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Thinking Mathematically Paperback – January 11, 1982

ISBN-13: 978-0201102383 ISBN-10: 0201102382 Edition: 1st

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Product Details

  • Paperback: 224 pages
  • Publisher: Pearson; 1 edition (January 11, 1982)
  • Language: English
  • ISBN-10: 0201102382
  • ISBN-13: 978-0201102383
  • Product Dimensions: 6 x 0.6 x 8.9 inches
  • Shipping Weight: 10.4 ounces
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #541,150 in Books (See Top 100 in Books)

Customer Reviews

4.9 out of 5 stars
5 star
86%
4 star
14%
3 star
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See all 7 customer reviews
I used this book for a course I taught at the University of Connecticut.
David E. Molnar
I strongly suggest that you try to apply these principles to solving the Olympiad problems in Arthur Engel's book on math Olympiad problems.
Abhi
After reading this book, though, I learned the tricks of specializing and generalizing.
William Stevenson

Most Helpful Customer Reviews

39 of 40 people found the following review helpful By William Stevenson on May 17, 2001
Format: Paperback
This book helped me quite a great deal with my foray into university mathematics, which are quite different from the algorithmic problems one is often dealt in highschool. Before reading this book, I would often read a problem and just be /stuck/. If it were a test, I would put a question mark in the answer blank and just move along. This is because I didn't have a sense of where to begin with novel problems. After reading this book, though, I learned the tricks of specializing and generalizing. Much of the advice given in the book might seem obvious ("start with small cases," "draw a picture," etc.) but doesn't really get thought of during a stressful exam. By working through this book (and you have to *work* through it, don't expect to read it like a novel trying to glean advice), any sufficiently mathematically-minded person can deserve to call themself a mathematician, for they will truly begin to think like one. After it, they should check out Velleman's "How to Prove It" and R.P. Burn's "Numbers and Functions."
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34 of 38 people found the following review helpful By David E. Molnar on September 5, 2000
Format: Paperback
I used this book for a course I taught at the University of Connecticut. It has a lot to offer, especially for the price. Sample problem: draw a bunch of lines across a piece of paper. Can the resulting picture be colored only in black and white, with no adjoining regions sharing the same color? Works through examples like this one in excruciating detail, encourages the reader to sweat through problems, the payoff coming when you start to see patterns not in the problems themselves, but in how you approach them. Last chapter consists entirely of problems, with suggestions on how to attack, and then extend them.
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14 of 14 people found the following review helpful By Abhi on September 23, 2012
Format: Paperback Verified Purchase
The big idea is that for someone who is new to math research, there is no guidance available to solve problems (not exercises in texts but true math problems....there is a difference.....problems can be solved only through research while exercises are meant to be solved by simply understanding the concepts well.....) in math and this book is a great substitute. For example, contest problems like that in the Olympiads are really hard. Traditionally, most trainers in the Olympiads teach the kids the various "tricks" involved in solving contest problems; however, if the kid has not seen a particular type of trick to be used in a problem, he simply fails. This has also been admitted by Arthur Engel in his preface to the fantastic problem solving book that he has written. This book (i.e. Thinking Mathematically) does not talk about tricks. As far as I am concerned, this is the REAL deal. After you graduate from that phase of life where you are done with Olympiads and Putnams, you will encounter a phase where people are actively trying to figure out facts about twin prime conjectures etc. No trick is going to help you there. Professors usually guide the student when it comes to problem solving in pure math. They talk about how to break the problem down, look at it in different angles, understand the logic in the solution to a parallel problem etc..... For a novice who is doing self study, the ONLY other book close to this one is Poyla's Mathematics and plausible reasoning. That seems to be a great book but is more detailed and speaks about induction and all that. He does speak a little bit about specialization and generalization. His other book titled How to Solve it is useless according to me.

Start from this book.
Read more ›
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7 of 7 people found the following review helpful By M. Singh on February 12, 2010
Format: Paperback Verified Purchase
This book really makes you think mathematically. It gives you a systematic approach to solving mathematically and analytical problems. It gives you tips for keeping your concentration on working problems involving numbers.

If you make the effort to really go through this book bit by bit it will really help you think mathematically in all areas of your life.
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