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Gullberg J. — Mathematics: from the birth of numbers
Gullberg J. — Mathematics: from the birth of numbers



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Название: Mathematics: from the birth of numbers

Автор: Gullberg J.

Аннотация:

A gently guided, profusely illustrated Grand Tour of the world of mathematics. This extraordinary work takes the reader on a long and fascinating journey — from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology. Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings. Over 1000 technical illustrations and cartoons and drawings


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 1110

Добавлена в каталог: 22.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Digits, valid      164
Digon      404
Dilation of time      905
Dilution, continuous      1004
Dimension/dimensions, concept      376 635
Dimension/dimensions, definitions      376 635
Dimension/dimensions, fractals      636
Dimension/dimensions, Hausdorff — Besicovich      636
Dimension/dimensions, matrix      640
Dimension/dimensions, one      376
Dimension/dimensions, similarity      636
Dimension/dimensions, three      376
Dimension/dimensions, two      376
Dimension/dimensions, zero      376
Diophantine equations      330
Diophantos      134 298 330
Direct proof, symbolic logic      227
Direct proportionality      349
Directrix      401
Directrix, conic sections      406
Dirichelet’s condition      910
Dirichlet, P.G.L.      336 910
discontinuous functions      355
Discontinuous functions, expansion, Fourier series      915
Discriminant      311 319
Disjunctions      222
Disk method, volume      873
dispersion      976
Distance      550 896 1090
Distance, formulas      550
Distribution, binomial      969
Distribution, Gaussian      979
Distribution, normal      979
Distribution, standard normal      983 985
Distribution, theory      682
Distributive laws      132
Distributive laws, Boolean algebra      253
Distributive laws, sets      250
Distributive properties, vectors      615
Dividend      120
Divine section      418
Divisibility, rules of      121
Division, complex numbers      790
Division, fractions      125
Division, fundamental operations      120
Division, polynomials      129
Division, symbols of      104
Divisor      120
Divisor, common      303
Doctrine of opposites      291
dodecahedron      397 398 448
Dodecahedron, formulas      451
Dodecahedron, rhombic      399
Dodgson, C.L.      227
Domains, functions      339 342 505
Domains, trigonometric functions      505
Douady, A.      634
Double integral      753 754 887
Double integral, transforming, coordinates      887
Double saw      43
Double-angle identities      510
Dual      3
Dual elements      387
Dual elements, projective geometry      434
dual operations      387
Dual theorem, projective geometry      434
Duality principle, Boolean algebra      253
Duality principle, projective geometry      434
Duodecimal numeration      46 61
Duodenary numeration      46
Duplation, Egyptian method      118
Duplication of the cube      421
Durer, A.      206
Dutch number names      25
Dyadic      46
d’Alambert’s ratio test      277
D’Alembert      see "ALEMBERT"
d’ALEMBERT, J.L.R., harmonic analysis      909
d’ALEMBERT, J.L.R., ratio test      277
d’EPEE, C.M.      67
e      85
East Arabic numerals      49
EBBE, A.      2
Eccentricity      406
Echelon form, system of linear equations      661
Edge, polyhedron      396
Egyptian numeration      34
Egyptian papyri      98
Egyptian triangle      393
Eine messbare Unendlichkeit      30
Einstein, A.      369 383 904 964
Einstein’s energy-mass relation      906
Electric charge      1011
Electric current      1011
Electromotive force      1011
Element/elements, blocks of, systems      198
Element/elements, determinant      646
Element/elements, leading      640
Element/elements, matrix      640
Element/elements, series      264
Element/elements, set      232
Elementary functions      348
Elementary geometry, definition      376 386
Elementary row operations      661
Elevation, angle of      494
Eleven, etymology      27
ellipse      406
Ellipse, area      442 852
Ellipse, definition      390 559
Ellipse, equations      560 568 587
Ellipse, equations, parametric      587
Ellipse, perimeter      440
Ellipse, super-      571
Ellipsoid      405
Ellipsoid of revolution, volume      876
Ellipsoid, oblate      405
Ellipsoid, prolate      405
Ellipsoid, reflectors      431
Elliptic geometry      383
Elliptic helix      597
Empty sets, identities      250
Endpoint extrema      804
Energy-mass relation, Einstein’s      906
Energy/mass      904
English number names, etymology of      26
ENGSTROEM, A.      30
Entry, determinant      646
Entry, leading      640
Entry, matrix      640
Entry, pivot      662
Epicycles      894
Epicycloids      592
Epicycloids, equations, parametric      592
EPIMINEDES      219
Epiminides’ paradox      219
Equality, sign, Rhind Papyrus      99
Equality, symbols of      99 107
Equation/equations, absolute value      308
Equation/equations, astroid, parametric      594
Equation/equations, auxiliary      1018
Equation/equations, Bernoulli      998
Equation/equations, biquadratic      311
Equation/equations, characteristic      1018
Equation/equations, circle      559 568 586
Equation/equations, circle, parametric      586
Equation/equations, conditional      303
Equation/equations, cubic      316
Equation/equations, cycloid, parametric      591
Equation/equations, definition      302
Equation/equations, differential      989
Equation/equations, differential, first-order ordinary      994
Equation/equations, differential, harmonic      1022
Equation/equations, differential, homogeneous      995
Equation/equations, differential, ordinary      991 994
Equation/equations, differential, partial      991
Equation/equations, differential, second-order ordinary      1015
Equation/equations, Diophantine      330
Equation/equations, ellipse      560 568
Equation/equations, ellipse, parametric      587
Equation/equations, epicycloid, parametric      592
Equation/equations, exponential      314
Equation/equations, fractional      307 309
Equation/equations, functional      354
Equation/equations, general form      305
Equation/equations, helix, right elliptic      597
Equation/equations, history      297 316
Equation/equations, homogeneous      328
Equation/equations, hyperbola      565 568 588
Equation/equations, hyperbola, parametric      588
Equation/equations, hypocycloid, parametric      593
Equation/equations, intersecting lines      556
Equation/equations, linear      307
Equation/equations, linear differential      1016
Equation/equations, linear, systems, solution      661
Equation/equations, logarithmic      315
Equation/equations, monic form      305
Equation/equations, normal      688
Equation/equations, parabola      563 568 589
Equation/equations, parabola, parametric      589
Equation/equations, parallel lines      555
Equation/equations, parametric      586
Equation/equations, parametric, area, surface of revolution      864
Equation/equations, parametric, helix, conical      596
Equation/equations, parametric, helix, cylindrical      595
Equation/equations, parametric, helix, spherical      596
Equation/equations, perpendicular lines      555
Equation/equations, point-slope      553
Equation/equations, polar      578
Equation/equations, polynomial      307
Equation/equations, quadratic      309
Equation/equations, quartic      320
Equation/equations, quintic      300
Equation/equations, reduced      1017
Equation/equations, root      313
Equation/equations, root/coefficient relationships      350
Equation/equations, slope-intercept      553
Equation/equations, solution, iterative methods      935 941
Equation/equations, solutions, graphic methods      931
Equation/equations, standard form      305
Equation/equations, straight lines      553
Equation/equations, symmetric      329
Equation/equations, systems of      325
Equation/equations, systems of, graphic solution      933
Equation/equations, tangent      688
Equation/equations, terminology      302
Equation/equations, theory of      295
Equation/equations, trigonometric      516
Equation/equations, two-point      553
Equation/equations, types of      302
Equiangular spiral      580
Equilateral triangle      392
Equilateral triangle, Euclidean construction      415
Equilibrium, vector forces      610
Equivalence, logical      223 224
Equivalence, topological      369 378
Equivalent switch circuits      230
ERATOSTHENES, circumference of the Earth      462 467
ERATOSTHENES, prime numbers      77
Erlangen program      370
Error/errors      161
Error/errors, absolute      161
Error/errors, estimate, Taylor’s series      770
Error/errors, relative      161
Error/errors, rounding      165
Error/errors, trapezoidal rule      952
Error/errors, type I      970
Error/errors, type II      970
Escher, M.C.      375
Etruscan alphabet      12
Etruscan number names      15
Etymology, a, an, one      27
Etymology, eleven      27
Etymology, English number names      26
Etymology, hundred      27
Etymology, million      28
Etymology, thousand      27
Etymology, twelve      27
EUCLID of Alexandria, common notations      381
EUCLID of Alexandria, equations      297
EUCLID of Alexandria, Euclidean geometry      381
EUCLID of Alexandria, history of calculus      674
EUCLID of Alexandria, history of geometry      365 367
EUCLID of Alexandria, Mersenne prime      82
EUCLID of Alexandria, postulates      381
EUCLID of Alexandria, prime numbers      78
EUCLID of Alexandria, QED      159
EUCLID of Alexandria, reductio ad absurdum      159
EUCLID of Alexandria, regular polygons      415
Euclid of Megara      365
Euclidean algorithm      126
Euclidean common notations      381
Euclidean construction      413
Euclidean geometry      381
Euclidean postulates      381
EUDOXUS (EUDOXOS)      89 110
EUDOXUS (EUDOXOS), history of calculus      674
EUDOXUS (EUDOXOS), history of geometry      365
Euler diagram      242
Euler paths      203
EULER, L., $\pi$      86 93
EULER, L., amicable numbers      83
EULER, L., calculus of variations      681
EULER, L., combinatorics      184
Euler, L., constant      273
EULER, L., diagrams, logic reasoning      177
EULER, L., e      85
EULER, L., Euler diagram      177
EULER, L., Euler’s formula      507 802
EULER, L., Fermat numbers      78
EULER, L., Fermat’s last theorem      334
EULER, L., functions      336
EULER, L., graph theory      184 221
EULER, L., harmonic analysis      909
EULER, L., history of calculus      680 681
EULER, L., history of geometry      369
EULER, L., history of trigonometry      465
EULER, L., Koenigsberg bridge problem      202
EULER, L., magic square      209
EULER, L., multiplier, Euler’s      997
EULER, L., perfect numbers      82
EULER, L., polyhedron formula      448
EULER, L., powers      134
EULER, L., prime numbers      78
EULER, L., quintic equation      300
EULER, L., summation notation      105
EULER, L., zeta function      778
Euler’s characteristic      448
Euler’s constant      273
Euler’s formula      507 792
Euler’s formula, line      433
Euler’s formula, multiplier      997
Euler’s formula, polyhedron formula      448
Euler’s formula, product      778
EVCLEIDIS      see "EUCLID of Alexandria"
Even functions, expansion      918
Even-odd identities      508
Even/odd functions      340
Exa      54
Excess, spherical      404
Excluded middle, principle of      216
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