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Katz V.J. — A History of Mathematics: An Introduction

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Название: A History of Mathematics: An Introduction

Автор: Katz V.J.

Аннотация:

Provides a world view of mathematics, balancing ancient, early modern and modern history. Problems are taken from their original sources, enabling students to understand how mathematicians in various times and places solved mathematical problems. In this new edition a more global perspective is taken, integrating more non-Western coverage including contributions from Chinese/Indian, and Islamic mathematics and mathematicians. An additional chapter covers mathematical techniques from other cultures.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1998

Количество страниц: 903

Добавлена в каталог: 22.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Geometry, Indian      21 225
Geometry, Islamic      259 268—274
Geometry, Lambert      628—639
Geometry, medieval European      292—299 327—328
Geometry, nineteenth century      766—800
Geometry, of conic sections      117—129
Geometry, of perspective      389—393
Geometry, Riemannian      779—781
Gerard of Cremona      290—291
Gerardi, Paolo      345—346
Gerbert d’Aurillac (Pope Sylvester II)      289
Germain, Sophie      655—656
Gibbs, Josiah Willard      651 686 752
Gilbert, William      413
Girard, Albert      431 446—447
Gnomon      27
Golden ratio      67
Goursat, Edouard      796—797
graphs      338—339 848—851
Grassmann, biography      793
Grassmann, Hermann      767 792—796
Great circle      137—139
Greece      46—47
Greek Anthology      168
Greek mathematics      46—191
Greek mathematics, and Babylonian mathematics      176—177 181—182 188
Greek mathematics, and Egyptian mathematics      184
Greek mathematics, and Indian mathematics      212
Greek mathematics, and Islamic mathematics      239 243 244 249 259 263 266 268 272—274
Greek mathematics, and medieval Europe      289—291 297 299—300 310 312 314-316
Greek mathematics, and Renaissance mathematics      365 368 385—388
Greek mathematics, and seventeenth century mathematics      432—434 437—439 460
Greek mathematics, Apollonius      117—127
Greek mathematics, Archimedes      110—116
Greek mathematics, Aristotle      54—58
Greek mathematics, Diophantus      173—183
Greek mathematics, early astronomy      136—145
Greek mathematics, Euclid      54—96
Greek mathematics, Heron      158—163
Greek mathematics, Hypatia      187—188
Greek mathematics, isoperimetric figures      183
Greek mathematics, Nicomachus of Gerasa      170—173
Greek mathematics, Pappus      183—187
Greek mathematics, place value system      230
Greek mathematics, Plato      52—54
Greek mathematics, Ptolemy      145—156
Greek mathematics, Pythagoras      48—51
Greek mathematics, summary      101 134 167 191
Green, George      743
Greenwood, Isaac      640
Green’s Theorem      743 745—746 749 750 752
Gregory of St. Vincent      491—492
Gregory, James      493—494 498—500
Group theory      339 651 667—676 798—799 832-833
Group theory, axiomatization      674—676
Group theory, in Cayley      672—674
Group theory, in Clairaut      620—621
Group theory, in Euler      617
Group theory, in Galois      667—669
Group theory, in Gauss      662 670—671
Group theory, in Jordan      669—670
Group theory, in Klein      791—792
Group theory, in Kroneker      671—672 (see also Abstract algebra)
Guthrie, Frederick      850
Hailey, Edmond      516 582—583
Haken, Wolfgang      805 851
Hamilton, and Cayley      691
Hamilton, and complex numbers      737
Hamilton, and Eisenstein      689
Hamilton, William Rowan      650 651 682—685 848—850
Hamming, Richard      846—847
Hankel, Hermann      751
Harmonic tetrad      789
Harmonics      53 86—87 173 411—412
Harriot, Thomas      431 445—446
Harvard University      640—641
Hasse, Helmut      829
Hausdorff, Felix      818—819
Hayes, Charles      532 534—535
Heath, Thomas      59 108
Heaviside, Oliver      651 686
Heawood, Percy      850
Hebrew mathematics      see Jewish mathematics
Heiberg, J. L.      59
Heine — Borel property      814—815 819
Heine, Axiom of Choice      809
Heine, continuity      710
Heine, Eduard      728—729 731
Heine, functions      724
Heliocentric system      402—408 (see also Astronomy)
Helmholtz, Hermann von      748 767 781—782
Hensel, Kurt      806 824—825
Heraclides      137
Hermite, Charles      664
Heron      136 158—162 368
Herschel, John      706
Heuraet, biography      498
Heuraet, Hendrick van      496—498
Heytesbury, William      318—319 583
Hiero      102 105 107
Hilbert, address to International Congress      808
Hilbert, and Emmy Noether      830
Hilbert, and Zermelo      810
Hilbert, axioms      811 822
Hilbert, biography      798
Hilbert, David      767—768 797—800
Hilbert, well-ordering principle      807—808
Hindu mathematics      see Indian mathematics
Hindu — Arabic place-value system      230—232 240—243
Hindu-Arabic place-value system, and logarithms      418
Hindu-Arabic place-value system, and money      640
Hindu-Arabic place-value system, in medieval Europe      290 302 307
Hindu-Arabic place-value system, in Renaissance mathematics      342—343 349 375—378
Hipparchus      142—145
Hipparchus and astronomy      136
Hipparchus and Indian mathematics      212
Hipparchus and Ptolemy      146 148
Hippocrates of Chios      50—52 74 91 116 128
Holzmann, Wilhelm      385
Homology      806 820—822 832—833
Hopf, Heinz      832
Horocycle      776
Hudde, Johann      473—475 510 526
Hugo of St. Victor      293—294
Hundred fowls problem, in Indian mathematics      228
Hundred fowls problem, in Mahavira      228
Hundred fowls problem, in medieval Europe      308
Hundred fowls problem, in Yang      210
Hundred fowls problem, in Zhang      198—199
Husserl, Edmund      808
Huygens, and Leibniz      522
Huygens, Christian      432 456—458 496 596 599
Huygens, differential equations      545
Hydrostatics      108
Hypatia      168 170 187—188
Hyperbolic function      569—570 630
Hyperbolic geometry      790
ibn al — Baghd $\bar{a}$ d $\bar{\imath}$ , Ab ‘Abdall $\bar{a}$ h      272—273
ibn al — Bann $\bar{a}$ Abu-l—Abbas Ahmad      267
ibn al — Haytham, Abu ‘Al $\bar{\imath}$ al — Hasan      256—258 269—270 273 482 495 599
ibn Mun’im, Ahmad al — Ab’dari      264—266
ibn Turk, ‘Abd al — Ham $\bar{\imath}$ d      247—248
Icosian game      848—849
Ideal numbers      659—661
imaginary numbers      447 48 677—678 682—684
Inca mathematics      334—336
incommensurability      252 272—273
Incommensurability, in Archimedes      106—107
Incommensurability, in Euclid      80 88—90
Incommensurability, in medieval Europe      317

Incommensurability, in Pythagoreans      50—51
Incommensurability, in Renaissance mathematics      378
Incompleteness theorems      806
Indeterminate equations      615—616
Indeterminate equations, Chinese      197—202
Indeterminate equations, Greek      175
Indeterminate equations, in medieval Europe      284 308—309
Indeterminate equations, Indian      218—225
India      4 210—212
Indian mathematics      4 8 494—496
Indian mathematics, algebra      225—228
Indian mathematics, and Chinese mathematics      196 220—221
Indian mathematics, and European mathematics      299 307
Indian mathematics, and Indian mathematics      212
Indian mathematics, and Islamic mathematics      239 240 274
Indian mathematics, combinatorics      228—230
Indian mathematics, cultural influences      327—330
Indian mathematics, geometry      21
Indian mathematics, indeterminate analysis      218—225
Indian mathematics, medieval      210—232
Indian mathematics, place value system      230—232
Indian mathematics, Pythagorean theorem      32 34—35
Indian mathematics, square root      28—29
Indian mathematics, summary      45 237
Indian mathematics, trigonometry      212—218
Indians, North American      336—337
Indivisibles      162 476—477
Induction      255
Induction, in medieval Europe      302—305
Induction, in Pascal      452 454—457
Induction, in Wallis      486
Infinitesimals, and indivisibles      162 476—477
Infinitesimals, in eighteenth century mathematics      571 578—580 583—584 623
Infinitesimals, in Galileo      421
Infinitesimals, in medieval Europe      293
Infinitesimals, in Newton      510—511
Infinitesimals, in seventeenth century mathematics      475—478 531 533
infinity      171
Infinity, and sets      733—734
Infinity, axiom of      811
Infinity, in Desargues      461
Infinity, in Galileo      476
Infinity, in Renaissance mathematics      421
Institute for Advanced Study      830 844
Integers, classification of      171
Integrals      717—720 (see also Calculus)
Interior point      817
Intermediate Value Theorem      710—711 713 819
Irrational numbers      677—678
Irrational numbers, Greek      160
Irrational numbers, in Dedekind      729—731
Irrational numbers, in Euclid      88—90
Irrational numbers, in medieval Europe      314 317
Irrational numbers, in Renaissance mathematics      377—378
Irrational numbers, Islamic      250 252 272—273
Ishango bone      5
Islam      238—240
Islamic mathematics      238—282 482 834
Islamic mathematics, algebra      243—264
Islamic mathematics, and Chinese mathematics      206 220
Islamic mathematics, and medieval Europe      289—291 299—300 307 312 314
Islamic mathematics, and Renaissance mathematics      343—346 348 363 376
Islamic mathematics, combinatorics      263—268
Islamic mathematics, cultural influences      327—331
Islamic mathematics, decimal system      240—243
Islamic mathematics, geometry      268—274
Islamic mathematics, influences      239 240 243 244 246 249 259 263 266 268 272—274
Islamic mathematics, summary      287
Islamic mathematics, trigonometry      274—282
Isoperimetric figures      183
Iterative procedure      281—282
Jabir ibn Aflah al — Ishbili, Abu Muhammad      280
Jacob Staff      303 330
Jacquard, Joseph      837
James of Venice      291
Jefferson, Thomas      642
Jewish mathematics, calendars      26—27
Jewish mathematics, geometry      20
Jewish mathematics, in Mishnat ha — Middot      163—164
Jewish mathematics, medieval      288 299—306 329
Jewish mathematics, number symbols      6
Jewish mathematics, probability      449
Jia Xian      202—204
John of Palermo      309—310
John of Seville      290—291
Jordan, Camille      651 669—670 691 694—695
Jordan, Wilhelm      755
Jordanus de Nemore      310—314 329 372
Jordanus de Nemore, biography      311
Jyesthadeva      494—496 599
Kantorovich, Leonid V.      847
Kempe, Alfred      850
Kepler, biography      409
Kepler, Johannes      126 409 116 469—470 475—476
Kepler, laws of planetary motion      412—416
Khayyam, Omar      see al — Khayyaml ‘Umar
Kinematics, and Greek mathematics      160
Kinematics, in medieval Europe      314—321
Kinematics, in Renaissance mathematics      420—425 (see also Newton)
King, Ada Byron (Lady Lovelace)      807 837—838 845
King, Ada Byron (Lady Lovelace), biography      838
Kirkman, Thomas P.      848—849
Klein, biography      790
Klein, Erlanger Programm      833
Klein, Felix      767 784 798 816
Klein, projective metrics      789—792
Kossak, Ernst      731
Kovalevskaya, Sofia      728—729
Kronecker, biography      672
Kronecker, Leopold      651 671—672 676—677 732 735
Kummer, biography      658
Kummer, Ernst      650—651 656—659 671 727
Lacroix, calculus      705
Lacroix, functions      724
Lacroix, integrals      717—718
Lacroix, limits      708
Lacroix, Sylvestre      637—638 678 706—707
Lagrange, and Cauchy      693
Lagrange, and Germain      656
Lagrange, biography      587
Lagrange, calculus      560 575 586—590 705
Lagrange, continuity      709—711
Lagrange, derivatives      715—717
Lagrange, integrals      748
Lagrange, Joseph Louis      678
Lagrange, number theory      617
Lagrange, power series      706—707
Lagrange, solution of equations      619—621 662 665
Lam $\acute{e}$ , Gabriel      655
Lambert, biography      629
Lambert, Johann      570 597 628—630 772 799
Laplace, and education      637—639
Laplace, biography      609
Laplace, Pierre — Simon de      420 678
Laplace, probability      608—609
Laplace, statistics      755—758
Latitude, astronomy      142 154—156
Latitude, geography      394—397 (see also Coordinate systems)
Law of Cosines      152 300 772 778
Law of Large Numbers      599—600
Law of Sines      300 778
Law of the lever      103—107
Least upper bound property      713—715
Lebesgue, Henri      815
Legendre, Adrien-Marie      618—619 653 753—755
Legendre, and education      637
Leibniz, and Maclaurin      612
Leibniz, and Newton      510 591
Leibniz, biography      523
Leibniz, differentials      522—524 546—547

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