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



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Íàçâàíèå: A History of Mathematics: An Introduction

Àâòîð: Katz V.J.

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: 2-nd edition

Ãîä èçäàíèÿ: 1998

Êîëè÷åñòâî ñòðàíèö: 903

Äîáàâëåíà â êàòàëîã: 22.12.2013

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Descartes, normal lines      472—473
Descartes, Rene      129 368—369 496 613
Descartes, theory of equations      447—448
Determinants      612 651 689—690
Dickson, Leonard Eugene      823
Diez, Juan      642
Differential equations, exact      554 751—752
Differential equations, in Bernoulli, Daniel      580—582
Differential equations, in Bernoulli, Jakob      545 549
Differential equations, in Bernoulli, Johann      545—549
Differential equations, in Bernoulli, Nicolaus      552—553
Differential equations, in Cauchy      719—720
Differential equations, in D’Alembert      578—580 692
Differential equations, in eighteenth century mathematics      545—560
Differential equations, in Euler      545 553—558 570—574 580-582 692
Differential equations, in Leibniz      527—531 546—547
Differential equations, in Newton      509 512
Differential equations, linear      547—549 553—554 556-558
Differential equations, partial      573 578—582 635 721—722
Differential form      795—797
Differential geometry, in Clairaut      630—632
Differential geometry, in Euler      632—633
Differential geometry, in Gauss      768—770
Differential geometry, in Monge      633—635
Differential geometry, of curves      630—632
Differential geometry, of surfaces      632—633 768—771
Differential triangle      499 502—503
Differential triangle, in Leibniz      524—527
Differential triangle, in Newton      512
Differential triangle, in seventeenth century mathematics      490
Diodes      126—127 134
Diophantus      168 187
Diophantus, and Euler      615
Diophantus, and Renaissance mathematics      365 372
Diophantus, Arithmetica      173—183
Dirichlet, and continuity      710
Dirichlet, Peter Lejeune      655 659 705 725—726
Distributive law      81 226 823
Ditton, Humphry      532 534—535
Divergence theorem      748—749
Division      see Arithmetic computations
Dodgson, Charles L.      696
Domingo Gundisalvo      290—291
Donnolo, Shabettai      301
Double difference, method of      194
Doubling the cube      51—52 128 662—663
Duality      785—787
Durer, Albrecht      390—393
Dyck, Walther von      651 674—675
D’Alembert, and Lacroix      706
D’Alembert, and limits      708
D’Alembert, biography      579
d’Alembert, Jean le Rond      578—581 585—586 692 695
Eccenter      141 402
Eccentricity      141
Ecliptic      137—139
Edgeworth, Francis      759
Education, eighteenth century      637 678
Education, medieval      316 330—331
Education, nineteenth century      678 679 720
Education, Renaissance      359
Education, seventeenth century      704—705 (see also Textbooks)
Egypt      3
Egyptian Mathematical Leather Roll      10
Egyptian mathematics      1 188
Egyptian mathematics, algebra      13—14
Egyptian mathematics, and Greek mathematics      93 100 122 184 188
Egyptian mathematics, arithmetic computations      8—12
Egyptian mathematics, calendars      26—27
Egyptian mathematics, counting      5—6
Egyptian mathematics, geometry      20—21
Egyptian mathematics, square root      27
Egyptian mathematics, summary      45
Eigenvalues      691—694
Eighteenth century mathematics      544—642
Eighteenth century mathematics, algebra      610—621
Eighteenth century mathematics, analysis      544—590
Eighteenth century mathematics, differential equations      545—560
Eighteenth century mathematics, education      637—640
Eighteenth century mathematics, geometry      621—637
Eighteenth century mathematics, number theory      617—619
Eighteenth century mathematics, probability      597—609
Eilenberg, Samuel      806 833
Eisenstein, Ferdinand Gotthold      689
Elliptic geometry      790
Epicycle      140 402 413
Equations, abstract algebra      662—670
Equations, construction of solutions of      437—438 447—448
Equations, cubic      see Cubic equations
Equations, cyclotomic      620 657—659 661—667 669
Equations, differential      see Differential equations
Equations, indeterminate      175 197—202 218—225 284 308—309 615-616
Equations, linear      see Linear equations
Equations, polynomial      see Polynomial equations
Equations, quadratic      see Quadratic equations
Equations, systems      see Linear equations
Equations, theory of      373—375 445—448 667-670
Equinox      138
Eratosthenes      55 104 186
Error-correcting codes      846—847
Ethnomathematics      332—340
Euclid      58—59 184
Euclid, $Data$      186
Euclid, $Optics$      157
Euclid, analysis      185—186
Euclid, and Apollonius      118 122 124 129
Euclid, and Archimedes      107 108 111 114
Euclid, and Diophantus      177
Euclid, and education      678
Euclid, and eighteenth century mathematics      582 621—637
Euclid, and Heron      159—161
Euclid, and Islamic mathematics      241 249—250 262 269
Euclid, and medieval Europe      297 299 302 327 328
Euclid, and Nicomachus      171—173
Euclid, and Nicomedes      111
Euclid, and nineteenth century mathematics      659
Euclid, And Ptolemy      146
Euclid, and Renaissance mathematics      368 377—378 385—386
Euclid, and seventeenth century mathematics      437—439 504
Euclid, application of areas      71
Euclid, basic propositions      63—67
Euclid, circles and pentagons      73—77
Euclid, conic sections      116 117
Euclid, constructions      61—62
Euclid, geometric algebra      67—73 95—96
Euclid, Hilbert’s axioms      799—800
Euclid, irrational magnitudes      90
Euclid, number theory      84—88
Euclid, parallel postulate      62 (see also Parallel postulate )
Euclid, probability      601
Euclid, ratio and proportion      77—84
Euclid, similarity      67 77 82—84
Euclid, solid geometry      90—95 (see also Elements of Euclid)
Euclidean algorithm      78
Euclidean algorithm, and Chinese mathematics      201
Euclidean algorithm, and Indian mathematics      218
Euclidean algorithm, in Nicomachus      171
Euclidean constructions      66—69
Euclidean Domain      660
Eudemus      48
Eudoxus      46 50 91
Eudoxus, and astronomy      136 139—140
Eudoxus, biography      81
Euler, $Institutiones$ $Calculi$ $Differentiate$      570—573 585
Euler, $Institutiones$ $Calculi$ $Integralis$      573—574
Euler, $Introductio$ $in$ $Analysin$ $Infinitorum$      567—570
Euler, $Introduction$ $to$ $Algebra$      614—615
Euler, and nineteenth century analysis      706 739 744
Euler, biography      553
Euler, calculus of variations      558
Euler, continuity      709—710
Euler, curves      630 632—633
Euler, derivatives      715—718
Euler, differential equations      553—558 570—574 580—582 692
Euler, differential geometry      630 632—633
Euler, double integrals      575—578
Euler, Fourier series      720
Euler, functions      724
Euler, Leonhard      544
Euler, linear equations      615—617 695
Euler, matrices      692
Euler, multiple integration      577—578
Euler, number theory      617—619 652—653 655
Euler, primes      459
Euler, theory of surfaces      767
Euler, topology      635—637 848
Expectation      457—458
Exponents, rules of, in Diophantus      179
Exponents, rules of, in medieval Europe      317
Exponents, rules of, in Renaissance mathematics      346 350 370 416
Exponents, rules of, Islamic      252—253
Extensive quantity      793
Exterior derivative      796
Factor Theorem      448
Factorial rule      301
False position, in Egypt      15
False position, in Greece      181—182
False position, in medieval Europe      307 344
False position, in Renaissance mathematics      344
Faulhaber, Johann      482
Fermat, analytic geometry      431—436 442
Fermat, and Diophantus      182
Fermat, areas      481—485
Fermat, biography      433
Fermat, Last Theorem      459—460 655—657 659
Fermat, little theorem      459 617—618
Fermat, maxima and minima      470—472
Fermat, number theory      458—460 617—618 655
Fermat, Pierre de      129 182
Fermat, probability      448 451
Fermat, tangents      471
Ferrari, Lodovico      360—361 364 613
fibonacci      see Leonardo of Pisa
Fibonacci sequence      309
Fields      651
fields, defined      676—677
Fields, in nineteenth century mathematics      667 676—677
Fields, in twentieth century mathematics      823—826
Figurate numbers      49
Finck, Thomas      401
Finzi, Mordecai      306
Fisher, Ronald      760
Fluxions and fluents, in Agnesi      566
Fluxions and fluents, in Berkeley      582—583
Fluxions and fluents, in Dixon and Hayes      534—535
Fluxions and fluents, in Maclaurin      562—565
Fluxions and fluents, in Newton      509—514
Fluxions and fluents, in Simpson      560—562
foci      125—127
Forcadel, Pierre      386
Four-color theorem      805 850
Fourier, biography      720
Fourier, Charles      847
Fourier, Joseph      705 720—726
Fr$\acute{e}$chet, Maurice      816—819
Fractions, Babylonian      13
Fractions, Chinese      14
Fractions, decimal      242—243 375—378
Fractions, Egyptian      9—12
Fractions, Greek      78
Fractions, in Chuquet      349—351
Fractions, in exponents      317 446 485—488
Fractions, in Gerardi      345
Fractions, in medieval Europe      302 307
Fractions, in Renaissance mathematics      375—378
Fractions, in Richard of Wallingford      315—317
Fraenkel, Abraham      812
Franklin, Benjamin      641—642
Frege, Gottlob      736—737
French Revolution      637—640 707 721 775
Frend, William      678 838
Frobenius, Georg      651—652 674 691 695—697
Functions, and graphs      319—321
Functions, and wave equation      578—582 (see also Trigonometry)
Functions, continuous      581 709—711 715 723—726 817 819
functions, defined      567 587 723 724
Functions, in Euler      567—570
Functions, in Greece      143—145 157
Functions, integrable      726—727
Functions, representable as trigonometric series      722—726
Functions, spaces of      816—818
Functions, symmetric      375 446
Functions, uniformly continuous      727—729
functor      833
Fundamental theorem of algebra      447 738
Fundamental Theorem of Arithmetic      86
Fundamental theorem of calculus      498—503 719
Fundamental theorem of calculus, in Lagrange      589—590
Fundamental theorem of calculus, in Leibniz      529—531
Fundamental theorem of calculus, in Maclaurin      564—565
Fundamental theorem of calculus, in Newton      514
Fundamental theorem of calculus, in Ostrogradsky      749
Fundamental theorem of calculus, in Riemann      745
G$\ddot{o}$del, Kurt      806 813—814
Galilei, $Two$ $New$ $Sciences$      421—425
Galilei, biography      422
Galilei, Galileo      321 385 420—425 502
Galois, Evariste      651 667—669 676—677 694
Galton, Francis      758—759
Gauss — Jordan elimination      755
Gauss, $Disquisitiones$ $Arithmeticae$      652—653 662—664 670-671
Gauss, $Theorema$ $Egregium$      770—771
Gauss, and Abel      666
Gauss, and Dedekind      659—660
Gauss, biography      654
Gauss, Carl Friedrich      651
Gauss, complex analysis      738—739 744
Gauss, cyclotomic equations      662—664
Gauss, fields      678
Gauss, geometry      766—771 774 778—780 781
Gauss, integrals      748—749
Gauss, least squares      755—757
Gauss, number theory      652—655
Gauss, primes      657
Gauss, quadratic forms      670—671 677 688
Gaussian elimination      17—19 755
Gaussian integers      654—655
Geography      393—397
Geometric algebra      100 117
Geometric progression      86—87 416
Geometrical product      792
Geometry, absolute      778
Geometry, analytic      431—444
Geometry, and complex analysis      737—746
Geometry, Babylonian      19—25
Geometry, Chinese      20—23 193—197 207
Geometry, Egyptian      20—21
Geometry, eighteenth century      621—637
Geometry, Euclidean      58—96 776
Geometry, foundations of      797—800
Geometry, groups in      791—792
Geometry, in $n$ dimensions      780 792—797
Geometry, in African weaving      338
Geometry, in Archimedes      111—116
Geometry, in Clairaut      621—623 630—632
Geometry, in Dee      385—389
Geometry, in Euler      632—633 635—637
Geometry, in Monge      633—635
Geometry, in Plato      52—54
Geometry, in Saccheri      624—628 (see also Analytic geometry; Differential geometry; Non-Euclidean geometry; Projective geometry)
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