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, Béla Bollobás, 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, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò 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, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn 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, Rüdiger 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

CUSTOMER REVIEWS (Average Customer Rating: 4.5 based on 16 reviews)

A great companion with which to navigate higher mathematics by Thomas Fix

5 Stars
July 06, 2009
This book is a great companion with which to navigate higher mathematics. It allows you to quickly intuit the stunning abstract concepts of higher mathematics, that you often cannot easily see when following the traditional approach of deriving concepts rigorously, from a well-defined foundation. This companion guide gives you a top-down perspective to complement the necessary rigorous bottom-up perspective that you get elsewhere. Mathematical encyclopedias and wikipedia topics don't do this as effectively, so I heartily recommend this book.

An amazing tour de force by Vullierme

5 Stars
May 31, 2009
The Princeton Companion to mathematics is certainly one of the most important texts ever written in the very large field of the one concerning introduction to mathematics. It is not an illusion to believe that even the most complex concepts of mathematics , for example algebraic topology or analytic number theory , are accessible by anybody who has at the most, acquired the elementary mathematical knowledge taught in high school. Actually, it is the fact that all the papers collected in the book are written by the most influential mathematicians in the world that makes it possible. The utterly clear writing style of the authors also give a very attractive and agreable aspect to the book. The Companion is not only a collection of detailed introductions to concepts , but also a very useful tool (particularily because a very large part of the book is used to the study of the cultural aspect of mathematics , through biographies and sometimes very deep epistemological analysis of various concepts). The work is then way more important than a simple overview of the global today's knowledge (as an random encyloapedia or a random work of vulgarisation) , but rather a work on general mathematics and everything related to it (applied mathematics , philosophy etc...). Of course , I warmly recommand the PCM to anybody interested into mathematics , or more generally in "hard sciences" . For my part , I enjoyed a passionating and unique odyssea into the universe of mathematics , and it really helped me when studying . It is after all , the best companion you can always rely on. Enjoy A simple look to the panel of the contributors should convince .

excellent grand tour of contemporary mathematics by Daniele Bianchi (Jersey City, NJ)

5 Stars
May 11, 2009
I'm not a specialist in the field and I find this grand overview of contemporary mathematics fascinating. The topics range from accessible to intricate and sometimes obscure for the non-specialist. Nonetheless the authors - themselves specialists in the respective fields - manage to engage the reader through a balance between detail and anecdote, cross references, and historical prospective. The book list of topic is vast and comprehensive, although the coverage, by nature, not exhaustive (further readings are always suggested in bibliographic notes). I was pleasantly surprised by finding essays on the mathematics of music, chemistry, biology and economics, as well as biographic notes on the major mathematicians of history. Overall it makes an outstanding addition to the library of anyone interested in mathematics and its history.

The Princeton Companion to Mathematics by Mohan S. Shrikhande (Mt. Pleasant, MI USA)

5 Stars
May 01, 2009
It's an outstanding standing addition to the the field of mathematics. It should be of great interest to professional and amateur mathematicians,scholars, or anyone who is interested in mathematics. Individual chapters are written by world renowned experts in the field. If you want to learn of some of the various topics, famous problems, conjectures, new developments, history of mathematics, and about famouus mathematicians, etc. this is The Source to look at.

A must have for the math enthusiast by Petel (Israel)

5 Stars
March 23, 2009
I love math, and love testing out mathematical ideas and concepts using computers. The book has already given me hours of enjoyment. I pick up on a topic, explore it a bit, write a script and test it out. I'm not a mathematician by training (my background is engineering) but I do have a strong inclination to math. This book together with Numerical Recepies are my favourite two math books. Ideas and concepts are presented in an an excellent manner. Some of the topics are over my head but I believe in setting the bar a little high and letting people try an reach it. And when I don't want to scribble equations and expressions on paper, or program, I turn to the history and biographies of the great mathematicians and their impact on math and science.

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