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Analysis: With an Introduction to Proof (4th Edition)
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.
Customer Reviews:
Definitely a good first text
By Charlie Johnson - September 4, 2002I bought this book because I have been looking for a Introductory analysis text that isn't too advanced, but yet doesn't gloss over the essential stuff, and I found it in Lay's book. For the self-studier, this book is excellent! I have several books on analysis: Shilov, Kolomogorov, Rosenlicht, Ross,etc... For the beginner, this book is superior to all of them. A plethora of examples. Also, a good range of problems:from straight forward problems requiring only the use of a definition to more advanced problems requiring a little thought. If you already have had some Analysis, then this book is probably not for you. But, if you are a student who wants to learn Analysis on your own, then this book would be hard to beat. After this book, one should be able to tackle "Papa Rudin". For according to Rudin, all that is needed to study his "Real and Complex Analysis" tome, is the first seven chapters of his "Principles of Mathematical Analysis". This... read more
This book was surprisingly good
By Zachary Turner - July 2, 2002I didn't think this book was going to be very good, but the author has "proved" me wrong ;-) This book starts out so basic that in my class (which was the first analysis course in our math department) we actually skipped the first 1/3 or so of the book. The first 9 or 10 sections consist of stuff like basic set theory, logic, definition of a function, etc. I would think that even the most elementary Analysis books would completely leave this out and expect that the reader is already familiar with this. So if you need it, this book will be a good resource for you.Then the book goes into a very nice introduction to topology. Basic concepts like open/closed sets, accumulation points, compact sets, etc. Topology can be a little intimidating simply because it's _so_ abstract, but this book makes the basic concepts very easy to understand, and prepares one for a more advanced course in topology. Alot of (good) Elementary Analysis books leave topology out, but I'm glad this book... read more
Acceptable but could have been better.
By Gregory E. Hersh - April 20, 2008This 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... read more
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