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Thinking Mathematically [Paperback]

J. Mason , L. Burton , K. Stacey
5.0 out of 5 stars  See all reviews (6 customer reviews)

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Thinking Mathematically (2nd Edition) Thinking Mathematically (2nd Edition) 5.0 out of 5 stars (2)
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Book Description

January 11, 1982 0201102382 978-0201102383 1

Thinking Mathematically unfolds the processes which lie at the heart of mathematics. It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians. In this way, a deep seated awareness of the nature of mathematical thinking can grow. The book is increasingly used to provide students at a tertiary level with some experience of mathematical thinking processes.

Product Details

  • Paperback: 224 pages
  • Publisher: Pearson; 1 edition (January 11, 1982)
  • Language: English
  • ISBN-10: 0201102382
  • ISBN-13: 978-0201102383
  • Product Dimensions: 6.1 x 0.5 x 9.2 inches
  • Shipping Weight: 10.4 ounces
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #493,963 in Books (See Top 100 in Books)

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38 of 39 people found the following review helpful
5.0 out of 5 stars Great for the transition to university maths May 17, 2001
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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32 of 36 people found the following review helpful
5.0 out of 5 stars you learn mathematics by doing it. September 5, 2000
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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11 of 11 people found the following review helpful
5.0 out of 5 stars Best guidance available for an aspiring math researcher September 23, 2012
By Abhi
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.

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