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Introduction to Mathematical Thinking Paperback – July 18, 2012

4.2 out of 5 stars 102 customer reviews

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Editorial Reviews

About the Author

Dr. Keith Devlin is a mathematician at Stanford University in California, where he is Executive Director of the university's H-STAR institute. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 31 books and over 80 published research articles. His books have won a number of prizes, including the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio.
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Product Details

  • Paperback: 102 pages
  • Publisher: Keith Devlin (July 18, 2012)
  • Language: English
  • ISBN-10: 0615653634
  • ISBN-13: 978-0615653631
  • Product Dimensions: 6 x 0.2 x 9 inches
  • Shipping Weight: 7.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (102 customer reviews)
  • Amazon Best Sellers Rank: #40,947 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback Verified Purchase
This goes out as a "thank you" to Professor Devlin, but should prove informative to people who can relate to my situation,

All my life, I absolutely hated math. I mean the deep pains in my cortex, blood boiling derision of the concepts kind of hatred. I remember being 8 years old and absolutely loathing the thought of studying times tables. Then, variables were added - great, numbers and letters now! No one took the time to explain why we were studying such seemingly needless information. I understand now that I am quite the pragmatist, needing a defined practical application or goal for almost anything I do. Hence the reason I hated mindless calculations so much.

My disdain for the field grew to a point in my teenage years that I could no longer even look at the subject without my well-established biases taking over, driving me away. It affected my SAT score, with a perfect score in verbal comprehension being blemished by an embarrassingly subpar result in math. My educational experience was inhibited for almost two decades, simply because I saw no use for math past counting how many apples I wanted to buy at the grocery. After law school, I became interested in finance. From fairly light interactions with financial valuation methods grew a shameful realization that my hatred for math had caught up with me, finally affecting my daily life. I was a quantitative infant in the worst way, entirely handicapped in a vast and important arena.

Then I found Coursera, and through its curriculum I came across this course. Though I have not finished it, as it has just started, the book has opened my eyes. Math is a language, just like the ones we speak and master. Its algorithms are logical thought, its concepts proven by deductive and inductive reasoning.
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Format: Paperback
Keith Devlin's book "Introduction to mathematical thinking." is the textbook, the unnecessary and ridiculously inexpensive ($10) textbook, for his class on Coursera.com. The class obviously designed to be an introduction to mathematical thinking, a transition from the problem solving math of secondary school to college level mathematics where simply finding an answer is not the final goal.

I wanted to take a look at the free, non-credit classes that Coursera offers and this looked like a good one to try. It has been 30 years since I last took college calculus, and I have not looked at a math book since then. I knew I could do the work, I wanted to see just how a free, non-credit class, with 50,000 students worked.

Both the class and the book are excellent. Devlin begins by showing us that imprecision is often acceptable in spoken English. "One American dies every hour from heart disease" is his favorite example. Literally it says that there is one single American who dies, and apparently recovers, from heart disease every hour. We all understand the true meaning because in English we have background knowledge which allows us to make sense from nonsense based on the context. Mathematics requires precision because with it we will be dealing with concepts with which we do not have the background to guide our understanding.

Dr. Devlin focused on developing logical thinking and managed to arrange the lessons and exercises such that the mathematical logic required quickly evolves from simple "and" "or" statements into doing formal proofs, no small feat for a class only seven weeks long.
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Format: Kindle Edition Verified Purchase
This topic is very important and I appreciate Dr. Devlin taking the time to focus on what can be considered the glue that holds the other pieces together. However, the examples are few (most of the time just one), and not articulated well. When he explains the bi-conditional <=>, he explains how he proved that A => B (A implies B), but pulls out a completely unexplained argument for why B => A, and concludes that's how you prove it. And because it's in the middle of the book, you can't go on without understanding it thoroughly.

I am probably missing something simple, but again, the examples are few in numbers (most of the time one), and the logic is not well articulated.
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Format: Paperback Verified Purchase
I am taking the Coursera class, Introduction to Mathematical Thinking, and I bought the book to give me some background information. Keith Devlin is a brilliant mathematician and a really good writer! The writing was clear and easy to follow without the necessity of a math background. I recommend this book to anybody wanting to broaden their mathematical knowledge. There is one caveat: the author includes practice exercises, but no answer key. Some readers may find this challenging!
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By Lincoln on September 1, 2013
Format: Kindle Edition Verified Purchase
This book should be required reading for every student in the US that has been taught to focus on computational math rather then understand what is under the hood. Going back to finish my degree, I was taken back a little when I started my first Calculus course at the university. I thought something was wrong with me because I had been so good at math previous to being in this class, but when this book was suggested to me I thought I would give it a shot. I read sections several times over, took notes, researched things I didn't quite understand, but by the time I finished this book I was much better at math then I had ever been. The reason is that this book starts you on the path to being a problem solver. Now that I'm taking Calc 3 and Discrete Math, I have the tools I need to do well in these classes. The funny thing is that a lot of the stuff I'm learning in my Discrete class echos the ideas expressed in this book, which makes me think that they should be teaching students exiting high school with the intention of going to college some of the ideas that Discrete courses focus on. This kind of math helps you see the creative side of math. We often will play games in my class to solidify these concepts. Now, they are games based on logic and not easy by any means, but once you understand what is taking place then it makes math a very exciting language to learn. Anyway, Mr. Devlin wrote a very fine book and it is a book I would highly recommend to anyone trying to understand the language and grammers of mathematics. In fact, forget those "For Dummies" books or any of that other garbage. Learning tricks is all fine and good, but learn to be a problem solver because if you practice little by little and give yourself a chance you can find real joy in a skill far too few people have.
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