|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Graham R.L., Knuth D.E., Patashnik O. — Concrete mathematics |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Dice, fair 368 403
Dice, loaded 368 413
Dice, nonstandard 417
Dice, supposedly fair 378
Dickson, Leonard Eugene 496 583
Dieudonne, Jean Alexandre 500
Difference operator 47—55 456—457
Difference operator, nth order 187—192
Differentiably finite power series 360 366
Differential operators see “Derivative operator and Theta operator”
Difficulty measure for summation 181
Dijkstra, Edsger Wybe 173 583 604
Dimers and dimes 306 (see also “Dominoes and Change”)
Diphages 420 424
Dirichlet, box principle 95 130 497
Dirichlet, generating functions 356—357 359 418 437
Dirichlet, Peter Gustav Lejeune 356 583 602
Dirichlet, probability generating functions 418
Discrepancy 88—89 97 304 478 481
Discrete probability 367—424
Discrete probability, defined 367
Disease 319
Distribution of probabilities 367
Distribution of things into groups 83—85
Distributive law 30 35 60 64 83
Divergent sums 60 334 517
Divide and conquer 79
Divides exactly 112—114 146 233
Divisibility 102—105
Divisibility of polynomials 225
Dixon, Alfred Cardew 583 603
Dixon, formula 214
DNA, Martian 363
Dodgson, Charles Lutwidge see “Carroll”
Dominoes 306—313 357
Double sums 34—41 105 237
Doubly exponential recurrences 97 100 101 109
Doubly infinite sums 59 98 468—469
Dougall, John 171 583
Downward generalization 2 95 306—307
Doyle, Sir Arthur Conan 162 227—228 391 583
Drones 277
Drysdale, Robert Lewis (Scot) III 601
du Bois-Reymond, Paul David Gustav 426 580 589
Duality 63 (exercise 17) 68—69 253 515
Dubner, Harvey 600 602
Dudeney, Henry Ernest 583 602
Dunkel, Otto 586 602
Dunn, Angela Fox 597 604
Dunnington, Guy Waldo 583
Duplication formulas 186 232
Dupre, Lyn Oppenheim ix
Durst, Lincoln Kearney viii
Dyson, Freeman John 172 587
e 70 122 570
Edwards, Anthony William Fairbank 583
Eeny-meeny-miny-mo see “Josephus problem”
Efficiency 24
EGF see “Exponential generating function”
Eggs 158
Egyptian mathematics 95 150 581
Einstein, Albert 72 293
Eisele, Carolyn 595
Eisenstein, Ferdinand Gotthold Max 202 583
Elementary events 367—368
Elkies, Noam David 131
Ellipsis 21 50 108
Empirical estimates 377—379 413
Empty case 2 244 306—307 335 541
Empty product 48 106
Empty sum 23 48
Entier function see “Floor function”
Equality, one-way 432—433
Equivalence relation 124
Eratosthenes, sieve of 111
Erdelyi, Arthur 599 605
Erdos, Pal (=Paul) 510 526 550 583—584 603 604
Error function 166
Error, absolute versus relative 438 441
Eswarathasan, Arulappah 584 604
Euclid 107—108 584
Euclid, algorithm 103—104 123 289—290
Euclid, numbers 108 145 150 151
Euler, constant 264 292 304 467
Euler, identity for hypergeometrics 233
Euler, Leonhard i vii ix 6 48 122 131 133 134 205 207 210 232 253 263 264 272 285 287 289 455 457 499 514 550 577 579 584—585 602—604
Euler, numbers 535 591
Euler, polynomials 549
Euler, summation formula 455—461
Euler, theorem 133 141 147
Euler, totient function 133—135 137—144 357 448—449
Euler, triangle 254 303
Eulerian numbers 253—257 296 302 364 550
Eulerian numbers, combinatorial interpretations 253—254 534
Eulerian numbers, generalized 299
Eulerian numbers, generating function for 337
Eulerian numbers, second-order 256—257
Euler’ s triangle 254
Event 368
Eventually positive function 428
Exact cover 362
Exactly divides 112—114 146 233
Excedances 302
Exercises, levels of viii 72—73 95 497
exp: Exponential function 441
Expectation see “Expected value”
Expected value 371—373 381
Exponential function, discrete analog of 54
Exponential generating functions 350—355 407—408
Exponential series, generalized 200—202 231 350 355
Exponents, law of 52
Factorial expansion of binomial coefficients 156
Factorial function 111—115 332—334
Factorial function, approximation to see “Stirling’s formula”
Factorial function, duplication formula 232
Factorial function, generalized to nonintegers 192 210—211 213—214 302
Factorial powers 47—48 63 248
Factorial powers, complex 211
Factorial powers, negative 52—53 63
Factorial powers, related to ordinary powers 248—249 572
Factorization into primes 106—107 110
Factorization of summation conditions 36
Fair coins 387 416
Fair dice 368 403
Falling factorial powers 47
Falling factorial powers, complex 211
Falling factorial powers, difference of 48 53
Falling factorial powers, negative 188
Falling factorial powers, related to ordinary powers 51 248—249 572
Falling factorial powers, related to rising powers 63 298
Fans ix 193 334
Farey, John, series 118—119 134 137 150 152 448 588
Feder, Tomas 604
Feigenbaum, Joan 601
Feller, William 367 585 605
Fermat, numbers 131—132 145 510
Fermat, Pierre de 130 131 585
Fermat’s Last Theorem 130 150 509 532
Fermat’s theorem (= Fermat’s Little Theorem) 131 141 149
Fermat’s theorem, converse of 148
Fibonacci numbers 276—287 288 307 317
Fibonacci numbers, combinatorial interpretations of 277 278 288 307
Fibonacci numbers, generating function for 283—285 323—326 337
Fibonacci numbers, second-order 361
Fibonacci, algorithm 95 101
Fibonacci, factorial 478
Fibonacci, Leonardo 95 278 527 585 602 603
Fibonacci, number system 282—283 287 293 296 303
Fibonacci, odd and even 293—294
Fine, Henry Burchard 595
| Fine, Nathan Jacob 577
Finite calculus 47—56
Finite state language 391
Finkel, Raphael Ari 598
Fisher, Michael Ellis 585 604
Fisher, Sir Ronald Aylmer 586 605
Fixed point 12 379—380 386—387 414
Floor function 67—69
Floyd, Robert W 603 604
Food see “Candy Cheese Eggs Pizza Sherry”
Football 182
Football victory problem 193196 199—200 414
Football victory problem, generalized 415
Football victory problem, mean and variance 379—380 386—387
Forcadel, Pierre 586 603
Formal powers 206 317 517
FORTRAN 432
Fourier, Jean Baptiste Joseph 22 586
Fourier, series 481
Fractional part 70 83 87 456
Fractions 116—123 151
Fractions, basic 134 138
Fractions, continued 287 290—295 304 540
Fractions, partial see “Partial fraction expansions”
Fractions, unit 95 150
Fractions, unreduced 134—135 151
Fraenkel, Aviezri S 500 535 586 602
Frame, James Sutherland 586 602
Francesca, Piero della 586 604
Fraser, Alexander Yule 2 578
Frazer, William Donald 586 603
Fredman, Michael Lawrence 499 586
Free variables 22
Freiman, Grigorii Abelevich 581
Friendly monster 526
Frisbees 420—421 423
Frye, Roger Edward 131
Fundamental Theorem of Arithmetic 106—107
Fundamental theorem of calculus 48
Fuss — Catalan numbers 347
Fuss, Nicolai Ivanovich 347 586
Fuss, Paul Heinrich von 584
Gale, Dorothy 556
Games see “Bowling Cards Cribbage Dice Penny Sports”
Gamma function 210—214 468 513
Gardner, Martin 586 603 605
Garfunkel, J. 587 605
Gauss, identity for hypergeometrics 222 235
Gauss, Karl (= Carl) Friedrich vii 6 7 123 205 207 212 496 514 583 587 602 603
Gauss, trick 6 30 112 299
GCD see “Greatest common divisor”
General convolution identities 202
Generalization 11 13 16
Generalization, downward 2 95 306—307
Generalized binomial series 200—204 232 240 349
Generalized exponential series 200—202 231 350 355
Generalized factorial function 192 210—211 213—214 302
Generalized harmonic numbers 263 269 272 297 302 356
Generating function manipulations 320
Generating functions 196—204 283—285 306—366
Generating functions for Bernoulli numbers 271 337 351
Generating functions for convolutions 339—350 355 407
Generating functions for Eulerian numbers 337
Generating functions for Fibonacci numbers 283—285 323—326 337
Generating functions for harmonic numbers 337—338
Generating functions for probabilities 380—387
Generating functions for simple sequences 321
Generating functions for special numbers 337
Generating functions for Stirling numbers 337 407
Generating functions of generating functions 337 339 407
Generating functions, Dirichlet 356—357 359 418 437
Generating functions, exponential 350—355
Generating functions, Newtonian 364
Generating functions, super 339 407
Genocchi, Angelo 587
Genocchi, numbers 528 549
Geometric progression 32—33 54 114 205—206
Gessel, Ira Martin 256 587
Gibbs, Josiah Willard 599
Gilbert, William Schwenck 430
Ginsburg, Jekuthiel 587
Glaisher, James Whitbread Lee, constant 569
God 1 293
Goldbach, Christian 584
Goldbach, theorem 6
Golden ratio 285
Golf 417
Golomb, self-describing sequence 66 481
Golomb, Solomon Wolf 446 493 587 602
Good, Irving John 587 603
Goodfellow, Geoffrey Scott 598
Gopinath, Bhaskarpillai 487 592
Gordon, Peter Stuart ix
Gosper, algorithm 224—226 519
Gosper, algorithm, examples 227—228 233 519
Gosper, Ralph William, Jr. 224 487 540 587 603
Goto, considered harmful 173
Gottschalk, Walter Helbig vii
Graffiti vii ix 59 606
Graham, Cheryl ix
Graham, Ronald Lewis iii iv vi ix 102 492 582—584 587—588 598 601 602
Grandi, Luigi Guido 58 588
Graph 334 360
Graves, William Henson 601
Gravity, center of 259—260
Gray, Frank, code 483
Greatest common divisor 92 103—104 107 145
Greatest integer function see “Floor function”
Greatest lower bound 65
Greed 74 373—374
Greedy algorithm 101 281
Green, Research Sink 581
Greene, Daniel Hill 588
Greitzer, Samuel Louis 588 602
Griinbaum, Branko 484 588
Gross, Oliver Alfred 588 604
Grundy, Patrick Michael 597 602
Guibas, Leonidas loannis (= Leo John) 588 601 605
Guy, Richard Kenneth 500 510 588
Haar, Alfred vii
Hacker’s Dictionary 124 598
Haiman, Mark 601
Half-open interval 73—74
Hall, Marshall, Jr. 588
Halmos, Paul Richard v vi 588
Halphen, Georges Henri 291 588
Halving 79 186—187
Hamburger, Hans Ludwig 566 589
Hammersley, John Michael v 589 604
Hanoi, Tower of 14 26—27 109 146
Hanoi, variationson 17—19
Hansen, Eldon Robert 42 589
Hardy, Godfrey Harold 111 428 589 602 605
Harmonic numbers 29 258—268 466
Harmonic numbers, analogous to logarithms 53
Harmonic numbers, approximate values of 262—264
Harmonic numbers, complex 297 302
Harmonic numbers, divisibility of 297 300 304
Harmonic numbers, generalized 263 269 272 297 302 356
Harmonic numbers, generating function for 337—338
Harmonic numbers, second-order 263 266 297 529
Harmonic numbers, sums of 41 56 265—268 298—299 302 340—341
Harmonic series, divergence of 62 262
Harry, Matthew Arnold, double sum 237
Hashing 397—412
Hats 193—196 199—200 379—380 386—387 414 415
HCF 103
Heath-Brown, David Rodney 599
Heiberg, Johan Ludvig 584
Heisenberg, Werner Karl 467.
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå