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Title: Mathematics and the Imagination by Edward Kasner, James Newman, James Roy Newman ISBN: 0-486-41703-4 Publisher: Dover Publications Pub. Date: 01 April, 2001 Format: Paperback Volumes: 1 List Price(USD): $12.95 |
Average Customer Rating: 4.5 (6 reviews)
Rating: 4
Summary: Great for high schoolers with interest
Comment: My only complaint is its lack of rigor and the fact that it is getting rather out-of-date; besides that, this is the sort of book that everyone interested in math should read while they're in high school.
Rating: 5
Summary: Indulge your enjoyment of mathematics and expand your mind
Comment: My school teacher gave me this book to read when I was 13 years old, based on the interest I showed in Mathematics that went beyond the curriculum at school. In many ways it was way beyond my comprehension at the time, but little did I know that it would have such a lasting effect on me. Reading about concepts of infinity, that you could only describe to a fellow teenager as "different sizes of infinity", I realized that there really is a philosophy of mathematics that transcends all other subjects and that there is also an art to working with the subject. I can't recommend this book enough, and I never did give it back to my teacher!
Rating: 4
Summary: Somewhat dated but still well worth reading
Comment: Originally published in 1940, the material in this book is beginning to show a little age. However, the quality of the writing renders those defects to near irrelevancy. Popular descriptions of mathematics are differentiated by the quality of the writing rather than the distinctiveness of the mathematics, and this one shines.
I like this book, starting with the title. It takes an enormous amount of imagination to do mathematics, something unappreciated by the public. It is easy to understand the use of linear segments to approximate the length of a curve. However, it requires an enormous leap of abstraction to believe that if they are made of zero length and then summed up, the result is the true length. Calculus students dutifully record and apply this, but in most cases don't appreciate the significance of the idea. In nearly all cases of major mathematical advancement, a fundamental change in thought processes was necessary. Those changes require imagination and the advances explained in this book are well documented and described.
Mathematicians are containers of some of the greatest concentrations of imagination that humans possess. Their leaps of abstraction often include descriptions of objects that cannot be visualized. Kasner and Newman capture this essential ingredient, serving it up in palatable portions.
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Title: 100 Great Problems of Elementary Mathematics: Their History and Solution by Heinrich Dorrie ISBN: 0486613488 Publisher: Dover Publications Pub. Date: 01 February, 1965 List Price(USD): $12.95 |
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Title: Journey Through Genius: The Great Theorems of Mathematics by William Dunham ISBN: 014014739X Publisher: Penguin Books Pub. Date: 01 August, 1991 List Price(USD): $14.95 |
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Title: Math Through the Ages: A Gentle History for Teachers and Others by William P. Berlinghoff, Fernando Q. Gouvea ISBN: 1881929213 Publisher: Oxton House Pub Pub. Date: 01 August, 2002 List Price(USD): $19.95 |
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Title: Mathematics, Magic and Mystery by Martin Gardner ISBN: 0486203352 Publisher: Dover Publications Pub. Date: 01 June, 1956 List Price(USD): $7.95 |
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Title: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio ISBN: 0767908163 Publisher: Broadway Books Pub. Date: 23 September, 2003 List Price(USD): $14.95 |
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