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Gullberg J. — Mathematics: from the birth of numbers
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Название: Mathematics: from the birth of numbersАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 1110Добавлена в каталог: 22.11.2014Операции: Положить на полку |
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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., 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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