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

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Ќазвание: A History of Mathematics: An Introduction

јвтор: Katz V.J.

јннотаци€:

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: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 2-nd edition

√од издани€: 1998

 оличество страниц: 903

ƒобавлена в каталог: 22.12.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$Anthyphairesis$      79 89
$Artis$ $cuiuslibet$ $consummatio$      295Ч296
$Bayt$ $al-Hikma$ (House of Wisdom)      239
$Elements$ of Euclid      58Ч95
$Elements$ of Euclid, Book I      63Ч67 71
$Elements$ of Euclid, Book II      67Ч73 124 249Ч250
$Elements$ of Euclid, Book III      73Ч76
$Elements$ of Euclid, Book IV      76Ч77
$Elements$ of Euclid, Book IX      86Ч88 458
$Elements$ of Euclid, Book V      77Ч82
$Elements$ of Euclid, Book VI      71Ч72 82Ч84 116
$Elements$ of Euclid, Book VII      84Ч86
$Elements$ of Euclid, Book VIII      86Ч87
$Elements$ of Euclid, Book X      88Ч90
$Elements$ of Euclid, Book XI      90Ч91 117
$Elements$ of Euclid, Book XII      91Ч94
$Elements$ of Euclid, Book XIII      94Ч95
$Elements$ of Euclid, Definitions and Postulates      60Ч62
$Elements$ of Euclid, structure of      59Ч60 (see also Euclid)
$Jiuzhang$ $suanshu$      4
$Jiuzhang$ $suanshu$, geometry      20Ч23
$Jiuzhang$ $suanshu$, linear equations      14Ч18
$Jiuzhang$ $suanshu$, square root      29 (see also Chinese mathematics)
$Maestri$ $diТabbaco$ (abacists)      343Ч348
$Mishnat$ $ha Ч Middot$      163Ч164 268
$Modus$ $ponens$      55Ч56
$Modus$ $tollens$      55Ч56
$N$-dimensional geometry      792Ч797
$Nine$ $Chapters$ $of$ $the$ $Mathematical$ $Art$      see $Jiuzhang$ $suanshu$
$p$-adic numbers      824Ч825 829
$Paitamahasiddhanta$      212
$Plimpton$      322 30Ч32
$Reductio$ $ad$ $absurdum$, in Archimedes      105 107
$Reductio$ $ad$ $absurdum$, in eighteenth century mathematics      585
$Reductio$ $ad$ $absurdum$, in Euclid      64Ч65
$Sulvasutras$      4 21 28Ч29
$S\bar{u}rya Ч Siddh\bar{a}nta$      214
$Tripos$ exam      679 816
$Zhoubi$ $suanjing$      4
$\acute{E}$cole Polytechnique      637Ч639 668 683 692 706Ч707
$\acute{E}$cole Polytechnique, and Cauchy      719 720
$\acute{E}$cole Polytechnique, and Germain      656
$\acute{E}$cole Polytechnique, and Monge      633 635
$\bar{A}$ryabhata      212Ч213 215Ч218 231
Ab$\bar{u}$ K$\bar{a}$mil ibn Aslam      250Ч251 293
Ab$\bar{u}$ Nasr Mans$\bar{u}$r      277Ч281
Abacists      343Ч348
Abel, and Fourier series      720 723
Abel, and Jordan      670
Abel, and Kronecker      671Ч672
Abel, and Weber      675
Abel, biography      666
Abel, Niels Henrik      638 651 665Ч667 704 715
Abraham bar Hiyya      288 290Ч291 292Ч293
Abraham ibn Ezra      301Ч302
Absolute geometry      778
Abstract algebra, Boolean algebra      686Ч687 842Ч844
Abstract algebra, categories and functors      806 833
Abstract algebra, division algebra      682
Abstract algebra, equations      662Ч670
Abstract algebra, equivalence classes      671Ч672 732
Abstract algebra, fields      651 667 676Ч677 797 806 822Ч826
Abstract algebra, groups      339 617 620Ч621 651 662 667Ч676 791Ч792 797Ч799 832Ч833
Abstract algebra, ideals and ideal numbers      659Ч661 671Ч672
Abstract algebra, integral domain      831
Abstract algebra, matrices      687Ч695
Abstract algebra, number theory      652Ч661
Abstract algebra, rings      617 806 828Ч829
Abstract algebra, set theory      812
Abstract algebra, symbolic      677Ч687
Abstract algebra, vector spaces      763 794Ч795 833
Abu-lЧWaf$\bar{a}$, Muhammad      277Ч281
Acarya Jayadeva      223
Acceleration      318Ч319 421Ч423
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      290Ч291
African mathematics      337Ч339 (see also Egyptian mathematics)
Agnesi, Maria Gaetana      565Ч567
al Ч Din, Sadr      271
al Ч Karaj$\bar{\imath}$, Ab$\bar{u}$ Bakr      186 251Ч252 255 258
al Ч Khal$\bar{\imath}$l ibn Ahmad      263Ч264
al Ч Khayy$\bar{a}$m$\bar{\imath}$, СUmar      238 269Ч271 437 624
al Ч Khayy$\bar{a}$m$\bar{\imath}$, СUmar, biography      260
al Ч Khayy$\bar{a}$m$\bar{\imath}$, СUmar, cubic equations      259Ч262
al Ч Khw$\bar{a}$rizml$\bar{\imath}$, Muhammad      240Ч241 244Ч249
al Ч Khw$\bar{a}$rizml$\bar{\imath}$, Muhammad, biography      245
al Ч SamawТal, ibn Yahy$\bar{a}$      252Ч255 258Ч259 376
al Ч SamawТal, ibn Yahy$\bar{a}$, biography      253
al Ч Uql$\bar{\imath}$d$\bar{\imath}$s$\bar{\imath}$, Abu-lЧHasan      241Ч243
al-B$\bar{\imath}$r$\bar{u}$n$\bar{\imath}$, Abu-l-Rayh$\bar{a}$n      238 275Ч277 281 330
al-Batt$\bar{a}$n$\bar{\imath}$, Abu СAbdall$\bar{a}$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 Ч D$\bar{\imath}$n      243 281Ч282
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-SamawТal, ibn Yahy$\bar{a}$, combinatorics      264
al-SamawТal, ibn Yahy$\bar{a}$, number system      243
al-Tus$\bar{\imath}$, Nas$\bar{\imath}$r al Ч D$\bar{\imath}$n      270Ч271 405
al-Tus$\bar{\imath}$, Sharaf al Ч D$\bar{\imath}$n      262Ч263 363 437
Alberti, Leon Battista      389Ч390
Alcuin of Yor      289
Aleksandrov, Pavel Sergeiivich      832
Alexander, James W.      821Ч822
Alexandria Museum and Library      58Ч59 96 168 187 188
Algebra, and trigonometry      371Ч372
Algebra, Babylonian      16 35Ч39
Algebra, boolean      686Ч687
Algebra, Chinese      15Ч19 35 197Ч210
Algebra, Diophantine      173Ч183
Algebra, Egyptian      14Ч15
Algebra, etymology      244
Algebra, French      349Ч351
Algebra, geometric      67Ч73 95Ч96 122-125
Algebra, in Euler      614Ч619
Algebra, in Lagrange      619Ч621
Algebra, in Maclaurin      611Ч613
Algebra, in Newton      610Ч611
Algebra, in Vi$\grave{e}$te      370Ч375 (see also Abstract algebra; Equations)
Algebra, Indian      225Ч228
Algebra, Islamic      243Ч263 343Ч346 348
Algebra, Italian      343Ч348 358Ч367
Algebra, linear      14Ч19 755
Algebra, medieval European      282Ч290 293 307Ч314 328Ч329
Algebra, polynomials      251Ч254 346Ч348
Algebra, quadratic equations      35Ч39
Algebra, symbolic      677Ч687
Algebra, twentieth century      822Ч833
Algebra, vectors      794Ч795
Algebraic symbolism      370Ч371 445Ч446
Algebraic symbolism, in Descartes      438
Algebraic symbolism, in Diophantus      174Ч175
Algebraic symbolism, in Fermat      432 435
Algebraic symbolism, in medieval Europe      312
Algebraic symbolism, in Renaissance mathematics      345Ч346 350Ч352 356 365
algorithm, defined      8
Algorithm, etymology      241
American Mathematical Society      805
American mathematics, computers      839Ч851
American mathematics, eighteenth century      640Ч642
American mathematics, twentieth century      823 828 830
Amicable numbers      266
Analysis, complex analysis      737Ч746
Analysis, eighteenth century      544Ч590
Analysis, nineteenth century      704Ч760
Analysis, probability and statistics      753Ч760
Analysis, summary      595 765
Analysis, vector analysis      746Ч752
Analytic geometry      431Ч434 633Ч635
Anasazi mathematics      336Ч337
Angle of parallelism      775
Apogee      141
Apollonius      102Ч103 134 678
Apollonius, $Conics$      117Ч129 184
Apollonius, and astronomy      140Ч141
Apollonius, and Renaissance mathematics      368
Apollonius, and seventeenth century mathematics      432Ч433 435 438 460
Apollonius, biography      118
Appel, Kenneth      805 851
Approximation methods      214Ч215
Arabia      see Islamic mathematics
Arabic names      241
Arc length      293 469 496Ч498
Archimedes      55 102Ч117 134 368
Archimedes, $On$ $Floating$ $Bodies$      108
Archimedes, $On$ $Spirals$      114Ч115
Archimedes, $On$ $the$ $Equilibrium$ $of$ $Planes$      105Ч106
Archimedes, $On$ $the$ $Measurement$ $of$ $the$ $Circle$      108Ч111 187
Archimedes, $On$ $the$ $Sphere$ $and$ $Cylinder$      115
Archimedes, $Quadrature$ $of$ $the$ $Parabola$      113Ч114
Archimedes, $The$ $Method$      111Ч113
Archimedes, and Islamic mathematics      259 262Ч263 273
Archimedes, and Leibniz      531
Archimedes, and Renaissance mathematics      368
Archimedes, biography      102 107 111 116
Archimedes, engineering      107Ч108
Archimedes, geometry      111Ч116
Archimedes, HilbertТs axioms      799
Archimedes, law of the lever      103Ч107
Archimedes, method of discovery      111Ч113
Archimedes, principle of insufficient reason      105
Archimedes, sums of series      113Ч115
Archimedes, velocity      160Ч161
Archytas      86Ч87
Area of circle      19Ч22 162 268 488
Area of polygon      161 296
Area of rectangle      622
Area of region bounded by curves      468Ч469 487Ч488 499-503 513Ч514 623 717Ч718
Area of segment of a circle      22 162 273 293 297
Area of segment of a parabola      113Ч115
Area of segment of a spiral      114Ч115
Area of surface      574Ч575
Area of surface of a sphere      115Ч116
Area of triangle      19Ч20 160Ч161 269
Argand, Jean Ч Robert      738
Aristaeus      117 134 184 186
Aristarchus      137 368
Aristotle      54Ч58 159
Aristotle, and astronomy      140
Aristotle, HilbertТs axioms      800
Aristotle, in medieval Europe      314Ч316 319
Aristotle, logic      54Ч56
Arithmetic computations      349
Arithmetic computations, Babylonian      12Ч14
Arithmetic computations, Chinese      14
Arithmetic computations, Egyptian      8Ч12
Arithmetic computations, Greek      175
Arithmetic computations, in medieval Europe      307Ч308
Arithmetic computations, Indian      226
Arithmetic computations, Islamic      240 242
Arithmetic computations, Mayan      333
Arithmetic computations, with decimals      376Ч377
Arithmetization of analysis      683 729Ч737
Associative law      81 823
Astrolabe      294
Astrology      301Ч302
Astronomy, ancient      25Ч27
Astronomy, and logarithms      416Ч420
Astronomy, Babylonian      136 138 142
Astronomy, Chinese      195Ч197
Astronomy, early Greek      135Ч145
Astronomy, in Brahe      408
Astronomy, in Copernicus      404Ч408
Astronomy, in Kepler      409Ч416
Astronomy, in Newton      516Ч522
Astronomy, Indian      212 218 221
Astronomy, Islamic      274 277
Astronomy, Mayan      332
Astronomy, Ptolemaic      145Ч157
Astronomy, Renaissance      398Ч416
Astronomy, summary      167 (see also Trigonometry) )
Asymptote      122Ч123
Augustine      289
Autolycus      137 160 368
Axioms      55
Axioms, algebraic      822Ч823
Axioms, Boolean      686Ч687
Axioms, completeness      806
Axioms, for group theory      674Ч676
Axioms, for natural numbers      735Ч737
Axioms, for non Ч Euclidean geometry      781
Axioms, for set theory      810Ч814
Axioms, for topology      817Ч818
Axioms, for vector spaces      826Ч827 (see also Proof)
Axioms, HilbertТs      767Ч768 797Ч800
Axioms, in Peacock      678Ч680
Axioms, of choice      809Ч810
B$\ddot{u}$rgi, Jobst      416
Babbage, Charles      678 707 807
Babbage, difference and analytical engines      835Ч838 844
Babylonia      2
Babylonian mathematics      1Ч3
Babylonian mathematics, and Chinese mathematics      206
Babylonian mathematics, and Greek mathematics      67Ч68 70 72Ч73 96 176Ч177 181Ч182 188
Babylonian mathematics, and Islamic mathematics      239 240 243 244 263
Babylonian mathematics, arithmetic computations      12Ч14
Babylonian mathematics, astronomy      136 138 142 156
Babylonian mathematics, calendars      26Ч27
Babylonian mathematics, geometry      19Ч25
Babylonian mathematics, number symbols      6Ч8
Babylonian mathematics, place value system      230
Babylonian mathematics, quadratic equations      35Ч39
Babylonian mathematics, square roots      27Ч28
Babylonian mathematics, summary      45
Bakhsh$\bar{a}$l$\bar{\imath}$ manuscript      231
Banach space      827
Banach Ч Tarski paradox      812Ч813
Banach, Stefan      806
Banneker, Benjamin      641
Barrow, Isaac      498 500Ч503
Barrow, Isaac, biography      502
Bartels, Martin      654 775
Bayes, Thomas      605Ч608 755Ч756
Beltrami, Eugenio      783Ч784 789
Berkeley, George      582Ч583
Berkeley, George, response to      583Ч585
Bernoulli, Daniel      555 578 580Ч582 705 837
Bernoulli, Jakob (Jacques, James)      458 545 549 575
Bernoulli, Jakob (Jacques, James), $Ars$ $conjectandi$      597Ч601
Bernoulli, Jakob (Jacques, James), biography      546
Bernoulli, Johann (Jean, John)      519 528 531Ч535 556Ч557 575
Bernoulli, Johann (Jean, John), biography      546
Bernoulli, Johann (Jean, John), differential equations      545Ч549
Bernoulli, Johann (Jean, John), orthogonal trajectories      551Ч552
Bernoulli, Nicolaus      552Ч553
Bessel, Friedrich Wilhelm      738 757
Betti number      820Ч821 833
Betti, Enrico      819Ч820
Bh$\bar{a}$skara I      214Ч215
Bh$\bar{a}$skara II      218Ч226
Bh$\bar{a}$skara II, and combinatorics      229Ч230
Bh$\bar{a}$skara II, biography      192 224
Billingsley, Henry      386
binary number      844
Binomial theorem      506Ч509
Boethius      173 289
Bolyai, J$\acute{a}$nos      785
Bolyai, J$\acute{a}$nos, biography      779
Bolyai, J$\acute{a}$nos, non Ч Euclidean geometry      767 774 778Ч779
Bolzano Ч Weierstrass property      814Ч815
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