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

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

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

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

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

Leibniz, Gottfried Wilhelm      468 490 522—531 583 834—835
Leibniz, integrals      718
Leibniz, interchangeability theorem      550—552
Leibniz, limits      708
Leibniz, transmutation theorem      524—527
Leonardo da Vinci      393
Leonardo of Pisa      288 297—299 307—309
Leonardo of Pisa, biography      299
Lever, law of      103—107
Levi ben Gerson      299—300 302—306 329
Levi ben Gerson, biography      303
Li Ye      207—208
Limits, and -adic numbers      825
Limits, and nineteenth century analysis      706—709
Limits, defined      708
Limits, in Bolzano      712—713
Limits, in Cantor      732
Limits, in Cauchy      708—709 719—720
Limits, in eighteenth century mathematics      586
Limits, in Maclaurin      584—585
Limits, in Newton      511 515 520
Limits, in twentieth century mathematics      815—819
Lindemann, Ferdinand      664—665
Line integrals      742—743 747—748
Linear congruence      197—199 218—221 328
Linear equations, Chinese      197—202
Linear equations, Greek      175—176
Linear equations, in ancient mathematics      14—19
Linear equations, in medieval Europe      309 314
Linear equations, in Renaissance mathematics      350
Linear equations, solutions to      695—697
Linear equations, systems of      309 314 328 350 372 612—613 615—617 687-697
Liouville, Joseph      656—657 664 669 805
Liu Hui      193—195
Lobachevsky, biography      775
Lobachevsky, Nikolai      789
Lobachevsky, non — Euclidean geometry      767 774—779 782—785
Loci      see Analytic geometry; Three- and four-line locus problem
Logarithms      418—420 493 614
Logarithms, in Euler      567 568
Logarithms, in Leibniz      528—529
Logarithms, in Newton      508—509
Logarithms, in Renaissance mathematics      416—420
Logarithms, in seventeenth century mathematics      535
Logarithms, invention of      416—418 834
Logic, Aristotelian      50—51 54—56
Logic, Boolean      686—687
Logic, in Euclid      63—65 (see also Proof)
Longitude, astronomy      142 154—156
Longitude, geography      394—397 (see also Coordinate systems)
Lovelace, Lady (Ada Byron King)      807 837—838 845
Lovelace, Lady (Ada Byron King), biography      838
Lunes      52
L’Hospital, Guillaume      532—534 575 612
M $\acute{e}$ r $\acute{e}$ , Chevalier de      431 448 452 158 599 601—602
M $\ddot{u}$ ller, Johannes      398—401
Mac Lane, Saunders      806 833
Maclaurin,       611—613
Maclaurin,       562—565 583—585
Maclaurin, Colin, biography      563 708
Madhava      494
Mah $\bar{a}$ v $\bar{\imath}$ ra      228
Manifolds      780—783 791—792
Map-making      393—397
Mapping      833
Maseres, Francis      678
Mathematical games      338—339
Mathematical model      127—129
Mathematical model, in Archimedes      103
Matrices      687—695
Matrices, and canonical forms      694—695
Matrices, and eigenvalues      691—694
Matrices, defined      651 689
Matrices, in ancient mathematics      17—19
Maxima and minima      468—469 473—475 819
Maxima and minima, in eighteenth century mathematics      561 566 572
Maxima and minima, in Lacroix      706
Maxima and minima, in Leibniz      528
Maxima and minima, in l’Hospital      533
Maxima and minima, in Newton      512
Maxwell, James Clerk      685—686 747—748 750 752
Mayan mathematics      332—334
Mayer, Walther      832—833
Mazzinghi, Antonio de      346
Mean speed rule      319 320—321 421
Mean value theorem      717 719
Medieval mathematics, European      288—321
Medieval mathematics, European, algebra      307—314
Medieval mathematics, European, and Greek mathematics      289—291 297 299—300 310 312 314—316
Medieval mathematics, European, and Indian and Chinese mathematics      299 307
Medieval mathematics, European, and Islamic mathematics      289—291 299—300 307 312 314
Medieval mathematics, European, combinatorics      300—306
Medieval mathematics, European, cultural influences      327—331
Medieval mathematics, European, geometry      292—299
Medieval mathematics, European, kinematics      314—321
Medieval mathematics, European, probability      449
Medieval mathematics, European, summary      326
Medieval mathematics, European, trigonometry      293 296 298—300
Menabrea, L. F.      838
Menaechmus      116 134
Menelaus      136 152—153
Meray, Charles      731
Mercator, Gerard      397
Mercator, Nicolaus      493 505
Mersenne, Marin      306 436 458
Mesopotamia      see Babylonian mathematics
Method of analysis      115—116 127—128 183—185 187 369—370 432
Method of exhaustion      91
Method of exhaustion, in Archimedes      113 114
Method of exhaustion, in Islamic mathematics      273—274
Method of least squares      753—758
Method of least squares, in Gauss      755—757
Method of least squares, in Legendre      753—755
Metric      780—781 784
Metric system      639
Metric, functional spaces      817—818
Metric, projective      789—791
Monge, and education      637—639
Monge, and projective geometry      785
Monge, Gaspard      597 633—635 721
Moon      see Astronomy
Moore, Eliakim H.      822
Moscow Mathematical Papyrus      3 14—15 23—25
Multiple integration      574—578
Multiplication      see Arithmetic computations
MUSIC      48—49 53 86—87 171 173 411—412
Napier, John      416—420
Natural numbers      734 807 814
Natural numbers, axioms      735—736
Navigation      393—394
negative numbers      677—678
Negative numbers, Chinese      19
Negative numbers, in Euler      614
Negative numbers, in Hamilton      682—684
Negative numbers, in Maclaurin      612
Negative numbers, in medieval mathematics      329
Negative numbers, in Peacock      678—680
Negative numbers, in Renaissance mathematics      353—354 364
Negative numbers, Indian      226
Negative numbers, Islamic      245 252
Nehemiah, Rabbi      136 163—164
Neile, William      496
Neiuwentijdt, Bernard      528
Netto, Eugen      674
Newton,       515—516 520—522
Newton, and       516—519
Newton, and Berkeley      582—585
Newton, and Cambridge University      678—679
Newton, and Leibniz      510 591
Newton, and Maclaurin      613

Newton, and nineteenth century analysis      705
Newton, and probability      610—611
Newton, biography      468 504
Newton, differential equations      547
Newton, fluxions and fluents      509—514
Newton, Isaac      503—522
Newton, limits      708
Newton, power series      505—506
Nicomachus      170—173
Nicomedes      110—111 134
Nilakantha, Kerala Gargya      494
Nineteenth-century mathematics      650—804
Nineteenth-century mathematics, -dimensional geometry      792—797
Nineteenth-century mathematics, algebraic equations      662—670
Nineteenth-century mathematics, analysis      704—760
Nineteenth-century mathematics, complex analysis      737—746
Nineteenth-century mathematics, differential geometry      768—771
Nineteenth-century mathematics, groups and fields      670—677
Nineteenth-century mathematics, Hilbert’s axioms      797—800
Nineteenth-century mathematics, matrices      687—697
Nineteenth-century mathematics, non — Euclidean geometry      772—785
Nineteenth-century mathematics, number theory      652—661
Nineteenth-century mathematics, probability and statistics      753—760
Nineteenth-century mathematics, projective geometry      785—792
Nineteenth-century mathematics, summary      703 765 804
Nineteenth-century mathematics, symbolic algebra      677—687
Nineteenth-century mathematics, vector analysis      746—752
Noether, biography      830
Noether, Emmy      805—806 829—832
Noetherian ring      829—832
Non-Euclidean geometry      767 772—785
Non-Euclidean geometry, in Bolyai      778—779
Non-Euclidean geometry, in Helmholtz and Clifford      781—783
Non-Euclidean geometry, in Islamic mathematics      271
Non-Euclidean geometry, in Klein      789—792
Non-Euclidean geometry, in Lambert      628—630
Non-Euclidean geometry, in Lobachevsky      774—779 782—785
Non-Euclidean geometry, in Riemann      779—781
Non-Euclidean geometry, in Saccheri      624—628
Non-Euclidean geometry, in Taurinus      772—774
Non-Euclidean geometry, metrics in      789—791
Non-Euclidean geometry, models      783—785
Normal curve      604—605 758—760
Normal set      817
Normals      124 472—473
North American Indians      336—337
Notation      see Algebraic symbolism
Nu $\tilde{n}$ es, Pedro      357—358 396—397
Number symbols, ancient      5—8
Number symbols, European      308
Number symbols, Mayan      333
Number symbols, origin of      230—231
Number theory, algebraic      659—661 677—678
Number theory, in Euclid      84—88
Number theory, in Euler      617—619
Number theory, in Fermat      458—460
Number theory, in Gauss      652—655
Number theory, in Leonardo of Pisa      310
Number theory, in Nicomachus      171—173
Number theory, Islamic      266
Number theory, Pythagorean      48—51 73
Number vs. magnitude      56 85—86
Number vs. magnitude, in Islamic mathematics      272—273
Number vs. magnitude, in medieval Europe      314 327 329
Number vs. magnitude, in Nicomachus      171
Number vs. magnitude, in Renaissance mathematics      349 377—378 386—388
Number words      5
Olbers, Heinrich      766
Oldenburg, Henry      468 531
Oracle      46
Oresme, Nicole      317—318 502
Ostrogradsky, Mikhail      705 748—749 792
Oughtred, William      504 834
Oxford University      316 318 695
Pacific Island mathematics      339—340
Pacioli, Luca      342 345—346 348 357 451
Pandrosian      183
Pappus      170 183—187
Pappus and analytic geometry      432
Pappus and Renaissance mathematics      368
parabola      119 122
Parabolic geometry      790
Parallel postulate      62 720
Parallel postulate, in eighteenth century geometry      624—630
Parallel postulate, in Islamic mathematics      269—271
Parallel postulate, in non-Euclidian geometry      772 775—776 785
PARAMETER      119
Parmenides      54
Pascal, adding machine      834
Pascal, and Desargues      462
Pascal, and Fermat      482—484
Pascal, and Leibniz      522
Pascal, biography      452
Pascal, Blaise      431—432 490
Pascal, probability      448 451 156
Pascal, projective geometry      785
Pascal’s triangle      329—330 452 156
Pascal’s triangle, and probability      599
Pascal’s triangle, Chinese      202—203 205—206
Pascal’s triangle, in Fermat      482
Pascal’s triangle, in Leibniz      522—524
Pascal’s triangle, in medieval Europe      311
Pascal’s triangle, in Newton      507—508
Pascal’s triangle, in Renaissance mathematics      354—355
Pascal’s triangle, in Wallis      488
Pascal’s triangle, Islamic      258—259 266
Peacock, and Boole      686
Peacock, and Lagrange      706
Peacock, biography      680
Peacock, George      651 677—680
Peano, Giuseppe      736—737 795
Peano, vector spaces      767 827
Pearson, Karl      759
Peirce, Benjamin      828
Peirce, Charles      850
Pell equation      221—225 615
Pentagon construction      76—77
Perfect numbers      88 458
Perfect set      817
Perigee      141
permutations      651 665 669—670
Permutations, in Lagrange      619—621
Permutations, in medieval Europe      305—306 (see also Combinatorics)
Perspective      389—393 (see also Projective geometry )
Pi ( $\pi$ ), ancient      18
Pi ( $\pi$ ), and probability      604
Pi ( $\pi$ ), in Archimedes      110—111
Pi ( $\pi$ ), in Leibniz      526—527
Pi ( $\pi$ ), in Wallis      488
Pi ( $\pi$ ), Islamic      268
Pitiscus, Bartholomew      401—402
Pl $\ddot{u}$ cker, Julius      767 787
Place-value system, and logarithms      418
Place-value system, and money      640
Place-value system, Hindu — Arabic      230—232
Place-value system, in ancient mathematics      6—8
Place-value system, in medieval Europe      290 302 307
Place-value system, in Renaissance mathematics      342—343 349 375—378
Place-value system, Islamic      240—243
Place-value system, Mayan      333
Plane numbers      172
Plane triangle      149—152 399 101
Planet      see Astronomy
Plato      52—54 135
Plato of Tivoli      288 290—291
Plutarch      104 107
Poincar $\acute{e}$ , and Stokes      752
Poincar $\acute{e}$ , biography      821
Poincar $\acute{e}$ , Henri      784 785
Poincar $\acute{e}$ , homology      820—821

1 2 3 4 5 6 7

О проекте