Analysis: With an Introduction to Proof (4th Edition) | 
| Author: Steven R. Lay
Publisher: Prentice Hall
Category: Book
List Price: $130.20
Buy New: $75.52
You Save: $54.68 (42%)
New (29) Used (22) from $75.00
Avg. Customer Rating:  8 reviews
Sales Rank: 19932
Media: Hardcover
Edition: 4
Number Of Items: 1
Pages: 400
Shipping Weight (lbs): 1.9
Dimensions (in): 9.2 x 7.8 x 0.8
ISBN: 0131481010
Dewey Decimal Number: 515
EAN: 9780131481015
ASIN: 0131481010
Publication Date: December 9, 2004
Availability: Usually ships in 1-2 business days
Shipping: International shipping available
Condition: Brand new book delivered from the UK in 10-14 days.
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Product Description
By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.
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| Customer Reviews: Read 3 more reviews...
 School book January 9, 2009
This book is going to be used for school but looks like it will be a hard book to understand.
Couldn't Ask for Anything More September 7, 2008
This item was in great condition, shipped quickly, and not overpriced. I feel pretty comfortable recommending doing your purchase through this seller.
 Acceptable but could have been better. April 21, 2008
2 out of 2 found this review helpful
This is fairly basic introduction to Principles of Analysis, on intermediate undergrad level, strictly in R^1. The only other similar book I'm familiar is Kirkwood. The books of Rudin, Apostol, etc present the subject on much higher level.
My original intention was to take a course with Rudin, but after I've realized I had a hard time digesting his style, I've decided to take more elementary course. I knew the course would be using Lay, so I got this textbook and tried to learn it on my own, but wasn't sure how I was doing and ended up taking the course (still with Lay) anyway. So I'm quite familiar with this textbook. The only topics we didn't cover is "series" and "sequences and series of functions".
Now overall I would say it's a mixed bag. First, the good things. The first few introductory sections on sets and proof techniques are excellent, highly recommended, that's how I learned how to prove. I found exercises very useful.
Now things I don't like. First, lots of typos. I think I had 4th edition, and still I've managed to find over 20 misprints, incorrect references, etc, etc, all were reported directly to author. Second, and that's probably more important, in several instances the proofs are too convoluted and not self-motivating. To be more specific, the proof of Heine-Borell theorem is less than adequate. It is correct, but that's the kind of proof you read and then entirely forget how it went. I remember on the first reading I didn't feel comfortable with this proof at all. When I discussed this book with professor I was going to take that course with, he (surprisingle) agreed with me and told me he would present a different proof (and he did, much better one). Another example: proof that the modified Dirichlet function is Riemann-integrable. The proof can be substantially simplified. In fact, I've managed to simplify it. Finally, the same professor told me Lay's presentation of Riemann integrals had some holes in them, so he used Kirkwood instead. In fact he told me he was making choice between Kirkwood and lay (but ended up choosing Lay because he didn't like Kirkwood's book layout. Kind of funny reason, I think.)
In any case, I think Kirkwood is a bit better for self-study. Unfortunately it doesn't have intro to proofs, logic and sets. Ideally you should have both books, if you plan for self-study.
(note: I did took the Principles of analysis, after I've finished that one with Lay, and did quite well.)
Great Book for Intro to Analysis March 13, 2008
2 out of 2 found this review helpful
This is a very good book for someone to look at before going into an analysis class with Rudin. If you have never done proofs or seen metric spaces or uniform continuity, etc., this is a nice, but brief, intro. This book will NOT teach you analysis - you have to use Rudin for that. But it is great for acquainting/preparing you for Rudin.
Great book April 29, 2007
2 out of 3 found this review helpful
Analysis at this level is probably the most challenging class for an undergraduate degree. However, this book made it very manageable. I found the introduction to proof very helpful. I encourage anyone who is using this book to study this chapter ahead of time. It will make the subsequent chapters a lot easier to handle. If it was not for this book and the outsdanting professor I had, I would never have passed this class. Go for it!
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