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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

Poincar $\acute{e}$ , topology      806
Point of accumulation      814
Point set      732—733
Point-set topology      806
Pole      785—786
Polygonal numbers      172
Polyhedra      88 94—95 393
Polynomial equations      328
Polynomial equations, Chinese      202—210
Polynomial equations, in eighteenth century mathematics      613 619—621
Polynomial equations, in nineteenth century mathematics      651 662—663 665—667 694
Polynomial equations, in Renaissance mathematics      346—348 350—351 363-364
Polynomial equations, in seventeenth century mathematics      446—447 505—506
Polynomial equations, Islamic      244—249 251—254
Poncelet, Jean — Victor      767 785—787
Power series      505—506
Power series, in eighteenth century mathematics      563—564 568—570
Power series, in Lagrange      586—590
Power series, in Leibniz      530
Power series, in nineteenth century analysis      706—707
Power series, in seventeenth century mathematics      492—496
Power series, in twentieth century mathematics      825
Price, Richard      608
Prime field      826
Prime numbers      171 657—659
Prime numbers, in Euclid      85—88
Prime numbers, in Fermat      458—460
Principal ideal domain      832
probability      448—458
Probability, and de M $\acute{e}$ r $\acute{e}$ problems      431 448 452—458 599 601—602
Probability, and statistics      605—609 753—760
Probability, in Bayes      605—608
Probability, in Bernoulli, Jakob      458 597—609
Probability, in De Moivre      601—605
Probability, in Huygens      456—458
Probability, in medieval Europe      318 449
Probability, in Pascal      451—456
Proclus      48
Projective geometry      767 785—792
Projective geometry, and perspective      389—393
Projective geometry, cross ratio      788—790
Projective geometry, in Chasles      788—789
Projective geometry, in D $\ddot{u}$ rer      390—393
Projective geometry, in Desargues      460—462
Projective geometry, in Galileo      424—425
Projective geometry, in Klein      791—792
Projective geometry, in mapmaking      394—397
Projective geometry, in Monge      633—635
Projective geometry, in Pascal      462
Projective geometry, in Pl $\ddot{u}$ cker      787
Projective geometry, in Poncelet      785—787
Projective geometry, metric for      789—791
Proof, and Hilbert’s axioms      797—800
Proof, in Archimedes      115—116
Proof, in Diophantus      183
Proof, in Euclid      58 185
Proof, in medieval mathematics      292 300 328
Proof, in Renaissance mathematics      366 (see also Axioms)
Proof, Indian      215 218 225
Proof, Islamic      244—245
Proof, Jewish      163
Proportion      173
Proportion, rules of      313
Pseudosphere      782—784 789
Ptolemy I      58—59
Ptolemy III      59
Ptolemy,       145—157 834
Ptolemy,       145 395
Ptolemy, and Renaissance mathematics      398 402—404 406—408
Ptolemy, Claudius      135 145—157 212 782
Pyramid, volume of      20—21 23—25 92—93 163 269
Pythagoras      48—51
Pythagorean Theorem      50
Pythagorean theorem, Chinese proof of      32—35
Pythagorean theorem, Euclidean proof of      66—67
Pythagorean theorem, in ancient mathematics      30—35
Pythagorean theorem, Indian proof of      32 34—35
Pythagorean triples      30—32 50
Pythagoreans      48—51 136 410
Qin Jiushao      199—202 204—206 220
Qin Jiushao, biography      200
Quadratic equations, Babylonian      35—39
Quadratic equations, Chinese      35 207—208
Quadratic equations, in analytic geometry      436 437 144
Quadratic equations, in Diophantus      176—179 181—182
Quadratic equations, in Euclid      70
Quadratic equations, in medieval mathematics      293 309 314
Quadratic equations, in Renaissance mathematics      328 357—358 366—367
Quadratic equations, Indian      221—227
Quadratic equations, Islamic      246—249
Quadratic formula      226—227 441
Quadratic reciprocity theorem      618—619 651 653
Quadratrix      110—111 441
Quadrivium      289
Quaternions      650 682—686 752
Quetelet, Adolphe      758
Quintic equation      619 665—667
Quipu      334—336
Ratio, compound      315—317
Ratio, duplicate      81 83—84 89
Ratio, in Euclid      77—82 89
Ratio, in medieval Europe      314—318 320
Ratio, in Nicomachus      171—173
Ratio, triplicate      81
Rawlinson, Henry      2
Real numbers      729—731 787 806
Reciprocal table      13—14
Recorde, Robert      355—357
Regiomontanus (Johannes M $\ddot{u}$ ller)      398 401
Regression      759
Regular polyhedra      88 94—95 393
Reinhold, Erasmus      408
Renaissance mathematics      342—430
Renaissance mathematics, and Greek mathematics      365 368
Renaissance mathematics, and Islamic mathematics      343—346 348
Renaissance mathematics, astronomy and trigonometry      398 16
Renaissance mathematics, complex numbers      364—367
Renaissance mathematics, cubic equations      358—367
Renaissance mathematics, Dutch      375—378
Renaissance mathematics, English      355—357
Renaissance mathematics, French      349—351 369—375
Renaissance mathematics, geography and navigation      393—397
Renaissance mathematics, German      351—355
Renaissance mathematics, Italian      343—348 358—368
Renaissance mathematics, kinematics      420 25
Renaissance mathematics, logarithms      416 20
Renaissance mathematics, perspective      389—393
Renaissance mathematics, Portuguese      357—358
Renaissance mathematics, summary      384 430
Residue      741—742
Rheticus, George      401
Rhind Mathematical Papyrus      1 3 10 11—12 15 20—21
Ricci, Matteo      210
Richard of Wallingford      299—300 315—317
Riemann mapping theorem      744
Riemann, Bernhard      705
Riemann, biography      744
Riemann, complex analysis      743—746
Riemann, geometry      779—781
Riemann, integration      726—727 819
Riemann, non — Euclidian geometry      766—767
Riemann, topology      806
Rings      617 806 828—829
Rittenhouse, David      641
Robert of Chester      290—291
Roberval, Gilles Persone de      473 481 82 489 90
Robinson, Julia      831
Roman mathematics      169 188
Royal Society      531 561
Rudolff, Christoff      351—355 376

Ruffini, Paolo      665
Rule of four quantities      277—281
Russell, Bertrand, Axiom of Choice      810
Russell, Bertrand, Russell’s paradox      808—809 811
Russell, Bertrand, set theory      806
Saccheri, algebra      822—833
Saccheri, computers      834—851
Saccheri, Girolamo      271 597 772—773 785 799
Saccheri, parallel postulate      624—628
Saccheri, set theory      807—814
Saccheri, topology      814—822
Sarasa, Alfonso Antonio de      492
Scheubel, Johannes      355 385
Schickard, Wilhelm      834
Schooten, Frans van      440 42 456 473 496 504 522 546
Schooten, Frans van Varahamihira      228
Sea Island Mathematical Manual      193—195
Sebokht, Severus      231
Sefer Yetsirah      300—301
Seki Takakazu      612—613
Set theory      733—735
Set Theory, Axioms for      809—814
Set theory, cardinality      733—734 806
Set theory, in Galileo      421
Set theory, in twentieth century mathematics      807—814
Set theory, paradoxes of      808—809 812—813
Set theory, well-ordering theorem      807—809
Seventeenth-century mathematics      431—543
Seventeenth-century mathematics, calculus      468—543
Seventeenth-century mathematics, number theory      458 60
Seventeenth-century mathematics, probability      448 58
Seventeenth-century mathematics, projective geometry      460 62
Seventeenth-century mathematics, summary      467 543
Shannon, Claude      841—844
Similarity      67 77 82—84
simplex      806
SIMPSON, THOMAS      560—562 755
Sine      151
Sine, etymology      213
Sine, Islamic      275—282
Sine, law of      300 778
Sine, tables      212—214
Sine, theorem      278—281 (see also Trigonometry)
Slide rule      834
Sluse, Ren $\acute{e}$ Fran $\c{c}$ ois de      473 75 526
Smith, Henry J. S.      695—697
Snell’s law      547
Solid numbers      172
Solstice      138
Sphere, coordinate systems on      142—144
Sphere, in Euclid      91—95
Sphere, in Greek astronomy      136—140
Sphere, volume of      91—95 574—575
Spherical geometry      401
Spherical space      782
Spherical triangle      152—157
Spherical trigonometry      277—281
Spiral      114—115
Square root calculations, Babylonian      24 27—28
Square root calculations, Chinese      29 202—203
Square root calculations, Egyptian      27
Square root calculations, Greek      147 161
Square root calculations, in Chuquet      349—351
Square root calculations, Indian      28—29
Square root calculations, Islamic      244—249
Square root calculations, medieval European      309—310
Square root calculations, via power series      505—506
Squaring the circle, in Archimedes      108—109
Squaring the circle, in Gauss      662—663
Squaring the circle, in Leibniz      526—527
Squaring the circle, in Newton      507—508
Squaring the circle, in Wallis      488
Squaring the circle, Indian      21
Squaring the circle, Pythagorean      51—52
St. Vincent, Gregory of      491 92
Statistical inference      605—609
Statistics      753—760
Statistics, and social science      758—760 (see also Probability)
Statistics, Gauss      755—757
Statistics, Laplace      755—758
Statistics, Legendre      753—755
Staudt, Christian von      789—790
Steinitz, Ernst      806 826—827
Stevin, Simon      375—378 446
Stickelberger, Ludwig      674
Stifel, Michael      353—355 416
Stokes, George      750—752
Stokes’ Theorem      796—797
Stonehenge      25
Strato      160
Subtraction      see Arithmetic computations
Sums and differences      522—524
Sums of arithmetic series      203—204
Sums of geometric series      113—115 711—712
Sums of infinite series      321 601—604 711—712 715 723-726
Sums of integral powers      255—256 304—305 481 182 599
Sums of trigonometric series      582
Sun      see Astronomy
Sun Zi      197—198 210
Surds, in Renaissance mathematics      352
Surds, Islamic      252
surface      632—633 635 692—693
Surface integrals      748—749
Surface, theory of      766—767
Surveying, Chinese      193—195
Surveying, medieval European      293 296—297
Surveying, Roman      169
Susruta      228
Syllogisms      54—55
Sylvester, James Joseph      651 689—691
Symbolic algebra      677—687
Symbolism      see Algebraic symbolism
Tait, Peter      685 850
Tangent      500—502 631
Tangent, Chinese      195—196
Tangent, in Apollonius      123—125
Tangent, in Euclid      74
Tangent, in Maclaurin      584—585
Tangent, in medieval mathematics      329
Tangent, in Newton      512
Tangent, in seventeenth century mathematics      469 175
Tangent, Islamic      275—277
Tarski, Alfred      812—813
Tartaglia, Niccol $\grave{o}$       359—361 451
Taurinus, Franz      772—774 777—778 784
Taylor series      494 588 706
Taylor, Brook      564
Textbooks, algebra      676 678
Textbooks, calculus      532 534 560—574 706
Textbooks, eighteenth century      597
Textbooks, geometry      621—630 633—635 637-639
Th $\bar{a}$ bit ibn Qurra      249—250 273
Thaetetus      85 88
Thaetetus, biography      79
Thales      46 48
Theon of Alexandria      59 147 187
Thomson, William      705 748 750—752
Three- and four-line locus problem      129 186
Three- and four-line locus problem, and analytic geometry      432 439 444
Topological space      818
topology      814—822
Topology, algebraic      822 832—833
Topology, axioms for      817—818
Topology, Bolzano — Weierstrass theorem      713 814—815
Topology, combinatorial      806 819—822
Topology, differential      743 747—748 753 795—797
Topology, Heine — Borel theorem      729 814—815 819
Topology, in Euler      635—637
Topology, point set      732—733 806 815—816
Topology, well-ordering theorem      807—809

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