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  - Arun Kumar - Goodreads

Excellent companion/reference book to delve into pure mathematical concepts, theorems and many more in mathematics. I have not read this completely, but started refering to it frequently. Read full review

Contents

II
6
V
13
VI
21
VII
53
VIII
82
XI
88
XII
100
XIII
111
CXLI
701
CXLII
703
CXLIII
704
CXLIV
705
CXLV
707
CXLVI
708
CXLIX
711
CL
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
XLV
219
XLVI
220
XLVII
221
XLVIII
224
XLIX
226
LII
227
LIII
228
LIV
230
LV
232
LVI
233
LVII
234
LVIII
239
LIX
244
LX
246
LXI
249
LXIII
251
LXIV
252
LXV
253
LXVI
254
LXVII
255
LXVIII
257
LXIX
259
LXX
260
LXXI
262
LXXII
263
LXXIII
264
LXXIV
266
LXXVI
268
LXXVII
272
LXXVIII
274
LXXIX
277
LXXX
280
LXXXI
284
LXXXII
287
LXXXIII
288
LXXXIV
289
LXXXV
290
LXXXVII
293
LXXXVIII
295
LXXXIX
299
XC
300
XCI
302
XCII
306
XCIV
308
XCV
312
XCVI
314
XCVII
315
XCVIII
318
CI
319
CII
320
CV
337
CVI
368
CVII
377
CVIII
388
CIX
401
CX
413
CXI
424
CXII
436
CXIII
453
CXIV
460
CXV
488
CXVI
498
CXVII
515
CXVIII
528
CXIX
544
CXX
555
CXXI
567
CXXII
580
CXXIII
609
CXXIV
620
CXXV
640
CXXVI
652
CXXVII
662
CXXVIII
675
CXXIX
686
CXXXIII
689
CXXXIV
690
CXXXV
691
CXXXVI
692
CXXXVII
694
CXXXIX
696
CXL
698
CLI
715
CLII
716
CLIII
718
CLIV
719
CLVI
720
CLVII
723
CLVIII
725
CLIX
727
CLX
728
CLXI
730
CLXII
731
CLXIII
733
CLXIV
734
CLXV
738
CLXIX
739
CLXXI
740
CLXXIII
741
CLXXV
742
CLXXVI
743
CLXXVII
744
CLXXVIII
745
CLXXIX
746
CLXXX
747
CLXXXI
748
CLXXXII
750
CLXXXIV
752
CLXXXV
754
CLXXXVI
755
CLXXXVII
756
CLXXXVIII
757
CLXXXIX
759
CXC
760
CXCI
762
CXCII
763
CXCIII
764
CXCV
765
CXCVI
767
CXCVII
769
CXCVIII
770
CXCIX
771
CC
772
CCI
773
CCII
774
CCIII
775
CCIV
776
CCV
777
CCVI
778
CCVII
779
CCVIII
781
CCX
782
CCXI
783
CCXII
785
CCXIV
787
CCXV
788
CCXVI
789
CCXVII
790
CCXVIII
792
CCXIX
793
CCXX
794
CCXXI
795
CCXXII
796
CCXXIII
797
CCXXV
799
CCXXVI
800
CCXXVII
801
CCXXVIII
802
CCXXIX
803
CCXXX
804
CCXXXI
805
CCXXXII
806
CCXXXIV
807
CCXXXV
808
CCXXXVI
810
CCXXXVII
811
CCXXXVIII
812
CCXXXIX
813
CCXL
814
CCXLI
816
CCXLII
817
CCXLIII
818
CCXLIV
819
CCXLV
821
CCXLVII
822
CCXLVIII
824
CCXLIX
827
CCL
828
CCLI
832
CCLIV
842
CCLV
853
CCLVI
867
CCLVII
876
CCLVIII
883
CCLIX
892
CCLX
900
CCLXI
915
CCLXII
921
CCLXIII
926
CCLXIV
933
CCLXV
940
CCLXVI
949
CCLXVII
960
CCLXIX
971
CCLXX
982
CCLXXI
988
CCLXXII
996
CCLXXIII
1005
CCLXXIV
1015
CCLXXV
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