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156 of 168 people found the following review helpful
5.0 out of 5 stars Changed the way I thought of Math
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...
Published on September 20, 2012 by DanP

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37 of 44 people found the following review helpful
2.0 out of 5 stars Good topic, but not well explained
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...
Published 21 months ago by Quantstyle


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156 of 168 people found the following review helpful
5.0 out of 5 stars Changed the way I thought of Math, September 20, 2012
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This review is from: Introduction to Mathematical Thinking (Paperback)
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. All you need is a good handle on core concepts and, if you are like myself, a tangible application (even if its somewhat metaphorical or anodyne), and you will be able to appreciate what Professor Devlin has done with this course.

If you are willing and able to learn past the age of 20, hated math your entire existence but are finding useful applications for it as you age, then this book and the corresponding course are entirely for you.

Thank you, Professor Devlin, for doing what no teacher was able to for decades - finally get through to a smart kid who just lacked the appropriate impetus to apply himself.
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44 of 48 people found the following review helpful
4.0 out of 5 stars Thinking like a mathmatician, October 29, 2012
This review is from: Introduction to Mathematical Thinking (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. The book was not really necessary for the class, the video lectures were very close to the text and the problem sets could be printed out and worked on offline but I do feel that having the book helped me. I find it impossible to highlight a point in a video lecture.

I was concerned about how a class this large could be taught, in all the math classes I have taken the learning takes place not during the lecture but answering questions that come up after attempting to work problems related to the lecture. Advanced students were recruited to act as Teaching Assistants to keep an eye on the discussion threads and answer questions when they could. Threads that had heavy traffic were brought to professor Devlin's attention and he, most often, just confirmed what the TA's had said. Learning directly from the book is possible but would mean losing what for me was the most helpful part of the class, the forums.

I learned a lot taking the class, principally that you can forget a lot in thirty years. I was over a week behind in the work and struggling not to fall farther behind when it came time for the final exam. Needless to say I will not be getting a certificate of completion. I also learned several other things, Coursera classes really are college level, someone only a few years out of high school would have had to work to finish the class and would have been prepared for higher mathematics classes and would be better able to think logically.

It was expected that out of the over 50,000 students that started the class as few as 5,000 would successfully finish it but as Dr. Devlin pointed out, teaching 5,000 students in traditional classes of 25 students would represent one professor's entire career. This one class introductory level class freed up one career to teach higher level classes.
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37 of 44 people found the following review helpful
2.0 out of 5 stars Good topic, but not well explained, March 21, 2013
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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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26 of 30 people found the following review helpful
5.0 out of 5 stars Welll Written & Informative, September 16, 2012
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This review is from: Introduction to Mathematical Thinking (Paperback)
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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8 of 8 people found the following review helpful
5.0 out of 5 stars Thanks for reminding me its fun to be smart, September 28, 2012
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This review is from: Introduction to Mathematical Thinking (Paperback)
I bought this book because I had signed up for the Introduction to Mathematical Thinking on line course just for the heck of it. At 64 I wanted to challenge myself with something more difficult than reruns of Jeopardy. This book and the course, taught by the author, have been not only a challenge but a delight as well. The author's enthusiasm for his subject and his obvious joy in teaching shine through. I will probably never do anything more complicated than balancing my check book but I feel just a bit like a mathematician. And that makes me smile.
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10 of 11 people found the following review helpful
2.0 out of 5 stars Slow to get to the point, March 30, 2013
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College level mathematics is different to AP/ IB mathematics and there is a need to bridge the transition. This book just takes a loooong time to get to the differences. Too much repetition about the need to make the transition and the need to go slow, when does it ever get to the depth of the topic?
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9 of 10 people found the following review helpful
3.0 out of 5 stars If you take the course it will help to have the book., December 25, 2012
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This review is from: Introduction to Mathematical Thinking (Paperback)
I took the course online. There isn't any information in the book that's not already
in the lectures for the course.

The problem is actually the course itself. This is a very difficult change to make in your
approach to higher mathematics and getting a passing grade in college math.

My personal opinion is that the course was poorly presented.
It was a typical top down approach. Time spent on discussion and information that
caused more confusion than anything. There were also large gaps in the flow of
information that leads a student from one concept to another. Just as you began to
grasp a concept the material would jump ahead so far that you felt as though you just
missed an entire chapter somewhere.
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12 of 14 people found the following review helpful
3.0 out of 5 stars Good companion for course, November 5, 2012
This book was very worthwhile as a reference while taking the Cousera course of the same name. However, without the answers to posed questions, or at least some guidance in how to develop the answer, it is quite limited in value to someone buying it without taking the course and having access to the discussion forums.
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6 of 6 people found the following review helpful
3.0 out of 5 stars Not for everyone, February 13, 2013
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This review is from: Introduction to Mathematical Thinking (Paperback)
You need a fresh background in math to get much out of the book. I would not have purchased it if I had known it is a transitional book for those coming put of a high school math program and entering a university math program.
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22 of 28 people found the following review helpful
4.0 out of 5 stars Love It, September 13, 2012
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This review is from: Introduction to Mathematical Thinking (Paperback)
Picked up the book for the Coursera class and am loving it. Concise, precise and thoughtful. You can tell Dr. Devlin loves mathematics. Knocked a star off because there are no margins, and I really miss not having space to mark up the text. I understand the book is self-published and what a deal for ten dollars, but I would have been willing to pay another dollar or two for margins.
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Introduction to Mathematical Thinking
Introduction to Mathematical Thinking by Keith Devlin (Paperback - July 18, 2012)
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