How to Prove It: A Structured Approach | 
| Author: Daniel J. Velleman
Publisher: Cambridge University Press
Category: Book
List Price: $90.00
Buy New: $67.95
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New (11) Used (6) from $62.00
Avg. Customer Rating:  28 reviews
Sales Rank: 1475457
Media: Hardcover
Edition: 2
Number Of Items: 1
Pages: 398
Shipping Weight (lbs): 1.4
Dimensions (in): 9.1 x 6.1 x 1
ISBN: 0521861241
Dewey Decimal Number: 511.3
EAN: 9780521861243
ASIN: 0521861241
Publication Date: January 16, 2006
Availability: Usually ships in 1-2 business days
Shipping: International shipping available
Condition: Brand New. Delivery is usually 5 - 8 working days from order, International is by Royal Mail Airmail
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Product Description
Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5
Book Description
Beginning with the basic concepts of logic and set theory, this book teaches the language of mathematics and how it is interpreted. The author uses these concepts as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. He shows how complex proofs are built up from these smaller steps, using detailed "scratch work" sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
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| Customer Reviews: Read 23 more reviews...
 Outstanding! December 1, 2008
This is an incredible book -- one of the best mathematics books I have ever read. I have not yet found any other books that cover the material of sets, logic, proof nearly as effectively than this book does.
The most unique and helpful part for me was the concept of "structured proofs" and the proof strategies. I have never encountered this information elsewhere, and it helped me progess very much with my mathematical thinking.
I just wish I had found this book earlier on in my studies...
 How To Prove It: A Structured Approach 2nd Edition August 27, 2008
How To Prove It: A Secured Approach 2nd Edition by Daniel J. Velleman
I highly recommend this book for any student who is trying to improve his or her understanding of mathematical or computational proofs. I am an undergraduate student in the Northeastern United States and this book will undoubtly help me with my mathematics course that involve formal proofs. Some people try to understand proofs "naturally" in advanced math courses. This can be a time consuming and unfruitful venture if you don't get the proofs right away or have a bad TA. This book's step by step approach to mathematical logic will give you excellent strategies for tackling any type of proof.
I recommend only buying this book if you have a lot of time to invest. If you are looking for light reading or a quick review this is the wrong book. It took me about 2-4 hours to fully digest each chapter.
Good book, but it requires a lot of work to be useful June 22, 2008
0 out of 2 found this review helpful
Reading this book will not help you write proofs in the least. How to Prove It, to help you at all, will require lots of time and effort after reading each chapter, actually doing proofs.
Anyone who has done proofs, or attempted to do proofs, should not be surprised that there is no magic key. Working through this book is required for improvement, just a quick read will get you no where.
That said, the time is well worth it. When you think back to how hard proofs used to be after working through the book, you will feel like a super genius with your new found skill.
proofs give me headaches September 14, 2007
0 out of 2 found this review helpful
I am a math instructor, and hate proofs even more than the students do. However, this book is about the process of formal proof, from a logician's viewpoint. Understanding the structure of the proof process makes the pain tolerable.
The real reason I bought this is an interest in theorem proving software. What seemed a dead end is a useful although limited tool. I need to understand the process better to use the tools.
Quality overview March 8, 2007
0 out of 4 found this review helpful
This book does give you the important structure behind proofs and the methodology needed to produce them yourself.
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