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Bell E.T. — Mathematics: Queen and Servant of Science
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Название: Mathematics: Queen and Servant of ScienceАвтор: Bell E.T. Аннотация: An absorbing account of pure and applied mathematics from the geometry of Euclid to that of Riemann, and its application in Einstein's theory of relativity. The twenty chapters cover such topics as: algebra, number theory, logic, probability, infinite sets and the foundations of mathematics, rings, matrices, transformations, groups, geometry, and topology. Mathematics was republished in 1987 with corrections and an added foreword by Martin Gardner.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 437Добавлена в каталог: 16.04.2010Операции: Положить на полку |
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"Banach space" 162 "Bulldog, Darwin's" 258 "Hunting Big Game in the Theory of Numbers", by Lehmer 229 "Mathematical Machines", by Davis 251 "Mind Stuff" 269 Abel, N.H. xiii 12 184 355 397 Absolute value 158—161 Absorption, Law of 60 99 Abstraction 56 158—163 263 265—266 269 271 287 Abstraction and prediction 252—271 Abstraction, successive 271 Acceleration 210 213 325—327 action 347 350 Action at a distance 371 Action, least 346 348 Adams, J.C. xiii 287 293 295—296 Addition 67—68 105 Addition, algebraic 31 see Adjunction 86 Adjunction, algebraic 87 Adjunction, simple 86 Adjunction, transcendental 86 Aerodynamics 351 Aesop xiii 158 Airy, G.B. xiii 293 Alexander the Great xiii 272 Alexander, J.W. xiii 155 Algebra 7 9 22 56 95 101 131 140 175 193 221 Algebra of Cayley 159 Algebra of classes 99 Algebra of invariants 183 Algebra of logic 55—66 76 Algebra of mechanics 92 Algebra of rotations 92 Algebra of structures 55 Algebra, abstract 15 75 158 185 222 253 Algebra, abstract, modern 84 222 Algebra, associative 93 Algebra, associative, linear 54 89 93 183 Algebra, boolean 59—60 76 Algebra, classification of 91 Algebra, common 29—34 45 Algebra, common, changing rules of 34—37 Algebra, common, of complex numbers 72 Algebra, common, postulates for 30 351 Algebra, common, realizations of 45—46 Algebra, division 88 Algebra, fundamental theorem 87 240 409 Algebra, lattice 99 Algebra, Lie 183 Algebra, linear 89 91 93 Algebra, modern 91 119 232 Algebra, non-associative 93 Algebra, non-commutative 159 Algebra, semi-simple 91 Algebra, simple 91 Algebra, tensor 113 Algebra, vector 37 Algorithm(s) 412 Algorithm(s), Euclidean 243—244 Alice in Wonderland, by Carroll 361 Almanac, nautical 293 America 293 294 American Mathematical Monthly 239 288 American Mathematical Society 228 American Mathematical Society, Bulletin 230 Analysers, harmonic 369 Analysis 7 101 221 234—235 252 253 287 301—302 305 351 379 402 Analysis of random sample 380—381 Analysis, abstract 188 Analysis, combinatorial 374 Analysis, diophantine 236—239 Analysis, Fourier 2 Analysis, general 158 Analysis, harmonic 361 Analysis, mathematical 48 49 140 255 302 358 377 393—394 398 406—407 409 412 Analysis, modern 221 236 246 351—352 Analysis, situs 352 Analysis, tensor 210 Analysis, topologized 352 Analytical mechanics see "Mechanics" Analytical Society, Cambridge 249 Analytische Zahlentheorie, by Bachmann 236 angles 362—365 Angles, measurement of 365 Angles, Negative 363 Antipho xiii 310 Apogee 290 Apollonius xiii 277 Applied mathematics see "Mathematics" Approximations, successive 292 Archimedes xiii 6 226—227 334—335 337 339 394 areas 191 336—339 Aristotle 53 60 414 Arithmetic 4 76 220—251 300 403 Arithmetic, consistency of 412 415 Arithmetic, discoveries in 221 Arithmetic, elementary 79 Arithmetic, fundamental theorem 231 241—244 Arithmetic, Higher 7 9 220 222 253 Arithmetic, Keplerian 282 Arithmetic, ordinary 31—32 57 280 412 Arithmetica, by Diophantus 237 Arrays 103 Arrow symbol 102 Asquith, H.H. 295 Assemblage 406 Associative algebras see "Algebra" Associative law 59 79 110 Associative property 34 Associativity 168 assumptions 264 271 300 Asteroids 216—217 Astrology 280—281 Astronomy 157 218 220 259 276—277 280 287 292 Astronomy, dynamical 308 Astronomy, mathematical 272 Astronomy, observational 217 see Asymptotic 234 Atom bomb 116 Atomism 298 306 Atoms, structure of 178—181 309 Atoms, vortex theory of 155 Attraction 288—289 292 Attraction, force of 284 308 Automorphism(s) 73 186 Automorphism(s), inner 173 Automorphism(s), outer 173 Axioms 23 Axioms, Euclid's straight line 42 Axis 273 Axis, major 276 Axis, x 124 Axis, y 124 Babbage, C. xiii 249—250 Babylon 365 Babylonian mathematicians 94 189 191 238 290 365 Babylonian mathematicians, ancient 8 Bachet, C.G. de Meziriac xiii 237 Bachmann, P. xiii 236 Balboa 296 Ballistics 275 Baltimore lectures on molecular dynamics, Lord Kelvin 127 Banach, S. xiii 161—162 Baravalle, II. xiii 189 Barrow, I. xiii 397—398 Base, finite 81 Basis, finite 88 Berkeley, G. xiii 269 408 Biikhoff, G. xiii 76 99 187 Binary relation 69 78 Binary scale 248—249 Birkhoff, G.D. xiii 99 152 Body, rigid 263 Body, rotating 289 Bohr, N. xiii 209 Bombing, aerial 257 Boole, G. xiii 55—56 60 76 151 407 Boolean algebra see "Algebra" Boston 293 Boundary 156 boundary conditions 318—319 334 Boundary value 318 329 Boundary value problems 1 317—319 334 356 369 Boyle's law 130 Brahe, T. xiii 279 282 Britain 257 Brouwer, L.E.J. xiii 10 398 409—411 414 Bryso xiii 310 Bullet, movement of 298—299 Burali-Forti, C. xiii 403—404 Butler, S. xiii 5 Cable, transatlantic telegraph 121 Calculus 140 158 223 283 286—287 298 311 342—356 376 379 394 398 Calculus of finite differences 334 Calculus of propositions 61 Calculus of rates 308 310 Calculus of variations 342—350 Calculus, differential 11 211 283 292 307—308 316 320 334—335 340 394—395 Calculus, fundamental ideas of 231—235 Calculus, Fundamental Theorem of 336 340—341 Calculus, history of 310 Calculus, integral 11 292 320 334—340 394 Calculus, sum 334 Calculus, tensor 210—212 214—215 372 Cambridge 236 287 295 397 Cambridge Analytical Society 249 Candle as example of matter 118 Cantor, G. xiii 244 393 397—399 402—404 415 Cantor, M. xiii 310 Cardiogram 359—360 Carroll, Lewis xiii 361 Cartan, E. xiv 183 Cartesian revolution 132 Cartographers 150 Cauchy — Riemann equations see "Equations" Cauchy, A.L. xiv 72 165 242 252 351 397 Cayley, A. xiv 1—2 14 43 93 97 102—103 110—111 115 159 165 Certainty 387 Chance 374 377 Change, continuous 252 283 307 310 312 Change, rate of 322 325 343 356 Characteristics 84—85 Characteristics, universal 56 Charts 121 Chemistry 118 257 Chess 23 Chinese mathematicians 248 250 Choice, theory of 374 377 Christian warfare 115 Chromosomes 381 Cicero 227 circle 273 276—277 Circle, great 41 Circle, unit 362 364 Class(es) 29—32 60—61 79 168—169 321 402—403 Class(es) of lines 99 Class(es) of points 99 Class(es), closed 30 Class(es), congruence 83 Class(es), discrete 49 Class(es), finite 399 404 Class(es), group property of 143 Class(es), infinite 399—400 406 Class(es), infinite ordered 404 Class(es), lower 405 Class(es), null 99 Class(es), residue 83 172 Class(es), similar 398 400 Class(es), universal 99 Class(es), upper 405 Class(es), well-ordered 404 Class-inclusion 77 Clifford, W.K. xiv 37 120 204—205 269 Closure 169 Coefficients 102 Coefficients, equating 86 Cole, F.N. xiv 228 Collections, finite 410 Collisions 206 304 Collisions, space-time coordinates of 207 Columbus, C. xiv 294 Columns 102 104 106 108 comets 289 Commutative law 59 79 Commutative property 34 Commutative property of multiplication 36—37 compass 300 Complement 59 Complexes 171—172 Comte, I.A.M.F.X. xiv 259 Condition(s), initial 319 Cone(s) 273 351 Configuration 346 Configuration, invariant 179 181 Configuration, space 347 Conformal mapping 352—354 Congruence 69—70 91 220 Congruence classes 72 83—85 91 Congruence of ideals 81 Conic sections 272—277 Conic sections, invention of 272—283 Conies 132 147 272—277 283 Conjecture, Mersenne's 228—229 conjugate 244 Connectedness 153—154 Conservation of energy 117 290 Conservation of matter 117 Consistency 394 Constant, fine-structure 181 Construction, Euclidean 226—227 Continuity 234 297—306 310—311 Continuous fields 303 Continuous infinity 301 Continuum 48 303—304 411—412 Contradiction 25 63 414 Contradiction, law of 24 60 63 Converge 396 Convergence 397 Cooling, Newton's law of 319 coordinates 145—146 197 214 350 Coordinates cartesian 350 Copernicus, N. xiv 278—279 Correlation theory 122 Correspondence 73 Correspondence, one-one 73 398 400—401 404 cos 364 Coset 172—174 Cosine 362 364—368 Cosmology, relativistic 215 218 Couple, ordered 50 Covariance of physical laws 97 Covariant 214 Croton 7 Crystals, structure of 178 Crystals, X-ray analysis of 178 Cubes 184 Cubics 117 Curvature 41 138 194 202 213 Curvature, total 203 205
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