The Princeton Companion to Mathematics is a book, edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, and published in 2008 by Princeton University Press (ISBN978-0-691-11880-2). It provides an extensive overview of mathematics, and is noted for the high caliber of the contributors. The book was a 2011 winner of the Euler Book Prize of the Mathematical Association of America, given annually to 'an outstanding book about mathematics'.[1][2][3][4][5][6][7][8][9][10]
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Topics and organization[edit]
The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both applications of mathematics and the mathematics that relates to those applications;it provides a broad overview of the significant ideas and developments in research mathematics.[2][4][7] It is organized into eight parts:[4][5][6][7][10]
- An introduction to mathematics, outlining the major areas of study, key definitions, and the goals and purposes of mathematical research.[2][4]
- An overview of the history of mathematics, in seven chapters including the development of important concepts such as number, geometry, mathematical proof, and the axiomatic approach to the foundations of mathematics.[3][4][5][7] A chronology of significant events in mathematical history is also provided later in the book.[5]
- Three core sections, totalling approximately 600 pages. The first of these sections provides an alphabetized set of articles on 99 specific mathematical concepts such as the axiom of choice, expander graphs, and Hilbert space. The second core section includes long surveys of 26 branches of research mathematics such as algebraic geometry and combinatorial group theory. The third describes 38 important mathematical problems and theorems such as the four color theorem, the Birch and Swinnerton-Dyer conjecture, and the Halting problem.[2][3][4][5][6][9]
- A collection of biographies of nearly 100 famous deceased mathematicians, arranged chronologically,[2][3][4][5][7][9] also including a history of Nicolas Bourbaki's pseudonymous collaboration.[6][9]
- Essays describing the influences and applications of mathematics in the sciences, technology, business, medicine, and the fine arts.[2][3][4][5]
- A section of perspectives on the future of mathematics, problem solving techniques, the ubiquity of mathematics, and advice to young mathematicians.[4][5]
Despite its length, the range of topics included is selective rather than comprehensive: some important established topics such as diophantine approximation are omitted, transcendental number theory, differential geometry, and cohomology get short shrift, and the most recent frontiers of research are also generally not included.[6]
Target audience[edit]
The book's authors have attempted to keep their work accessible by forgoing abstraction and technical nomenclature as much as possible and by making heavy use of concrete examples and illustrations.[2] Compared to the concise and factual coverage of mathematics in sources such as Wikipedia and MathWorld, the articles in the Princeton Companion are intended to be more reflective and discursive,[5] and to convey the beauty and depth of modern mathematics.[8] Quoting a passage from Bertrand Russell that 'Pure Mathematics is the class of all propositions of the form p implies q', the editor of the Companion states that it 'is about everything that Russell’s definition leaves out.'[7][8]
The core sections of the Companion are aimed primarily at readers who are already familiar with mathematics at the undergraduate level.[2][5] Much of the rest of the book, such as its collection of biographies, would be accessible to a mathematically inclined high school student,[2][3][6] and there is enough depth of coverage in the book to interest even professional research mathematicians.[4][6] Reviewer Jonathan Borwein summarizes the audience for this book broadly:[7][11]
“ | Every research mathematician, every university student of mathematics, and every serious amateur of mathematical science should own at least one copy of the Companion. | ” |
Contributors[edit]
The contributors to The Princeton Companion to Mathematics consist of 133 of the world's best mathematicians.[1][2][9] Timothy Gowers, its editor, is the recipient of the Fields Medal, considered to be the top honor in mathematics.[2][4] Other contributors include Fields medalists Michael Atiyah, Alain Connes, Charles Fefferman, and Terence Tao, and well-known mathematicians Noga Alon, George Andrews, Béla Bollobás, John P. Burgess, Clifford Cocks, Ingrid Daubechies, Persi Diaconis, Jordan Ellenberg, Oded Goldreich, Andrew Granville, Jeremy Gray, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, János Kollár, Peter Lax, Dusa McDuff, Barry Mazur, Carl Pomerance, Eleanor Robson, Peter Sarnak, Madhu Sudan, Clifford Taubes, and Avi Wigderson. Among the historians who contributed to it are Charles C. Gillispie, Ivor Grattan-Guinness, Jeremy Gray, Niccolò Guicciardini, Ulf Hashagen, Eberhard Knobloch, Karen Hunger Parshall, Eleanor Robson, and Erhard Scholz.[1][4][5][6][7]
Awards[edit]
Gowers and the Princeton Companion were the 2011 winners of the Euler Book Prize of the Mathematical Association of America, given annually to 'an outstanding book about mathematics'.[1]
The Princeton Companion was also listed as an outstanding title by Choice Magazine, a publication of the American Library Association, in 2009.[12]
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See also[edit]
- The Princeton Companion to Applied Mathematics, published 2015 and edited by Nicholas Higham
References[edit]
- ^ abcdJanuary 2011 Prizes and Awards, American Mathematical Society, retrieved 2011-02-01.
- ^ abcdefghijkStewart, Ian (November 21, 2008), 'The Princeton Companion to Mathematics and The Numerati: How They'll Get My Number and Yours', The Times.
- ^ abcdefSiegfried, Tom (November 7, 2008), 'Book Review: The Princeton Companion to Mathematics, Timothy Gowers, ed', Science News.
- ^ abcdefghijklAziz, Haris (2010), 'Review of The Princeton Companion to Mathematics'(PDF), ACM SIGACT News, 41 (1): 31–33, doi:10.1145/1753171.1753183.
- ^ abcdefghijkFraser, Craig G. (2010), 'Book Review: The Princeton Companion to Mathematics', Historia Mathematica, 37 (1): 110–112, doi:10.1016/j.hm.2009.08.001.
- ^ abcdefghBirch, Bryan; Donaldson, Simon; Kalai, Gil; Kenyon, Richard; Macintyre, Angus (2009), 'The Princeton companion to mathematics'(PDF), Notices of the American Mathematical Society, 56 (10): 1276–1281, MR2572756.
- ^ abcdefghBorwein, Jonathan M. (2009), 'The Princeton companion to mathematics', SIAM Review, 51 (4): 790–794, MR2573944.
- ^ abcKennedy, Juliette (2009), 'The Princeton companion to mathematics', Bulletin of Symbolic Logic, 15 (4): 431–436, doi:10.1017/S1079898600008374, MR2723560.
- ^ abcdeTao, Terence (2009), 'The Princeton companion to mathematics', Mathematical Reviews, MR2467561.
- ^ abWilson, Robin (2009), 'The Princeton Companion to Mathematics', London Mathematical Society Newsletter, 378.
- ^In his review, Robin Wilson expresses very similar sentiments: 'Once in a while a book comes along that should be on every mathematician’s bookshelf. This is such a book.'
- ^Review by S. J. Colley, 2009, Choice Reviews Online, retrieved 2011-02-01.
External links[edit]
- Book homepage at Princeton University Press; contains several sample chapters
- Princeton Companion To Mathematics category in Gowers's blog
Retrieved from 'https://en.wikipedia.org/w/index.php?title=The_Princeton_Companion_to_Mathematics&oldid=912198284'
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 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
Princeton University Press
The Princeton Companion To Applied Mathematics PDF | |
Author | Timothy Gowers |
Isbn | 0691118809 |
File size | 41.7 MB |
Year | 2008 |
Pages | 1034 |
Language | English |
File format | |
Category | Mathematics |