Introduction to Mathematical Thinking Paperback Author: Visit Amazon's Keith Devlin Page | Language: English | ISBN:
0615653634 | Format: PDF, EPUB
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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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- Paperback: 102 pages
- Publisher: Keith Devlin (July 18, 2012)
- Language: English
- ISBN-10: 0615653634
- ISBN-13: 978-0615653631
- Product Dimensions: 9 x 6 x 0.2 inches
- Shipping Weight: 6.4 ounces (View shipping rates and policies)
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.
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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