Katz V.J. — A History of Mathematics: An Introduction :: Электронная библиотека попечительского совета мехмата МГУ

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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

      79 89
      295—296
(House of Wisdom)      239
of Euclid      58—95
of Euclid, Book I      63—67 71
of Euclid, Book II      67—73 124 249—250
of Euclid, Book III      73—76
of Euclid, Book IV      76—77
of Euclid, Book IX      86—88 458
of Euclid, Book V      77—82
of Euclid, Book VI      71—72 82—84 116
of Euclid, Book VII      84—86
of Euclid, Book VIII      86—87
of Euclid, Book X      88—90
of Euclid, Book XI      90—91 117
of Euclid, Book XII      91—94
of Euclid, Book XIII      94—95
of Euclid, Definitions and Postulates      60—62
of Euclid, structure of      59—60 (see also Euclid)
      4
, geometry      20—23
, linear equations      14—18
, square root      29 (see also Chinese mathematics)
(abacists)      343—348
      163—164 268
      55—56
      55—56
-dimensional geometry      792—797
      see $Jiuzhang$

-adic numbers      824—825 829
      212
      322 30—32
, in Archimedes      105 107
, in eighteenth century mathematics      585
, in Euclid      64—65
      4 21 28—29
$S\bar{u}rya — Siddh\bar{a}nta$       214
exam      679 816
      4
$\acute{E}$ cole Polytechnique      637—639 668 683 692 706—707
$\acute{E}$ cole Polytechnique, and Cauchy      719 720
$\acute{E}$ cole Polytechnique, and Germain      656
$\acute{E}$ cole Polytechnique, and Monge      633 635
$\bar{A}$ ryabhata      212—213 215—218 231
Ab $\bar{u}$ K $\bar{a}$ mil ibn Aslam      250—251 293
Ab $\bar{u}$ Nasr Mans $\bar{u}$ r      277—281
Abacists      343—348
Abel, and Fourier series      720 723
Abel, and Jordan      670
Abel, and Kronecker      671—672
Abel, and Weber      675
Abel, biography      666
Abel, Niels Henrik      638 651 665—667 704 715
Abraham bar Hiyya      288 290—291 292—293
Abraham ibn Ezra      301—302
Absolute geometry      778
Abstract algebra, Boolean algebra      686—687 842—844
Abstract algebra, categories and functors      806 833
Abstract algebra, division algebra      682
Abstract algebra, equations      662—670
Abstract algebra, equivalence classes      671—672 732
Abstract algebra, fields      651 667 676—677 797 806 822—826
Abstract algebra, groups      339 617 620—621 651 662 667—676 791—792 797—799 832—833
Abstract algebra, ideals and ideal numbers      659—661 671—672
Abstract algebra, integral domain      831
Abstract algebra, matrices      687—695
Abstract algebra, number theory      652—661
Abstract algebra, rings      617 806 828—829
Abstract algebra, set theory      812
Abstract algebra, symbolic      677—687
Abstract algebra, vector spaces      763 794—795 833
Abu-l—Waf $\bar{a}$ , Muhammad      277—281
Acarya Jayadeva      223
Acceleration      318—319 421—423
Acrostic      1 46 102 135 168 192 238 288 342 385 431 468 544 596 650 704 766 805
Addition      see Arithmetic computations
Adelard of Bath      290—291
African mathematics      337—339 (see also Egyptian mathematics)
Agnesi, Maria Gaetana      565—567
al — Din, Sadr      271
al — Karaj $\bar{\imath}$ , Ab $\bar{u}$ Bakr      186 251—252 255 258
al — Khal $\bar{\imath}$ l ibn Ahmad      263—264
al — Khayy $\bar{a}$ m $\bar{\imath}$ , ‘Umar      238 269—271 437 624
al — Khayy $\bar{a}$ m $\bar{\imath}$ , ‘Umar, biography      260
al — Khayy $\bar{a}$ m $\bar{\imath}$ , ‘Umar, cubic equations      259—262
al — Khw $\bar{a}$ rizml $\bar{\imath}$ , Muhammad      240—241 244—249
al — Khw $\bar{a}$ rizml $\bar{\imath}$ , Muhammad, biography      245
al — Samaw’al, ibn Yahy $\bar{a}$       252—255 258—259 376
al — Samaw’al, ibn Yahy $\bar{a}$ , biography      253
al — Uql $\bar{\imath}$ d $\bar{\imath}$ s $\bar{\imath}$ , Abu-l—Hasan      241—243
al-B $\bar{\imath}$ r $\bar{u}$ n $\bar{\imath}$ , Abu-l-Rayh $\bar{a}$ n      238 275—277 281 330
al-Batt $\bar{a}$ n $\bar{\imath}$ , Abu ‘Abdall $\bar{a}$ h      275
al-F $\bar{a}$ ris $\bar{\imath}$ , Kam $\bar{a}$ l al-D $\bar{\imath}$ n      266
al-K $\bar{a}$ sh $\bar{\imath}$ , Ghiy $\bar{a}$ th al — D $\bar{\imath}$ n      243 281—282
al-K $\bar{u}$ h $\bar{\imath}$ , Ab $\bar{u}$ Sahl      273
al-Khw $\bar{a}$ rizml $\bar{\imath}$ , Muhammad, and European mathematics      293 350
al-Samaw’al, ibn Yahy $\bar{a}$ , combinatorics      264
al-Samaw’al, ibn Yahy $\bar{a}$ , number system      243
al-Tus $\bar{\imath}$ , Nas $\bar{\imath}$ r al — D $\bar{\imath}$ n      270—271 405
al-Tus $\bar{\imath}$ , Sharaf al — D $\bar{\imath}$ n      262—263 363 437
Alberti, Leon Battista      389—390
Alcuin of Yor      289
Aleksandrov, Pavel Sergeiivich      832
Alexander, James W.      821—822
Alexandria Museum and Library      58—59 96 168 187 188
Algebra, and trigonometry      371—372
Algebra, Babylonian      16 35—39
Algebra, boolean      686—687
Algebra, Chinese      15—19 35 197—210
Algebra, Diophantine      173—183
Algebra, Egyptian      14—15
Algebra, etymology      244
Algebra, French      349—351
Algebra, geometric      67—73 95—96 122-125
Algebra, in Euler      614—619
Algebra, in Lagrange      619—621
Algebra, in Maclaurin      611—613
Algebra, in Newton      610—611
Algebra, in Vi $\grave{e}$ te      370—375 (see also Abstract algebra; Equations)
Algebra, Indian      225—228
Algebra, Islamic      243—263 343—346 348
Algebra, Italian      343—348 358—367
Algebra, linear      14—19 755
Algebra, medieval European      282—290 293 307—314 328—329
Algebra, polynomials      251—254 346—348
Algebra, quadratic equations      35—39
Algebra, symbolic      677—687
Algebra, twentieth century      822—833
Algebra, vectors      794—795
Algebraic symbolism      370—371 445—446
Algebraic symbolism, in Descartes      438
Algebraic symbolism, in Diophantus      174—175
Algebraic symbolism, in Fermat      432 435
Algebraic symbolism, in medieval Europe      312
Algebraic symbolism, in Renaissance mathematics      345—346 350—352 356 365
algorithm, defined      8
Algorithm, etymology      241
American Mathematical Society      805
American mathematics, computers      839—851
American mathematics, eighteenth century      640—642
American mathematics, twentieth century      823 828 830
Amicable numbers      266
Analysis, complex analysis      737—746
Analysis, eighteenth century      544—590
Analysis, nineteenth century      704—760
Analysis, probability and statistics      753—760
Analysis, summary      595 765
Analysis, vector analysis      746—752
Analytic geometry      431—434 633—635
Anasazi mathematics      336—337

Angle of parallelism      775
Apogee      141
Apollonius      102—103 134 678
Apollonius,       117—129 184
Apollonius, and astronomy      140—141
Apollonius, and Renaissance mathematics      368
Apollonius, and seventeenth century mathematics      432—433 435 438 460
Apollonius, biography      118
Appel, Kenneth      805 851
Approximation methods      214—215
Arabia      see Islamic mathematics
Arabic names      241
Arc length      293 469 496—498
Archimedes      55 102—117 134 368
Archimedes,       108
Archimedes,       114—115
Archimedes,       105—106
Archimedes,       108—111 187
Archimedes,       115
Archimedes,       113—114
Archimedes,       111—113
Archimedes, and Islamic mathematics      259 262—263 273
Archimedes, and Leibniz      531
Archimedes, and Renaissance mathematics      368
Archimedes, biography      102 107 111 116
Archimedes, engineering      107—108
Archimedes, geometry      111—116
Archimedes, Hilbert’s axioms      799
Archimedes, law of the lever      103—107
Archimedes, method of discovery      111—113
Archimedes, principle of insufficient reason      105
Archimedes, sums of series      113—115
Archimedes, velocity      160—161
Archytas      86—87
Area of circle      19—22 162 268 488
Area of polygon      161 296
Area of rectangle      622
Area of region bounded by curves      468—469 487—488 499-503 513—514 623 717—718
Area of segment of a circle      22 162 273 293 297
Area of segment of a parabola      113—115
Area of segment of a spiral      114—115
Area of surface      574—575
Area of surface of a sphere      115—116
Area of triangle      19—20 160—161 269
Argand, Jean — Robert      738
Aristaeus      117 134 184 186
Aristarchus      137 368
Aristotle      54—58 159
Aristotle, and astronomy      140
Aristotle, Hilbert’s axioms      800
Aristotle, in medieval Europe      314—316 319
Aristotle, logic      54—56
Arithmetic computations      349
Arithmetic computations, Babylonian      12—14
Arithmetic computations, Chinese      14
Arithmetic computations, Egyptian      8—12
Arithmetic computations, Greek      175
Arithmetic computations, in medieval Europe      307—308
Arithmetic computations, Indian      226
Arithmetic computations, Islamic      240 242
Arithmetic computations, Mayan      333
Arithmetic computations, with decimals      376—377
Arithmetization of analysis      683 729—737
Associative law      81 823
Astrolabe      294
Astrology      301—302
Astronomy, ancient      25—27
Astronomy, and logarithms      416—420
Astronomy, Babylonian      136 138 142
Astronomy, Chinese      195—197
Astronomy, early Greek      135—145
Astronomy, in Brahe      408
Astronomy, in Copernicus      404—408
Astronomy, in Kepler      409—416
Astronomy, in Newton      516—522
Astronomy, Indian      212 218 221
Astronomy, Islamic      274 277
Astronomy, Mayan      332
Astronomy, Ptolemaic      145—157
Astronomy, Renaissance      398—416
Astronomy, summary      167 (see also Trigonometry) )
Asymptote      122—123
Augustine      289
Autolycus      137 160 368
Axioms      55
Axioms, algebraic      822—823
Axioms, Boolean      686—687
Axioms, completeness      806
Axioms, for group theory      674—676
Axioms, for natural numbers      735—737
Axioms, for non — Euclidean geometry      781
Axioms, for set theory      810—814
Axioms, for topology      817—818
Axioms, for vector spaces      826—827 (see also Proof)
Axioms, Hilbert’s      767—768 797—800
Axioms, in Peacock      678—680
Axioms, of choice      809—810
B $\ddot{u}$ rgi, Jobst      416
Babbage, Charles      678 707 807
Babbage, difference and analytical engines      835—838 844
Babylonia      2
Babylonian mathematics      1—3
Babylonian mathematics, and Chinese mathematics      206
Babylonian mathematics, and Greek mathematics      67—68 70 72—73 96 176—177 181—182 188
Babylonian mathematics, and Islamic mathematics      239 240 243 244 263
Babylonian mathematics, arithmetic computations      12—14
Babylonian mathematics, astronomy      136 138 142 156
Babylonian mathematics, calendars      26—27
Babylonian mathematics, geometry      19—25
Babylonian mathematics, number symbols      6—8
Babylonian mathematics, place value system      230
Babylonian mathematics, quadratic equations      35—39
Babylonian mathematics, square roots      27—28
Babylonian mathematics, summary      45
Bakhsh $\bar{a}$ l $\bar{\imath}$ manuscript      231
Banach space      827
Banach — Tarski paradox      812—813
Banach, Stefan      806
Banneker, Benjamin      641
Barrow, Isaac      498 500—503
Barrow, Isaac, biography      502
Bartels, Martin      654 775
Bayes, Thomas      605—608 755—756
Beltrami, Eugenio      783—784 789
Berkeley, George      582—583
Berkeley, George, response to      583—585
Bernoulli, Daniel      555 578 580—582 705 837
Bernoulli, Jakob (Jacques, James)      458 545 549 575
Bernoulli, Jakob (Jacques, James),       597—601
Bernoulli, Jakob (Jacques, James), biography      546
Bernoulli, Johann (Jean, John)      519 528 531—535 556—557 575
Bernoulli, Johann (Jean, John), biography      546
Bernoulli, Johann (Jean, John), differential equations      545—549
Bernoulli, Johann (Jean, John), orthogonal trajectories      551—552
Bernoulli, Nicolaus      552—553
Bessel, Friedrich Wilhelm      738 757
Betti number      820—821 833
Betti, Enrico      819—820
Bh $\bar{a}$ skara I      214—215
Bh $\bar{a}$ skara II      218—226
Bh $\bar{a}$ skara II, and combinatorics      229—230
Bh $\bar{a}$ skara II, biography      192 224
Billingsley, Henry      386
binary number      844
Binomial theorem      506—509
Boethius      173 289
Bolyai, J $\acute{a}$ nos      785
Bolyai, J $\acute{a}$ nos, biography      779
Bolyai, J $\acute{a}$ nos, non — Euclidean geometry      767 774 778—779
Bolzano — Weierstrass property      814—815

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