The Princeton Companion to Mathematics

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. Accessible in 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 contributorsPresents major ideas and branches of pure mathematics in a clear accessible styleDefines and explains important mathematical concepts methods theorems and open problemsIntroduces the language of mathematics and the goals of mathematical researchCovers number theory algebra analysis geometry logic probability and moreTraces the history and development of modern mathematicsProfiles more than ninety-five mathematicians who influenced those working todayExplores the influence of mathematics on other disciplinesIncludes bibliographies cross-references and a comprehensive indexContributors 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