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Kline M. — Mathematical thought from ancient to modern times
Kline M. — Mathematical thought from ancient to modern times

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Название: Mathematical thought from ancient to modern times

Автор: Kline M.

Аннотация:

This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 436

Добавлена в каталог: 03.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abbati, Pietro      765
Abel's theorem      645 653 655 935 936
Abel, Niels Henrik      216 973 974 1024 1053 1097 1111 1137
Abel, Niels Henrik, Abelian integrals      653—655
Abel, Niels Henrik, biography      644 645
Abel, Niels Henrik, elliptic functions      645—650
Abel, Niels Henrik, rigorization of analysis      947 948 964 965 973 974
Abel, Niels Henrik, theory of equations      754 755
Abelian equation      755
Abelian function      665
Abelian integral      653 663 665 936 939 940
Absolute      907
Absolute differential calculus      see "Tensor analysis"
Absolutely continuous function      1048
Abstract algebra      945 1136 1157
Abstract algebra, Lie algebra      1153—1156
Abstract algebra, non associative algebra      1153—1156 see "Abstract "Group" "Ideal" "Ring"
Abstraction      29 43—44 171
Academies      227 370 396 397 401 404 621 1023
Academy of Plato      27 42 43 45 130 190
Ackerman, Wilhelm      1208
Ad Locos Planos et Solidos Isagoge      302 317
Adams, John Couch      369
Adelard of Bath      205 207
Adjoint curve      935
Aesthetics      172 173
Affine geometry      918
Agrippa von Nettesheim      286
Ahmes      16 18 20
Airy's integral      1100 1102 1103
Akkadians      4
Al Battani      195
Al-Biruni      190 195 241
Alberti, Leone Battista      232 233 285
Alembert, Jean Le Rond d'      623 867 1029
Alembert, Jean Le Rond d', algebra      598
Alembert, Jean Le Rond d', calculus      425 465 954
Alembert, Jean Le Rond d', complex function theory      626—628
Alembert, Jean Le Rond d', complex numbers      595
Alembert, Jean Le Rond d', Fourier series      458 459
Alembert, Jean Le Rond d', mechanics      616
Alembert, Jean Le Rond d', ordinary differential equations      477 484 494 500
Alembert, Jean Le Rond d', partial differential equations      503—505 510 512 513 516 517 532 542
Alembert, Jean Le Rond d', rigor      619
Alexander the Great      4 101 102
Alexander, James W.      1176 1777 1179 1180
Alexandria      101—103
Alexandroff, Paul S.      1181
Algebra      364
Algebra and analysis      323 324 361
Algebra as analysis      279 280 323
Algebra vs geometry      49 136 197 198 279—282 318 323 365 391 392 834—836
Algebra, Arabic      191—195
Algebra, Greek (Alexandrian)      104 135—144
Algebra, Hindu      184 188
Algebra, of throws      13 25 31 32 33 34 850 851 see
Algebra, Renaissance      236 237
Algebraic geometry      920 924—946 1168 1169
Algebraic invariants      925—932
Algebraic invariants, absolute      926
Algebraic invariants, complete system      928 929
Algebraic invariants, covariant      926
Algebraic numbers      593 594 818—826 980 996 997
Alhazen      193 196
Almagest      54 122—125 133 159 191
Analytic continuation      642—644 1114
Analytic geometry      see "Coordinate geometry"
Angle, pjojectivc definition of      907 911
Anharmonic ratio      see "Cross ratio"
Apollonian problem      99
Apollonius      56 89 99 135 157 158 168 300
Application of areas      34 74 77
Arabs      181 190—199 205
Archimedes      37 105—116 134 163—166 168 286 395
Archimedes' principle      165 166
Archytas      27 28 42 46 48 49
areas      1042
Areas, calculation of      343 348—354 360
Areas, of surfaces      355 1020
Argand, Jean-Robert      630 631 776
Aristacus the Elder      48
Aristarchus      156 157 156 162 163 207 395 436 776 992 1028
Aristarchus, concept of mathematics      51 151 153
Arithmetic, Arabic      191 192
Arithmetic, Babylonian      5—8
Arithmetic, Egyptian      16 18
Arithmetic, Greek, (Alexandrian)      131—135
Arithmetic, Hindu      183—186
Arithmetic, primitive      3
Arithmetic, Renaissance      251—259
Arithmetica      139 143
Arithmetica Universalis      252 271 272 281 312 318 358 392 607
Arithmetization of analysis      947—972 1025 1026
Arnauld, Antoine      252
Aronhold, Siegfried Heinrich      928
Ars Conjectandi      273 442 451
Ars Magna      236 253 263—265 267 268
Aryabhata      184 187 189
Arzela, Cesare      1046 1077 1078
Ascoli, Giulio      1077
Astrology      13 168 169 179 196 202 203 222
Astronomy      250 470 471 490—497
Astronomy, Arabic      196
Astronomy, Babylonian      11 12
Astronomy, Egyptian      21 22
Astronomy, Greek      119 125 126 148 149 151 154 160
Astronomy, Hindu      189 see "Gravitational "Heliocentric "Three-body
Asymptotic series      1097—1109
Asymptotic series, semiconvergent      1097 1104 see
Athens      37 101
Atomism      150 329
Augustine, Saint      204
Autolycus of Pitane      54
Automorphic functions      726—730
Automorphic functions, elliptic modular      727
Automorphic functions, Fuchsian      729
Automorphic functions, Kleinian      730
Automorphism      1142
Axes of a conic      93—95
Axiom of Archimedes      81 991 1012 1013
Axiom of Choice      1002 1186 1209
Axiom of reducibility      1195 1196
Axiomatization      1026 1027
Axiomatization, of set theory      1185 1187
Axioms      50 52 59 60
Axioms, Hilbert for geometry      1010 1013
Axioms, of Euclid      59 60 1005—1007
Axioms, of non-Euclidean geometry      1015
Axioms, of number      988 991
Axioms, of projective geometry      1007 1010
Axioms, of set theory      1185 1186 see "Parallel
Babbage, Charles      259 622
Backlund, Albert Victor      703
Bacon, Francis      225 226
Bacon, Roger      145 207 208 213 226
Baire, Rene      1079 1186 1199
Baldi, Bemadino      223 229
Baltzer, Richard      879
Banach space      1088—1091 1159 1178
Banach, Stephen      1088 1092
Barrow, Isaac      252 281 339 346 347 356 357 380 383 384
Bartels, Johann M      862 878 879
Base      5 6
Bede, Venerable      202
Beeckman, Isaac      316 478
Beltrami, Eugenio      896 901 902 905 914 1030 1122 1130
Bendixson, Ivar      737
Benedetti, Giovanni Battista      223 229 234 478
Berkeley, George, Bishop      400 427 428
Bernays, Paul      1205
Bernoulli numbers      449 451
Bernoulli, Daniel      401 446 479—481 492 507—510 512 521 524 578 677 1112
Bernoulli, James, calculus      380—383 407 412
Bernoulli, James, calculus of variations      575—577
Bernoulli, James, coordinate geometry      320
Bernoulli, James, differential geometry      562
Bernoulli, James, infinite series      439 442—446 451
Bernoulli, James, ordinary differential equations      471—475 478
Bernoulli, James, probability      273 274
Bernoulli, John      335 340 492 592
Bernoulli, John, calculus      380—383 387 388 406—411
Bernoulli, John, calculus of variations      574—577
Bernoulli, John, coordinate geometry      545
Bernoulli, John, differential geometry      556 562
Bernoulli, John, infinite series      441 442 444 446
Bernoulli, John, ordinary differential equations      472—476 478 479 497 503
Bernoulli, Nicholas (1687—1759)      412 447 461—463
Bernoulli, Nicholas (1695—1726)      401 475
Berry, G.G.      1183
Bessarion, Cardinal      238
Bessel functions      480—482 489 518 519 710 711
Bessel inequality      717 1083
Bessel, Friedrich Wilhelm      710 717 871 872 980
beta function      424
Betti numbers      1169 1173 1174 1176 1177 1179 1180
Betti, Enrico      1169
Beudon, Jules      703
Bezout, Etienne      553 606—608 796 798
Bhaskara      184—186 273
Bianchi, Luigi      554 1122
Binet, Jacques P.M.      796
Binoimal      560 561
Binomial equation      600 752 753 761—764
Binomial theorem      272 273 438 441 964 965
Biot, Jean-Baptiste      836
Biquadratic reciprocity      816—818
Biquaternions      792
Birational transformation      924 932
Birkhoff, George David      1106—1068 1178
Bocher, Maxime      599 607
Boethius, Anicius Manlius Severinus      201
Bolyai, John      873—874 877—881 914 921 1032 1033
Bolyai, Wolfgang Farkas      861 872 878 879
Bolzano, Bernhard      948 950—955 963 979 985 994 1025
Bombelli, Raphael      253—255 260
Bonnet, Ossian      865
Boole, George      927 1189—1191
Borchardt, Carl Wilhelm      624 667 981
Borel, Emile      953 954 1044 1078 1117—1119 1159 1186 1199
Bosse, Abraham      289
Bott, Raoul      1151
Bouquet, Jean—Claude      642 718 722
Bourbaki, Nicolas      1210
Boutroux, Pierre      1182
Bowditch, Nathaniel      496
Boyer, Carl B.      348
Boyle, Robert      227
Brachistochrone      574 575
Brahe, Tycho      203 219 242
Brahmagupta      183 184 192
Branch cut      642 656 657
Branch-point      641 657
Bravais, Auguste      768
Brianchon's theorem      841 848
Brianchon, Charles Julien      836 841
Briggs, Henry      275 276 440
Brill, Alexander von      938 940
Brillouin, Leon      1102
Briot, Charles A.A.      642 718 722
Brouncker, Lord William      255 278 468 469
Brouwer, Luitzen E.J.      1132 1162 1171 1177—1179 1199—1203 1208
Brunelleschi, Filippo      232
Bryson      42
Buchheim, Arthur      808
Burali Forti paradox      1003 1182
Burali-Forti, Cesare      1003
Burgi, Joost      258
Buridan, jean      211 212
Burnside's problem      1143
Burnside, William      1142—1145
Byzantine Empire      180 191 205 216
Caesar, Julius      178 180
Cajori, Florian      263 364
Calculus      342 390 400 435 615 798 see
Calculus of extension      782—785
Calculus of finite differences      440 441 452 453
Calculus of variations      573 591 685 739 751 1076 1078 1081
Calculus of variations, Jacobi condition      745
Calculus of variations, Legendre condition      589 590
Calculus of variations, Weieistrass conditions      748 see
calendar      12 13 21 22 119 178 179
Callett, jean-Charles (Francois)      463 464
Campanus, Johannes      217
Cantor, Georg      824 969 1021 1031 1040 1042 1044 1078 1159 1161 1184 1185
Cantor, Georg, irrational numbers      983—986
Cantor, Georg, sets and transfinite numbers      992—1003
Caratheodory, Constantin      838
Carcavi, Pierre de      275
Cardan, Jerome      221 222 234 236 251—253 260 263—271 1028
cardinal number      993
Carnot, Lazare N.M.      432 593 835 836 841
Carroll, Lewis      see "Dodgson Charles
Cartan, Elie      1151 1155 1156
Cassini, Jacques      320 469
Cassini, Jean Dominque      320
Cassinian ovals      320
Cassiodorus, Aurelius      202
Castelnuovo, Guido      934
Catalan Eugene Charles      788
Cataldi, Pietro Antonio      278
Categoricalness      104 115
Catenary      382 472 579
Cauchy integial theorem      599 636 637 639 640 668 669
Cauchy integral formula      639
Cauchy Lipschitz thcoiem      718
Cauchy Riemann equations      627 628 635 658
Cauchy, Augustin-Louis      465 947 993 1024 1029 1076 1099 1100
Cauchy, Augustin-Louis, algebra      796 798 801 802 815 816
Cauchy, Augustin-Louis, biography      633 634
Cauchy, Augustin-Louis, complex function theory      634—642 667
Cauchy, Augustin-Louis, differential equations      535 680 681 698 701 702 717—721 739 743
Cauchy, Augustin-Louis, differential geometry      560 561
Cauchy, Augustin-Louis, foundations of analysis      948 950—958 961 963—965 973—974 979 1024 1096 1097
Cauchy, Augustin-Louis, geometry      843
Cauchy, Augustin-Louis, group theory      765 766 768 1137
Cauchy, Augustin-Louis, theory of numbers      819
Cavalieri, Bonvaventura      349 350 383 384
Cavalieri’s theorem      349
Cayley Hamilton theorem      807 809
Cayley numbers      792
Cayley, Arthur      478 768 769 792 796 804—807 812 944 1030 1033 1138 1139 1142 1143 1166
Cayley, Arthur, algebraic invariants      927—929 931
Cayley, Arthur, biography      805
Cayley, Arthur, non-Euclidcan geometery      907—909 921—923
Cech, Eduard      1181
Cellerier, Charles      955 956
Cesaro, Ernesto      1018 1112 1113
Chain      1171 1172
Chain rule      376
Chain, oscillations of      480 481
Chaldeans      4
Characteiistic triangle      346 375 387
Characteristic equation of a determinant      800 801
Characteristic equation of a differential equation      485
Characteristic equation of a matrix      807
Characteristic equation of quadratic forms      800 801
Characteristic function      706 707 715 716 1063 1068
Characteristic root of a determinant      800 801
Characteristic root of a matrix      807 808
Characteristic value      480 673 706 707 715 716 1063 1068
1 2 3 4 5 6
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