How to Prove It: A Structured Approach | 
| Author: Daniel J. Velleman
Publisher: Cambridge University Press
Category: Book
List Price: $29.99
Buy Used: $9.99
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Avg. Customer Rating:  28 reviews
Sales Rank: 295562
Media: Paperback
Number Of Items: 1
Pages: 309
Shipping Weight (lbs): 1
Dimensions (in): 9 x 6 x 0.7
ISBN: 0521446635
Dewey Decimal Number: 511.3
EAN: 9780521446631
ASIN: 0521446635
Publication Date: 1994
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Product Description
Many mathematics students have trouble the first time they take a course, such as linear algebra, abstract algebra, introductory analysis, or discrete mathematics, in which they are asked to prove various theorems. This textbook will prepare students to make the transition from solving problems to proving theorems by teaching 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. The author shows how complex proofs are built up from these smaller steps, using detailed "scratchwork" sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. Numerous exercises give students the opportunity to construct their own proofs. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
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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