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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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Предметный указатель
Existential quantifier 221 Expansion, determinants, Laplace 648 Expansion, functions, even 918 Expansion, functions, odd 919 Explicit form, function 339 Exponent, power 136 Exponential equations 314 Exponential form, fundamental trigonometric functions 470 Exponential functions 353 Exponential functions, derivatives 699 Expression/expressions, algebraic 128 Expression/expressions, Boolean, simplifying 254 Extended mean-value theorem 718 Exterior angles 389 External force/electromotive force 1011 Extraction, roots 141 Extraneous solutions, trigonometric equations 523 Extrema and critical points 797 Extreme/extrema, endpoint 804 Extreme/extrema, functions 341 Extreme/extrema, relative 799 Extreme/extrema, two or more independent variables 815 Extremes 111 Face, diagonal 396 Face, lateral, prism 400 Face, lateral, pyramid 400 Factor/factors 303 Factor/factors, common 303 Factor/factors, integrating 996 Factor/factors, prime 303 Factor/factors, theorem 304 Factorial symbol 106 Factorial tree 186 Factoring 303 Factoring quadratic equations 309 Factoring trigonometric equations 519 Fall through resisting medium 1007 Family of curves 992 Faulhaber, J. 212 FEISTHAMEL 209 Femto 54 Ferguson, D.F. 94 Fermat numbers 78 Fermat prime-testing method 80 Fermat’s Last Theorem 333 Fermat’s spiral 581 Ferrari, L. 299 320 Fibonacci Association 288 Fibonacci numbers 287 Fibonacci sequence 286 FIBONACCI, L., 91 FIBONACCI, L., Fibonacci numbers 286 FIBONACCI, L., Hindu-Arabic numerals 50 FIBONACCI, L., prime numbers 77 FIBONACCI, L., quations 299 FIBONACCI, L., trigonometry 464 Field 71 Fifteen puzzle 193 Figurate numbers 289 Figurate numbers, four dimensions 293 Figurate numbers, higher dimension 294 FINCKE, T. 461 465 FINCKE, T., law of tangents 486 Finite decimal fractions 76 Finite series 266 Finite sets 234 First minor 648 First-order ordinary differential equations 994 Fisher, R.A. 964 Flat angle 388 Flow chart, bisection method 940 Flow chart, Newton’s method 946 Fluid ounce 409 Focus, conic sections 406 Focus, ellipse 390 Focused perspective 372 Fontana, Niccolo see "TARTAGLIA" Foot 409 Foot, U.S., definition 52 force 611 896 Force, external, as electromotive force 1011 Force, vectors 605 Forced oscillations 1010 Formula/formulas see also "Theorem" Formula/formulas, basic integration 724 Formula/formulas, Binet 288 Formula/formulas, boundary, trapezoidal rule 952 Formula/formulas, center of mass, solids of revolution 845 Formula/formulas, centroid, lamina 845 Formula/formulas, de Moivre’s 791 Formula/formulas, distance 550 Formula/formulas, Euler’s 507 792 Formula/formulas, Heron’s 444 Formula/formulas, Maclaurin’s 769 Formula/formulas, quadratic 311 Formula/formulas, quadrature 947 Formula/formulas, Taylor’s 767 Four simple rules of arithmetic 113 Four-color map theorem (problem) 203 Fourier coefficients 910 Fourier series 910 Fourier, J.B.J. 336 FOURIER, J.B.J., harmonic analysis 909 Fractals 625 Fraction/fractions 5 74 Fraction/fractions, Archimedes’ system 38 Fraction/fractions, basic counting rules 125 Fraction/fractions, common 74 Fraction/fractions, continued 127 Fraction/fractions, continued, root extraction 143 Fraction/fractions, conversion 75 76 125 Fraction/fractions, decimal 75 Fraction/fractions, Egyptian numeration 34 Fraction/fractions, Latin number names 16 Fraction/fractions, partial 130 Fraction/fractions, proper 74 Fraction/fractions, Roman numeral system 42 Fraction/fractions, sexagesimal 57 Fraction/fractions, unit 126 Fractional equation 307 309 Fraktur 19 Franklin, B. 208 Franklin, Ph. 204 Fredholm, E.I. 682 Free oscillations 1008 Frege, G. 216 235 French number names 20 24 Friction coefficient/resistance 1011 Friendly numbers 82 Frustum, cone 402 Frustum, pyramid 400 Full angle 388 Function/functions, algebraic 348 Function/functions, algebraic, derivatives 689 Function/functions, arcus 477 Function/functions, calculations with 343 Function/functions, composite 345 Function/functions, constraint 822 Function/functions, continuous 355 Function/functions, definition 336 Function/functions, discontinuous 355 Function/functions, discontinuous expansion, Fourier series 915 Function/functions, distribution, normal 979 Function/functions, elementary 348 Function/functions, even, expansion 918 Function/functions, even/odd 340 Function/functions, explicit form 339 Function/functions, exponential 353 Function/functions, exponential, derivatives 699 Function/functions, half-angle 512 Function/functions, history 336 Function/functions, hyperbolic 533 Function/functions, hyperbolic, derivatives 702 Function/functions, hyperbolic, inverse 539 Function/functions, hyperbolic, inverse, derivatives 704 Function/functions, implicit form 339 Function/functions, inverse hyperbolic, derivatives 704 Function/functions, inverses 346 Function/functions, linear 349 Function/functions, logarithmic 354 Function/functions, logarithmic, derivatives 699 Function/functions, normal distribution 979 Function/functions, odd, expansion 919 Function/functions, odd/even 340 Function/functions, one-to-one 346 Function/functions, polynomial 348 Function/functions, power 350 Function/functions, power, integration 723 Function/functions, probability, density 971 Function/functions, quadratic 351 Function/functions, rational 348 Function/functions, restrictions 822 Function/functions, Riemann zeta 778 Function/functions, transcendental 349 Function/functions, transcendental, derivatives 695 Function/functions, transcendental, expansion 771 Function/functions, trigonometric, fundamental 470 Function/functions, trigonometric, inverse 477 Functional equation 354 Fundamental hyperbolic functions, graphs 537 Fundamental theorem of algebra 299 305 Fundamental Theorem of Arithmetic 78 Fundamental theorem of calculus 748 Fundamental trigonometric functions 470 Fundamental trigonometric functions, derivatives 695 Fundamental trigonometric functions, exponential form 470 Fundamental trigonometric identities 507 G, grand 43 GAFURIUS, F. 922 GALILEI, G., combinatorics 184 GALILEI, G., history of calculus 674 GALILEI, G., introduction to transfinite numbers 257 GALILEI, G., motion 893 Gallon 409 Galois, E. 301 Galton, F. 979 Game, fifteen puzzle 193 Game, Saint Peter’s 184 Game, theory 965 GAULLAUDET, T.H. 67 Gauss — Jordan elimination 662 Gauss — Jordan reduction 662 GAUSS, C.F., complex numbers 88 GAUSS, C.F., determinants 639 GAUSS, C.F., Fermat’s last theorem 333 GAUSS, C.F., fundamental theorem of algebra 299 300 GAUSS, C.F., large numbers 30 GAUSS, C.F., Latin 19 GAUSS, C.F., modular arithmetic 123 GAUSS, C.F., non-Euclidean geometry 369 382 Gauss, C.F., normal distribution 979 GAUSS, C.F., prime number theorem 80 GAUSS, C.F., regular heptadecagon 417 GAUSS, C.F., regular polygons 417 GAUSS, C.F., row operations 661 GAUSS, C.F., statistics 964 GAUSS, C.F., vector history 600 Gaussian distribution 979 Gaussian elimination 661 Gaussian reduction 661 GB 55 GCD 126 GEMMA FRISIUS, R. 116 General Conference, Weights/Measures 53 General form of algebraic polynomial equation 305 General form of equation for line 555 General power rule 692 General solution, differential equation 992 General term, series 264 General theory of relativity 904 Generalized mean-value theorem 718 Generator 401 Generatrix 401 Genus, surface 379 Geocentric system 894 Geodesic 491 geoid 491 Geometric abstraction 370 Geometric mean 111 268 Geometric series, finite 268 Geometry/geometries, analytic 547 Geometry/geometries, analytic, history 548 Geometry/geometries, combinatorial 184 Geometry/geometries, coordinate 548 Geometry/geometries, elementary, definition 376 386 Geometry/geometries, elliptic 383 Geometry/geometries, Euclidean 381 Geometry/geometries, Euclidean, definition 376 Geometry/geometries, history 364 Geometry/geometries, hyperbolic 382 Geometry/geometries, infinitude of 384 Geometry/geometries, non-Euclidean 376 381 Geometry/geometries, parabolic 382 Geometry/geometries, plane, definition 376 Geometry/geometries, Riemann 383 Geometry/geometries, solid, definition 37 Geometry/geometries, types of 377 Gerard of Cremona 461 463 Germain, S. 334 681 German number names 25 Germanic languages 25 GHALIGAI 135 Gibbs, J.W. 601 Giga 54 Gigabyte 55 Gnomons 291 Gobar 50 Goedel, K. 160 262 Goldbach conjectures 81 Goldbach, C. 81 Golden number 287 Golden ratio 418 Golden rectangle 419 Golden section 418 Golden triangle 419 Gon 410 Googol 29 Googolplex 29 Grand 43 Graph theory 184 201 Graph, network 202 Graphical interpolation 927 Graphs, fundamental hyperbolic functions 537 Graphs, inverse hyperbolic functions 539 540 Graphs, trigonometric functions 502 GRASSMANN, G. 601 Great circle 403 Greater than, symbol 109 Greatest common denominator 126 Greek 10 Greek, alphabet 11 Greek, number names 10 Greek, numeration 36 Greek, transliteration 12 Greenlandic number names 7 Greenwich meridian 491 Gregorian calendar 18 GREGORIE, J. 93 301 768 GREGORIUS XIII 18 GREGORY XIII 18
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