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Young R.M. — Excursions in Calculus: An Interplay of the Continuous and the Discrete
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Название: Excursions in Calculus: An Interplay of the Continuous and the DiscreteАвтор: Young R.M. Аннотация: he purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1992Количество страниц: 408Добавлена в каталог: 13.04.2008Операции: Положить на полку |
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Предметный указатель
Replacement operation 27 Repunit 14 70 Revelations 37 Riele, H.J.J. te 101 Riemann zeta function 352 354 Riemann, G.F.G. 306 352 Ritt, J.F. 269 Robinson, A. 197 Robinson, G. 210 Rogers, D.F. 285 Root-mean-square see “Quadratic mean” Rosen, M. 231 Rota, G.-C 9 RSA cryptosystem 120 runs 226—230 Russell, B. 52 Sachs, A. 43 Salamin, E. 237 Sarrus, P. 8 116 Schinzel, A 244 Schneiderman, M.A. 140 Schrodinger, E. 208 Schwartz, J. 277 Schwartz, L. 277 Self-similarity 175 Self-similarity Koch curve 324 Self-similarity logarithmic spiral 149 Selfridge, J.L. 62 116 Series absolutely convergent 227 Series alternating 314 330 333—334 Series binomial 255—259 Series divergent 223—225 355—356 Series exponential 195—197 Series geometric 310—324 Series Gregory's 316 331 Series harmonic 287—288 295—296 Series Leibniz's 314—318 331 334 352 Series Newton's 330 Series telescoping 338 349 Seurat, G. 145—146 Shanks, D. 69 Sierpinski carpet 321—322 Sierpinski gasket see “Sierpinski triangle” Sierpinski triangle 334 Sierpinski's conjecture 307 Sierpinski, W. 295 Sieve of Eratosthenes 12 36 299 Simultaneous interpolation and approximation 287 Sine of the lemniscate 232 Sine product 346—347 Slowinski, D. 61 Snowflake curve see “Koch curve” Spira mirabilus see “Logarithmic spiral” Spiral 145 Spiral Archimedean 148 311 328—329 Spiral logarithmic 148—153 Square numbers 74 Square-free 291 Squares, sum of consecutive 78—81 Squaring the circle see “Circle quadrature St. Augustine 100 St. Petersburg paradox 242 Stark, E.L. 348 Steiner, J. 192 Steinhaus, H. 136 244 Stieltjes, T.J. 272 356 Stigler, S.M. 207 212 214 Stillwell, J. 231 Stirling numbers of the second kind 73 166 Stirling's formula 265 Stirling, J. 160 266 Struik, D.J. 223 277 Subfactorials 37 Sum of divisors see also “Pentagonal number theorem” 115 Summation by arithmetic means 224 Sun Tzu 375 Sun Tzu Arithmetic 375 Sylvester, J.J. 331 Sz.-Nagy, B. 275 Tables approximations to 304 Tables approximations to the nth prime 302 Tables Bernoulli numbers 91 Tables binomial coefficients 77 Tables digits of pi 236 Tables Euler's 117 Tables Euler's trinomial 64 Tables factorials 266 Tables Fibonacci numbers 125 Tables iterates of the logistic function 183 Tables Mersenne primes 106 Tables numbers of primes in intervals 298 Tables polygonal numbers 94 Tables prime numbers 59 Tables primitive Pythagorean triangles 44 Tables r(n) 220 Tables subfactorials 37 Tables sums of divisors 360 Tangent numbers 170 Tarski, A. 22 Telescoping series 338 349 Tetrahedral numbers 76 342 Theon of Smyrna 76 Theorem of the means 186—195 Thompson, D.W. 148 152 Todhunter, I. 32 Toeplitz, O. 60 310 Tower of Hanoi 24—26 Treatise on Natural Philosophy 209 Triangle area of 191 Triangle arithmetical 77—78 340—341 Triangle characteristic 343 Triangle harmonic 340—341 Triangle Pascal's see also “Binomial coefficients” 15 20 69 77 99 216 Triangle Pythagorean see “Pythagorean triangle” Triangle Sierpinski 334 Triangular numbers 18 74 118—119 308 342 Trisection of the angle 310 328 Turing, A. 51 Turnbull, H.W. 256 Twin primes 62 Ulam, S. 230 Undetermined coefficients, method of 161 355 Uniform approximation 275 282—284 287 Uniformly distributed sequence 240 Universal chord theorem 157 Vacca, G. 15 Vallee Poussin, C.J. de la 306 van Dam, A. 285 326 Van der Pol, B. 278 Van der Waerden, B.L. 10 41 192 295 Vandermonde's convolution 165 Vedamurthi Aiyar, T.V. 316 Viete's formula 21 29 Viete, F. 29 314 Vilenkin, N.Ya. 37 332 Virgil 318 Von Fritz, K. 27 von Koch, H. 323 von Neumann, J. 230 von Staudt, K.G.C. 99 Vorobyov, N.N. 145 Voss, R.F. 327 Wagstaff, S.S. 116 Wallis's formula 250—254 272—274 288 348 Wallis, J. 250 314 338 255—256 Wallis, J. Arithmetica infinitorum 251 255 Waring, E. Meditationes Algebraicae 107 Weber — Fechner law 219 Weierstrass approximation theorem 275—282 Weierstrass kernel 279 Weierstrass, K. 192 Weil, A. 114 339 Well-ordering principle 38 Weyl, H. ix 4 52—53 Wheeler, D.J. 105 Whitehead, A.N. 230 Whittaker, E.T. 210 Wilder, R.L. 38 Williams, H.C. 70 Wilson's theorem 69 107 Wythoff's game 156 Yaglom, A.M. and I.M. 348 Zagier, D. 119 297 Zeckendorf's theorem 138 Zeta function, Riemann 352 354
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