The Princeton Companion to Mathematics

Front Cover
Timothy Gowers, June Barrow-Green, Imre Leader
Princeton University Press, Jul 18, 2010 - Mathematics - 1056 pages
25 Reviews

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. Gouvęa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolň 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

 

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Review: The Princeton Companion to Mathematics

User Review  - So Hakim - Goodreads

Just five words: "General Map of Mathematical World". No, you're not supposed to read it from beginning to the end. No, you're not supposed to know it all by heart. But use it as reference, check ... Read full review

Review: The Princeton Companion to Mathematics

User Review  - SaЯRah Muhammad - Goodreads

The Princeton Companion to Mathematicsis a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. Over 200 entries by a panel of experts ... Read full review

Contents

II
6
V
13
VI
21
VII
53
VIII
82
XI
88
XII
100
XIII
111
CXL
701
CXLI
703
CXLII
704
CXLIII
705
CXLIV
707
CXLV
708
CXLVIII
711
CXLIX
713

XIV
122
XV
134
XVI
147
XVII
162
XVIII
164
XX
165
XXI
166
XXII
168
XXIII
170
XXIV
172
XXV
174
XXVI
175
XXVII
177
XXVIII
179
XXIX
180
XXX
185
XXXI
189
XXXII
192
XXXIII
195
XXXV
196
XXXVI
198
XXXVII
201
XXXVIII
204
XXXIX
207
XL
209
XLI
213
XLII
215
XLIII
218
XLIV
219
XLV
220
XLVI
221
XLVII
224
XLVIII
226
LI
227
LII
228
LIV
230
LV
232
LVI
233
LVII
234
LIX
239
LX
244
LXI
246
LXII
249
LXIII
251
LXIV
252
LXV
253
LXVI
254
LXVII
255
LXVIII
257
LXXI
259
LXXII
260
LXXIII
262
LXXIV
263
LXXV
264
LXXVI
266
LXXVIII
268
LXXIX
272
LXXX
274
LXXXI
277
LXXXII
280
LXXXIII
284
LXXXIV
287
LXXXV
288
LXXXVI
289
LXXXVII
290
LXXXVIII
293
LXXXIX
295
XC
299
XCI
300
XCII
302
XCIII
306
XCV
308
XCVI
312
XCVII
314
XCVIII
315
XCIX
318
CII
319
CIII
320
CIV
337
CV
368
CVI
377
CVII
388
CVIII
401
CIX
413
CX
424
CXI
436
CXII
453
CXIII
460
CXIV
488
CXV
498
CXVI
515
CXVII
528
CXVIII
544
CXIX
555
CXX
567
CXXI
580
CXXII
609
CXXIII
620
CXXIV
640
CXXV
652
CXXVI
662
CXXVII
675
CXXVIII
686
CXXXII
689
CXXXIII
690
CXXXIV
691
CXXXV
692
CXXXVI
694
CXXXVIII
696
CXXXIX
698
CL
715
CLI
716
CLII
718
CLIII
719
CLV
720
CLVI
723
CLVII
725
CLVIII
727
CLIX
728
CLX
730
CLXI
731
CLXII
733
CLXIII
734
CLXIV
738
CLXVIII
739
CLXX
740
CLXXII
741
CLXXIV
742
CLXXV
743
CLXXVI
744
CLXXVII
745
CLXXVIII
746
CLXXIX
747
CLXXX
748
CLXXXI
750
CLXXXII
752
CLXXXIII
754
CLXXXIV
755
CLXXXV
756
CLXXXVI
757
CLXXXVII
759
CLXXXVIII
760
CLXXXIX
762
CXC
763
CXCI
764
CXCIII
765
CXCIV
767
CXCV
769
CXCVI
770
CXCVII
771
CXCVIII
772
CXCIX
773
CC
774
CCI
775
CCII
776
CCIII
777
CCIV
778
CCV
779
CCVI
781
CCVIII
782
CCIX
783
CCX
785
CCXII
787
CCXIII
788
CCXIV
789
CCXV
790
CCXVI
792
CCXVII
793
CCXVIII
794
CCXIX
795
CCXX
796
CCXXI
797
CCXXIII
799
CCXXIV
800
CCXXV
801
CCXXVI
802
CCXXVII
803
CCXXVIII
804
CCXXIX
805
CCXXX
806
CCXXXII
807
CCXXXIII
808
CCXXXIV
810
CCXXXV
811
CCXXXVI
812
CCXXXVII
813
CCXXXVIII
814
CCXXXIX
816
CCXL
817
CCXLI
818
CCXLII
819
CCXLIII
821
CCXLV
822
CCXLVI
824
CCXLVII
827
CCXLVIII
828
CCXLIX
832
CCLII
842
CCLIII
853
CCLIV
867
CCLV
876
CCLVI
883
CCLVII
892
CCLVIII
900
CCLIX
915
CCLX
921
CCLXI
926
CCLXII
933
CCLXIII
940
CCLXIV
949
CCLXV
960
CCLXVII
971
CCLXVIII
982
CCLXIX
988
CCLXX
996
CCLXXI
1005
CCLXXII
1015
CCLXXIII
1020
Copyright

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About the author (2010)

Timothy Gowers is the Rouse Ball Professor of Mathematics at the University of Cambridge. He received the Fields Medal in 1998, and is the author of "Mathematics: A Very Short Introduction". June Barrow-Green is lecturer in the history of mathematics at the Open University. Imre Leader is professor of pure mathematics at the University of Cambridge.

Bibliographic information