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Title: The Language of Mathematics: Making the Invisible Visible by Keith J. Devlin ISBN: 0-8050-7254-3 Publisher: Owl Books (NY) Pub. Date: 01 March, 2000 Format: Paperback Volumes: 1 List Price(USD): $17.00 |
Average Customer Rating: 5 (10 reviews)
Rating: 5
Summary: Clear and engaging
Comment: Keith Devlin is one of the best popular mathematics writers around, and this is one of his best works. The eight chapters cover number theory, set theory, calculus, group theory, topology, probability and the application of mathematics to the physical world. The discussion in each chapter, couched generally in English, not mathematics, is so clear that a math-phobic can understand it. By the end of each chapter a great deal of fascinating mathematics has been described, and in some cases the formal basis is sketched--but the emphasis is always on narration, and a lay reader who doesn't even want to understand mathematics can still read this and get a sense of the dramatic history of mathematics.
Devlin states at the end that he decided to exclude many areas of mathematics in order to focus more effectively on what he did cover. As a result there is little or no coverage of chaos theory, game theory, catastrophe theory, or a long list of other topics. The fact is there will always be holes in a book this size--mathematics has expanded so much in the last hundred years that even a book ten times this size could barely survey it. The decision to focus was a good one, and the subjects chosen are good: the truly exciting stories are here: Archimedes, Fermat, Gauss, Galois, Riemann, Wiles, and many more.
Potential purchasers should note, by the way, that this book was reworked from Devlin's "Mathematics: The Science Of Patterns". In Devlin's words (not from either book): "The Language of Mathematics is a restructuring of Science of Patterns that omits most of the color illustrations (a minus) but has two new chapters covering topics not in Science of Patterns (a plus). If you want lots of color, go for patterns; Language of Mathematics covers more ground." I've read both, and I have to say they're both worth getting. The two new chapters in this book are the ones on probability and the applications of mathematics in science; they're well done and interesting. However, the pictures in Science of Patterns are very high quality.
They're both fine books, and I can strongly recommend each of them. If you have to get one, I'd say get Science of Patterns. Even though Language of Mathematics does have some colour plates, Science of Patterns is really a gorgeous book to read with many good illustrations. I ended up buying both, and you may end up doing that too.
Rating: 5
Summary: Step into the shoes of a mathematician
Comment: I've always had a like-hate relationship with math; I didn't do well in it in college, but I've long been fascinated by physics. There are many books for the lay person about the cutting edge in physics; books like that are harder to find in the world of mathematics.
But Keith Devlin has done it. He surely captured me near the beginning when he described mathematics as the study of patterns; a wonderful description that starts to get at why mathematics seems to be the language underlying the physical universe.
This was not an easy book for a slightly math-averse person, but Devlin's explanations were always clear, and more importantly, always gave a sense of context of what he was discussing.
Rating: 5
Summary: Perceiving patterns.
Comment: Devlin: "The particular topics I have chosen are all central themes within mathematics... But the fact is, I could have chosen any collection of seven or eight general areas and told the same story; That mathematics is the science of patterns, and those patterns can be found anywhere you care to look for them, in the physical universe, in the living world, or even in our own minds. And that mathematics serves us by making the invisible visible."
At this writing it has been more than a few years since my last class in mathematics. But I liked math as a student and still do, even at the point that notation and degree of abstraction begins to hurt my head, so to speak, I still like it. There is a solidity and a beauty in mathematics that eclipses the empirical sciences. It is not only the practical applicability, logical purity, and beauty of mathematics that interest me, it is also its very immateriality. As Devlin states, "music exists not on the printed page, but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics."
This is a wonderful book. Before 1900, mathematics could be wholly categorized within about a dozen subjects. While advances are still being made in some of these older disciplines -- Devlin discusses how developments in number theory are being applied to encryption for such purposes as banking security -- there are now at least 60-70 somewhat distinct disciplines of mathematics. The author reveals the logical foundations, history, and current applications of number theory, mathematical logic, the calculus, relativistic geometry, topology, and probability. Applications of mathematics to such seemingly far-flung fields as linguistics, electrodynamics, and astrophysics are briefly but aptly considered. He introduces us to the patterns and progressions of perceptive minds, from the Pythagoreans, Platonists, and Peripatetics, to Pascal and Penrose, with glances at Galileo, Gauss and Godel. [Okay, enough alliteration ... just having a little fun with patterns; and patterns, as Devlin instructs, is precisely what mathematics is all about.]
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Title: Concepts of Modern Mathematics by Ian Stewart ISBN: 0486284247 Publisher: Dover Publications Pub. Date: 01 February, 1995 List Price(USD): $12.95 |
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Title: Life by the Numbers by Keith Devlin ISBN: 0471328227 Publisher: Wiley Pub. Date: 17 March, 1999 List Price(USD): $18.95 |
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Title: What Is Mathematics?: An Elementary Approach to Ideas and Methods (Oxford Paperbacks) by Richard Courant, Herbert Robbins, Ian Stewart ISBN: 0195105192 Publisher: Oxford University Press Pub. Date: 01 May, 1996 List Price(USD): $21.50 |
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Title: Mathematics : The Science of Patterns by Keith Devlin ISBN: 0805073442 Publisher: Owl Books Pub. Date: 15 December, 1996 List Price(USD): $27.00 |
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Title: Foundations and Fundamental Concepts of Mathematics by Howard Eves ISBN: 048669609X Publisher: Dover Publications Pub. Date: 20 May, 1997 List Price(USD): $16.95 |
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