Princeton Companion to Mathematics

ISBN-10: 0691118809
ISBN-13: 9780691118802
Edition: 2008
List price: $99.50 Buy it from $44.24 Rent it from $63.21
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Description: What is a modular form? What is the point of symplectic geometry? This one-of-a-kind reference illuminates modern pure mathematics in all its diversity. More than 200 articles, organized thematically and written by many of the world's leading  More...

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Book details

List price: $99.50
Copyright year: 2008
Publisher: Princeton University Press
Publication date: 9/28/2008
Binding: Hardcover
Pages: 1056
Size: 8.50" wide x 10.50" long x 2.50" tall
Weight: 5.016
Language: English

What is a modular form? What is the point of symplectic geometry? This one-of-a-kind reference illuminates modern pure mathematics in all its diversity. More than 200 articles, organized thematically and written by many of the world's leading mathematicians, explain the major ideas and branches of mathematics in a clear, accessible style. Presenting not only definitions but also motivation and context for concepts, methods, theorems, and other topics of mathematical study, this is an indispensable resource for everyone with a serious interest in the field. 1. What is Mathematics? Introduces the language and grammar of mathematics fundamental definitions general goals of mathematical research the subject matter of mathematics 2. The Fundamental Ideas of Mathematics Explores algebra algorithms geometry how analysis became rigorous numbers the crisis in the foundations of mathematics the development of the idea of proof 3. Mathematical Objects Defines and explains more than 75 mathematical objects, concepts, and buzzwords, fromaxiom of choicetozeta function 4. Branches of Mathematics Includes detailed coverage of algebra algebraic geometry analysis combinatorics computation geometry logic and set theory number theory probability 5. Mathematicians Profiles 70 mathematicians, from Apollonius to Weyl, who influenced the field 6. Theorems and Problems Discusses notable theorems and open problems, from the four-color theorem to the Reimann hypothesis 7. The Influence of Mathematics Covers the intellectual and practical influence of mathematics on other disciplines such as analytic philosophy, art, biology, chemistry, economics, finance, and music 8. Miscellaneous Advice to a Young Mathematician Chronology of Mathematics Computer Experiments in Mathematics The Art of Problem Solving and more CONTRIBUTORS (partial list): Graham Allan Noga Alon George Andrews Tom Archibald Michael Atiyah David Aubin Joan Bagaria Keith Ball Alan Beardon David Ben-Zvi Vitaly Bergelson Nick Bingham Bela Bollabas Henk Bos Bodil Branner Haim Brezis Martin Bridson John Burgess Kevin Buzzard Peter Cameron Jean-Luc Chabert Eugenia Cheng Clifford Cocks Alain Connes Leo Corry Wolfgang Coy Tony Crilly Serafina Cuomo Mihalis Dafermos Partha Dasgupta Ingrid Daubechies Joseph Dauben John Dawson Franccedil;ois de Gandt Persi Diaconis Robbert Dijkgraaf Jordan Ellenberg Florence Fasanelli Solomon Feferman Anita Feferman Charles Fefferman Joseacute; Ferreiroacute;s Terry Gannon Tony Gardiner Charles Gillespie Oded Goldreich Catherine Goldstein Franccedil;ois Golse Fernando Gouvea Andrew Granville Ivor Grattan-Guinness Jeremy Gray Ben Green Niccolo Guicciardini Michael Harris Ulf Hashagen Nigel Higson Andrew Hodges Kollar Janos Frank Johnson Mark Joshi Dominic Joyce Jean-Pierre Kahane Frank Kelly Sergiu Klainerman Jon Kleinberg Israel Kleiner Jacek Klinowski Eberhard Knobloch Joe Kohn Tom Korner Peter Lax Jean-Franccedil;ois Le Gall Raymond Lickorish Martin Liebeck Jesper Lutzen Des MacHale Lech Maligranda David Marker Adrian Mathias Jean Mawhin Barry Mazur Colin McLarty Peter Neumann Catherine Nolan James Norris Marco Panza Karen Parshall Jeanne Peiffer Carl Pomerance Helmut Pulte Bruce Reed Mike Reed Adrian Rice Jeremy Rickard Eleanor Robson Igor Rodnianski John Roe Mark Ronan Edward Sandifer Norbe

Introduction
The Origins of Modern Mathematics
Mathematical Concepts
Branches of Mathematics
Theorems and Problems
Mathematicians
The Influence of Mathematics
Final Perspectives
Index

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