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How to Prove It: A Structured Approach, 2nd Edition 2nd Edition

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Daniel J. Velleman (Author)
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Daniel J. Velleman (Author)
4.4 out of 5 stars 89 customer reviews
ISBN-13: 978-0521675994
ISBN-10: 0521675995
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  • How to Prove It: A Structured Approach, 2nd Edition
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Product Details

  • Paperback: 384 pages
  • Publisher: Cambridge University Press; 2nd edition (January 16, 2006)
  • Language: English
  • ISBN-10: 0521675995
  • ISBN-13: 978-0521675994
  • Product Dimensions: 6 x 0.9 x 9 inches
  • Shipping Weight: 1.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (89 customer reviews)
  • Amazon Best Sellers Rank: #17,579 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

5.0 out of 5 starsThis Book Taught Me How to "Get" Math... Please Read On..
By Baze on July 17, 2012
Format: Paperback Verified Purchase
Before buying this book, I struggled in math. I excelled at "calculating" stuff by simply plugging in numbers into some sort of equation our high school teachers would spoil us with, but when I got to college, I had to start thinking abstractly- and it bothered me a lot, because I had no idea how to test or prove the logic of some statement. I was doing very poorly in linear algebra and desperately needed help- lo and behold, my professors weren't helpful (at all). Someone recommended this proof writing book to me, and I am VERY grateful for that referral.

The book takes the average student (it's shocking with how little math background one needs) and introduces him to basic boolean logic. You know, material like "If A is true, and B is false, then A implies B is false." In a discrete mathematics course, one would call this "truth tables." From there, the author takes the reader into set theory, basic proofs, group theory, etc- and into more advanced topics, like the Cantor-Schroeder-Bernstein theorem, countability, etc. So what makes this book stand out?

(1) Readability. Many math professors stop just short of taking pride in how confusing, abstract, or daunting their lectures can be. Velleman, however, goes the extra mile in the text to see that the reader UNDERSTANDS the logical buildup and concepts of mathematical proofs. Sure, set theory can be confusing- but after reading several other texts in discrete math, including "Discrete Math and its Applications" by Kenneth Rosen (if you're reading this, no offense) I've found that Velleman by far writes the most comprehensive and cohesive explanations for understanding set theory.Read more ›
3 Comments 119 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
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5.0 out of 5 starsCompletely changed my view of proofs.
By L. Burton on March 21, 2009
Format: Paperback
Now I understand how proofs are being constructed. I can read and write them the right way! After reading this book I went back to my Calculus textbook and started looking at the proofs. I was amazed at how differently I perceived them. I actually enjoyed reading them and understood why they were written that way.

A little info about the book. Basically, it teaches you the same material that you learn in a Discrete Mathematics course - Propositional logic, Sets and Proofs, Relations, Functions, and Mathematical Induction. However, it looks at those subjects from a completely different perspective. There's absolutely no practical information - all you do is prove stuff.

I strongly advise to learn Discrete Math before reading this book, because getting straight to the proofs of the material, that you just have learned and have no previous experience with, can get very tough.

The first two chapters were a bit boring and too easy - but only because I have already learned that stuff. Chapter 3 is where you start to do your own proofs and is where it gets fun.

The exercises are not hard, and shouldn't present any trouble for the reader. However, I did find the exercises in the last 3 chapters to be more challenging. There were some problems on which I was simply staring for an hour, literally, trying to figure out the way to prove it. The theorem made sense to me, but I couldn't find a way to put into strict mathematical proof! But let me tell you, there's nothing like getting a "Eureka!" moment and figuring out the answer all by yourself. I have just spent 1.5 hours doing 1 problem, and after getting the answer I've felt like I have accomplished something.

Get this book, NOW!
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5.0 out of 5 starsSolutions to: Does it work on Kindle? & Are there Solutions to the Exercises?
By DrTrips on July 4, 2014
Format: Paperback
My goal for this review is to make it as helpful as possible to someone considering to buy this Book !
-I will not go over most of the summaries of the text provided by my fellow reviewers but will provide two important clarifications.
1st:
I read in another review that that the Kindle version of the text interprets some logical operators or other notation incorrectly causing confusion with what the text or exercises are referring to....
This Statement is FALSE. I have purchased the kindle version and did not find one inconsistency and all notations are indeed accurate.
2nd:
I have found that a major complaint about this text is that it does not provide enough solutions to its exercises for one to verify whether they have actually learned the material or not.
This Statement is TRUE. On average, out of 7 question in each section, only 2 solutions are given in the back of the text.

HOWEVER!!! There is another way to circumvent this problem. The Department of Mathematics of the University of California, Santa Barbara has been so kind as to post the Solutions to the unlisted problems on their website.
Please visit this site to view them:
http://www.math.ucsb.edu/~dai/813wang.html

Now with both of these clarifications in place, and after going through a couple of other Mathematical Proof books, and I personally prefer this one. It is direct, and covers the basics needed for understanding and doing proofs.
One must understand that doing proofs is a skill a Mathematician gains through vast experience, practice and long hours of thought. Finding a book that breaks down a universal method of proofing in the same simple way an Algebra text shows how to use a formula will not be possible.Read more ›
1 Comment 26 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
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Most Recent Customer Reviews

5.0 out of 5 starsCLEAR, BUT WHERE'S THE COFFEE?

Since this treatment assumes only a high school background in problem solving I am looking forward to learning and benefitting from it.

Published 24 days ago by Mister Glashaus
5.0 out of 5 starsFive Stars

Very readable for a math book.

Published 1 month ago by Angela Stiles
5.0 out of 5 starsIt's basically exactly what I needed for my Mathematical Structures...

It's basically exactly what I needed for my Mathematical Structures class, furthermore the textbook is thorough in it's descriptions, explanations, and examples. Read more

Published 2 months ago by Amazon Customer
5.0 out of 5 starsMy favorite book about proofs so far

A fine book. It is very clear and concise, and in my opinion very enjoyable. It goes over the foundations needed to writing proofs (basic set theory and logic) and provides a lot... Read more

Published 4 months ago by A Man on the Moon.
3.0 out of 5 starsIt would have been nice if the author included a more diverse set of...

Review of the second edition:

My main issues with this book:

1) Most of the problems/exercises in this book revolve around set theory; and towards the end of... Read more

Published 4 months ago by RAO
3.0 out of 5 starsNot all THAT unique

My major complaint about this book is that it claims to offer a unique "structured approach" to proofs that's analogous to structured programming in software engineering. Read more

Published 4 months ago by EJS
5.0 out of 5 starsFive Stars

I am very happy with the book. It is easy to read and is helping me with my class.

Published 5 months ago by Amazon Customer
5.0 out of 5 starsAs good as you can get!

Great. Like a textbook but easy too understand! Probably as good as you'll get without a tutor or teacher.

Published 7 months ago by Justin Kappel
5.0 out of 5 starsGreat for transition to proof-based math

I was good at math in high school and the first year of college, but the transition to proof-based math classes was a real shock. Read more

Published 8 months ago by targetdemo
1.0 out of 5 starshate

i hate this book. i had to get it for my mathematical proofs and problem solving class and i cant stand it

Published 8 months ago by Amazon Customer

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