want a advanced calculas process and need a basement to the study of real analysis. This book has many example which are very helpful to the student and we can have a chance to think about the process to the solution. Best textbook of what i have read this year!!

The book is well written, easy to understand and full of pertinent exercises.
It is a "must-have" book.