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The Princeton Companion to Mathematics:

The Princeton Companion to Mathematics

Author(s): Timothy Gowers
Publisher: Princeton
Date    : October 5, 2008
Pages : 1
Format : PDF
OCR    : Y
Quality  :

Language :

ISBN-10  : 0691118809
ISBN-13  :

Review
This is a wonderful book. The content is overwhelming. Every practicing mathematician, everyone who uses mathematics, and everyone who is interested in mathematics must have a copy of their own.
(Simon A. Levin, Princeton University )
Product Description
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.
Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
* Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors
* Presents major ideas and branches of pure mathematics in a clear, accessible style
* Defines and explains important mathematical concepts, methods, theorems, and open problems
* Introduces the language of mathematics and the goals of mathematical research
* Covers number theory, algebra, analysis, geometry, logic, probability, and more
* Traces the history and development of modern mathematics
* Profiles more than ninety-five mathematicians who influenced those working today
* Explores the influence of mathematics on other disciplines
* Includes bibliographies, cross-references, and a comprehensive index
Contributors incude:
Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Bela Bollobas, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, Jose Ferreiros, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvea, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolo Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, Janos Kollar, T. W. Korner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-Francois Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lutzen, Des MacHale, Alan L. Mackay, Shan Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rudiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger

The Princeton Companion to Mathematics contains contributions by about 100 of the world's leading mathematicians, and its editor, Timothy Gowers, is a winner of the Fields Medal, the highest honour in mathematics. It concentrates on pure mathematics, done for its own sake without any specific application in mind. Its coverage is broad, but it is not an encyclopaedia.

Related Links
Critic's Chart: Tom Whitwell picks six books with big ideas
The Numerati by Stephen Baker plus Buy.ology by Martin Lindstrom
The core is a section on the different branches of mathematics. At school we encounter a few basic concepts in arithmetic, algebra, geometry, calculus, probability and not much else. The professional community recognises about 100 major branches of mathematics, with names such as “algebraic topology” and “stochastic processes”. They represent the hidden world of frontier research, and they are as unlike school mathematics as composing a symphony differs from playing scales on a piano.

It is almost impossible to convey much about these frontier activities without employing technical terms, formulas and abstract concepts. The Companion makes a heroic attempt to keep these to a minimum, but the minimum is fairly big. A mathematics undergraduate would feel comfortable with this part of the book, but a school student would struggle.

Most of the rest of the book is accessible to anyone with an interest in mathematics and some basic high school background. There are biographies of mathematicians and a discussion of the origins of modern mathematics. There are essays on applications of mathematics to areas such as chemistry, biology, traffic flow, transmission of digital information, money, medicine, music and art.

The Companion is an ambitious attempt to do something valuable, and it is not the fault of contributors or editor that it is impossible to realise this ambition completely. The book conveys the breadth, depth and diversity of mathematics. It is impressive and well written, and it's good value for money.

The Numerati is short, has no formulas, and no overt mathematical concepts beyond ordinary numbers. It's written in a breezy journalistic style and it avoids sensationalism even when this must have been tempting. It is about the numerical data that supermarkets, banks and internet service providers collect and how they use it - or hope to use it. The numerati have got your number. They've been collecting data for years but until recently had no idea what to do with it.

Your supermarket loyalty card is not free. You pay for it by allowing the supermarket to collect information about your purchases. They know that you always buy a particular brand of razor. Occasionally you pick up a chocolate bar at the checkout. They know how frequently you do this, what your total spend is. So far they've used this data in limited ways. But soon the numerati will be making more effective use of your personal data to persuade you to buy stuff that you wouldn't otherwise have bought. “You like Cherry Coke. How much would Pepsi have to slash the price of its Wild Cherry Cola to entice you to switch?” The hold over you will be even greater when they can track your shopping cart as you pass through the store, link that to your loy-alty card and flash messages on a screen pointing out bargains that they think will appeal to you. And this kind of thing will also happen in your relations with your employer, your vote, your doctor, even your love life.

Is this mathematics? Or is it just numbers? The data may be numbers, but what you do with it involves high-powered maths. Vast amounts of mathematics lurk just under the surface of our lives, making everything possible.

Some of these developments are good, some bad - loss of privacy, even a police state. Another key question, strangely missing from the book, is: will we let these things happen? As the numerati build ever more effective weapons to control our lives, we may decide not to play their games. For every advertisement on the web there is a free add-on to block it. And ultimately, we can spend only what we earn. The numerati may encourage us to spend it on them, rather than on the opposition, but this arms race has a cost. Like air miles, it could become self-defeating - expensive to operate and of little value once everyone is doing it.

The Princeton Companion to Mathematics.part1