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Kline M. — Mathematical Thought from Ancient to Modern Times, Vol. 1
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Íàçâàíèå: Mathematical Thought from Ancient to Modern Times, Vol. 1Àâòîð: Kline M. Àííîòàöèÿ: Now available in a new three-volume paperback edition, Morris Kline's monumental work presents the major creations in mathematics from its beginnings in Babylonia and Egypt through the first few decades of the twentieth century. Organized around the central ideas of mathematical thought, as well as the men responsible for them, this comprehensive history provides a broad panorama of the development of mathematics, displaying the unity behind the disconnected branches of the discipline today. Beginning with the origins of mathematics in Babylonia and Egypt, Volume One includes chapters on classical Greek and Alexandrian mathematics, Hindu and Arabic contributions, algebra in the sixteenth and seventeenth centuries, coordinate geometry, and the creation of calculus.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1990Êîëè÷åñòâî ñòðàíèö: 432Äîáàâëåíà â êàòàëîã: 03.04.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Folium of Descartes 549 Fontaine des Bertins, Alexis 425 471 Fontana, Niccolo See Tartaglia Niccolio Formalism 1203—1208 Foundations 979—1022 Foundations of mathematics 1182—1210 Foundations, algebra 176 282 772—775 980 Foundations, analysis 383—389 426—434 947—977 Foundations, arithmetic 176 596—597 775—776 950 972 Foundations, geometry 1005—1022 Fourier integral 679—681 Fourier series 456—459 513—514 674—678 966—972 1040 1046—1047 1119; Fourier transform 681 1052—1053 1074 Fourier transform, integral 679—681 Fourier, Joseph 502 949 937 961—962 1024 1036—1037 Fourier, Joseph, biography 671—672 Fourier, Joseph, partial differential equations 672—680 Fourier, Joseph, special functions 710 Fraenkel, Abraham A. 1186 Frechet, Maurice 1078—1080 1082 1084 1159—1161 Fredholm alternative theorem 1060 1067—1069 1090—1091 Fredholm, Erik, Ivar 1056 1058 Frege, Gottlob 988 1034 1191 Frenet, Frederic-Jean 562 Frenicle de Bessy, Bernard 276 Fresnel integrals 1100 Fresnel, Augustin Jean 697 1036 1052 Frobenius, F.Georg 464 725 793 808—809 1112 1113 1141—1142 1145 Fubini, Guido 1048—049 Fuchs, Lazarus 721—722 724—725 737 Function concept 338—340 403—406 505—507 677—679 949—954 Functional 1077—1081 Functional analysis 1076—1095 1159 Functional, differential of 1080 Functional, semi-continuity of 1079 Functions of bounded variation 971 1048 Functions of real variables 1040—1050 Fundamental group 1174—1175 Fundamental theorem of algebra 595 597—598 Fundamental Theorem of Arithmetic 79—80 817 819 824 Fundamental theorem of the calculus 373—374 956—957 Galen 103 Galilei, Galileo 203 219 223 229 323 478 993 Galilei, Galileo, astronomy 246—247 Galilei, Galileo, biography 327—328 Galilei, Galileo, calculus 348—349 356 Galilei, Galileo, methodology and philosophy of science 327—35 616 620 Galois theory 752—764 Galois, Evariste 633 752 1024 1137 1146 Galois, Evariste, algebla 271 595 598—599 752—753 776—777 793 796 Galois, Evariste, biography 870—871 882 1147 Galois, Evariste, complex numbels and functions 631—633 Galois, Evariste, constructions 753—754 Galois, Evariste, differential equations 682 684—685 712 723 Galois, Evariste, differential geometry 882—890 Galois, Evariste, foundations of analysis 949 962 Galois, Evariste, group theory 764—768 Galois, Evariste, mechanics 740 Galois, Evariste, non-Euclidean geometry 868 870—874 877—881 921 947—948 Galois, Evariste, special functions 424 Galois, Evariste, theory of equations 756—757 760—763 Galois, Evariste, theory of numbers 813—820 826—830 Galoisian equation 763 Gamma function 423—424 Gans, Richard 1108 Gassendi, Pierre 396 Gauss, Carl Friedrich 980 993 1006 1024 1032 1136—1137 1145 1164 Gcnelators of a group 1141 1143 Geminus of Rhodes 1045 Generality 394 Generalized coordinates 588—589 Gentzen, Gerhard 1209 Genus 654—655 661 936940 1166—1167 Genus, geometrical 944 Genus, numerical 944—945 Geocentric theory 154—160 241 Geodesic 562—563 575—577 886 891 Geodesy 116—117 Geography 119 160—162 Geometrical algebra 62—67 76—77 108 195 Geometry from the transformation viewpoint 917—920 Geometry of numbers 829 Geometry vs analysis 614—616 Gerard of Cremona 89 Gerbert (Pope Sylvester II) 202 Gergonne, Joseph Diez 624 837 842 845—846 1008 Germain, Sophie 702 739 884 Ghetaldi, Marino 280 Gibbs. Josiah Willard 786 87 791 Gilbert de la Poree 206 Gilbert, William 228 Girard, Albert 253 270 Glegory, Duncan F. 774 980 Gnomon 30—31 Godel, Kurt 1206—207 1209 Goldbach's "theorem" 616 Goldbach, Christian 422 462—463 597—598 616 Gombaud, Antoine, Chevalier de Mere 273 Gordan, Paul 929—930 934 939—940 Goudin, Matthieu B. 554 Goursat, Edouard 668—669 702 Gradient 781 786 789 901—902 Grandi, Guido 387 445—446 Grassmann, Hermann Guenther 782—785 791 793 914 984 1017 1030 Gravitational attraction 343 357—358 367—368 469 490—494 522—530 Greek mathematics summarized 171—177 Greek science 49—50 103 145—169 Green's function 683—685 692 1069 Green's theorem 683 692—696 Green, George 683—685 1101—1102 Gregory of St.Vincent 300 354 356 437 Gregory — Newton formula 440—441 Gregory, David 470 573 Gregory. James 270—271 339 355—356 388—389 438—439 441 461 Grelling, Kurt 1183—1184 Grosseteste, Robelt 207 213 226 580 Grossmann, MarceI 1131 Group 757—758 Group character 1145 Group in topology 1180 Group of an equation 758 Group representation 768 1143—1145 Group, abelian 767 Group, abstract 769 1137—1146 Group, alternating 762 Group, composite 766 1142 Group, continuous transformation 1139—1140 1154—1155 Group, discontinuous 726—730 Group, index 759 Group, infinite 726—730 769 Group, linear transformation 768—769 Group, monodromy 723 Group, order of 759 Group, permutation see substitution Group, primitive 765 1142 Group, simple 766 1142 Group, solvable 762 1142—1143 Group, substitution 758 764—769 Group, symmetric 762 Group, transitive 765 1142 Gua de Malves, Abbe Jean-Paul de 270 549—552 Gudermann, Christof 643 Guldin, Paul 129 Gunter, Edmund 258 Hachette. Jean Hicolas Pierre 547 801 Hadamard, Jaeque 626 703 1003 1026 1077—1078 1085 1186 1199 Hadamard, Jaeque, algebra 804 Hadamard, Jaeque, theory of numbers 831 Hahn — Banach theorem 1090 Hahn, Hans 1088 1090 Halley, Edmond 357—358 Halpben, Georges Henri 533 941—942 Halsted, George B. 1015 Hamilton — Jacobi equation 744 Hamilton's equations of motion 742—743 Hamilton, William R. 581 740—745 772 775—776 792—794 983 989 Hamilton, William R., biography 777—778 Hamilton, William R., quaternions 779—782 1025 Hankel, Hermann 711 986 1031 Hardy, Godfrey H. 831 1035—1036 Harmonic function 685 harmonic oscillator 482 Harmonic set of points 96 128 293 300 851 Harnack, Alex 1042 Harriot, Thomas 252 260 280 Hauptlvermutung of Poincare 1176 Hausdorff, Felix 1160—1161 Heath, Sir Thomas L. 57 118 Heaviside, Oliver 3 689 787 790—791 1096—1097 Hecataeus 160 Heiberg, J.L. 57 Heine — Borel theorem 953—954 Heine, (Heinrich) Eduard 689 711—713 969 Heisenberg, Werner 1092 Heliocentric theory 241—247 327—328 Helly, Eduard 1088 Helmholtz equation See Partial differential equation Helmholtz, Hermann von 525 693—694 920—921 1021 1030 1034—1035 Hensel, Kurt 808 942 1146—1147 Hermann, Jacob 475 544—545 562 Hermite function 714 Hermite, Charles 651 714 763 808—809 973 981 1035 1049 Heron 25 57 116—117 135—136 580 Herschel, John 622 Hesse, Ludwig Otto 857 Hessenberg Gerhard 1015 1132 hessian 858 917—928 Hieratic 15—16 Hieroglyphic 15 Higher degree equation 270 599—606 752—763; Higher plane curves 547—554 Higher plane curves, projective approach 855—858 Hilbelt curve 1018 19 Hilbert cube 1161 Hilbert space 1074 1082 1088 1091—1095 1159 Hilbert — Schmidt theorem 1064 1068 Hilbert's axioms for number 990—992 Hilbert's basis theorem 930—931 1158 Hilbert's invariant integral 749 Hilbert's Nullstellensatz 943 Hilbert, David 1003 1024 1031 1035 1038 1137 Hilbert, David, algebraic geometry 943 Hilbert, David, algebraic invariants 929—932 Hilbert, David, biography 1060—1061 Hilbert, David, calculus of variations 704 709 Hilbert, David, differential equations 726 Hilbert, David, foundations 990—992 1010—1016 1027 1203—1208 Hilbert, David, integral equations 1035 1060—1070 1082 Hilbert, David, non-Euclidean geometry 906 Hilbert, David, theory of numbers 609 825 Hill, George William 731—732 1023 Hindus 183—190 Hipparchus 119—120 158—159 Hippasus 32 Hippias of Elis 38 40 Hippocrates of Chios 26 45 47 57 Hobbes, Thomas 318 333 356 619 862 Hobson, E W. 712 Hoelder, (Ludwig) Otto 767 1112—1113 1142 Hoene-Wronski, Josef Maria 619 Holmboee, Berndt Michael 644 973 Holmgren, Erik 1060 Holomorphic 642 Homeomorphism 1158 Homogeneous coordinates 853—854 Homologous figures 842 Homology 1180—1081 Homomorphism 767 1139 Homotopy See Fundamental group Hooke, Robert 337 357 468 Horn angle 67—68 Horn, Jakob 1106 Hudde, John 262 Humanist movement 221—223 236 Hume, David 862 1032 Huntington, Edward V. 1014 1141 1146 Hurwitz, Adolf 793 1003 Huygens's principle 691 694 Huygens, Christian 337 357 367 395 478 492 575 581 Huygens, Christian, calculus 355 Huygens, Christian, coordinate geometery 555—556 Huygens, Christian, differential equations 471 72 Huygens, Christian, methodology of science 331—332 335 Hydrodynamics 368 520 540—542 686 696—697 Hydrodynamics, hydrostatics 165—166 211 Hypatia 129 181 Hyperbolic functions 404 Hyperelliptic integrals 651—653 Hypernumbers 782—785; see also Linear associative algebra; Quaternion Hypocycloid 367 Hypsicles 86 119 Ideal 822—823 1150—1151 1153 Ideal numbers 819—820 Imaginary elements in geometry 843—845 Impredicative definition 1184 In Artem Analyticam Isagoge 261 Incommensurable ratio See Irrational number Independence of axioms 1014 Indeterminate equations 140—143 187—188 Index of a curve 736—737 Indivisibles 349—351 Infinite series 360—361 410 465 480—482 488—489 Infinite series, comergence and divergence 460—466 961—966 Infinite series, Euler transformation of 452—453 Infinite series, harmonic 443—444 449—450 Infinite series, hypergeometric 489 Infinite series, uniform convergence of 964—966; see also Divergent series; Fourier series; Ordinary differential equation; Special functions; Trigonometric series Infinitesimal 69 361 385 388 429; infinity 53 69 175—177 Inflection points 549 551—552 556 587 857 Institutiones Calculi Differentialis 402 430 463 Institutiones Calculi Integralis 402 489 542 integral 360—362 372 956—961 Integral equations 1052—1074 1086 1089—1091 Integral, Fredholm 1055 Integral, Lebesque — Stieltjes 1050 Integral, Riemann 958—959 Integral, Stieltjes 1041 Integral, Volterra 1055—1058 Interpolation 422—423 440—405 454—456 Intersections of curves 553 856—858 Introductio Arithmetica 136—138 Introductio in Analysin Infinitorum 392 402 404—405 430 506 554 558 Intuitionism 1197—1203 Invariance 299—300 920 925—932 inversion 932—933 Involute 555 Involution 128 292—293 Ionia 25 146 Ionian school 27—28 Irrational number 8 18 32—33 48—49 72—73 80—81 104 134—135 143 149 173 176 185—186 191—192 197 209 251—252 593—594 Irrational number, definition 982—987 Irreducible polynomials 755 Isadore of Seville 202 Isidorus of Miletus 130 Isochrone 471 556 Isomorphism 765—767 1139 Isoperimetric figures 126 576—577 838—839 Isoperimetric theorem 838—839 Ivory, James 523
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