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| Graham R.L., Knuth D.E., Patashnik O. — Concrete mathematics |
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| Ïðåäìåòíûé óêàçàòåëü |
Helmbold, David Paul 601
Henrici, Peter Karl Eugen 318 526 576 589 603 605
Hermite, Charles 524 532 589 603
Herstein, Israel Nathan 8 589
Hexagon property 155 230 239
Hillman, Abraham P. 589 603
Hoare, Charles Antony Richard 28 73 589
Hofstadter, Douglas Richard 602
Hoggatt, Verner Emil, Jr. 589 593 603
Holden, Edward Singleton 595
Holmboe, Berndt Michael 578
Holmes, Thomas Sherlock Scott 162 227—228
Holomorphic functions 196
Horses 17 454 489
Hsu, Lee-Tsch (= Lietz = Leetch) Ching-Siur 589 603
Hurwitz, Adolf 604
Hyperbolic functions 271—272
Hyperfactorial 231 477
Hypergeometric series 204—223
Hypergeometric series, degenerate 210 216 222 235
Hypergeometric series, differential equation for 219—221
Hypergeometric series, partial sums of 165—166 223—230 233
Hypergeometric series, transformations of 216—223 235 241
Hypergeometric terms 224 231 233
i 22
Implicit recurrences 136—138 193—194 270
Indefinite summation 48—49 55—56 161 224—230
Independent random variables 370 413 423
Index set 22 30 61
Index variable 22 34 60
Induction 3 7 10—11 17 43
Induction, backwards 18
Induction, basis of 3 306—307
Induction, failure of 550
Induction, important lesson about 494 526
Inductive leap 4 43
Inequality, Cauchy’s 64
Inequality, Chebyshev’s 376—377 414 416 555
Inequality, Chebyshev’s summation 38
Infinite sums 56—62 64
Information retrieval 397—399
Inkeri, Kustaa 509 590
INT function 67
Integer part 70
Integration 45—46 48 319 351
Integration by parts 54 458
Interchanging the order of summation 3441 105 136 183 185
Interpolation 191—192
Intervals 73—74
Invariant relation 117
Inverse modulo m 125 132 147
Inversion formulas 136 138 192—193
Irrational numbers 87 122—123
Iverson, convention 24 31 34 68 75 587
Iverson, Kenneth Eugene 24 67 590 602
Jacobi, Carl Gustav Jacob 64 590
Jarden, Dov 533 590
Jeopardy 347
Joint distribution 370
Jonassen, Arne Tormod 590
Jones, Bush 590
Josephus, Flavius 8 12 19—20 590
Josephus, numbers 81 97 100
Josephus, problem 8—17 79—81 95 100 144
Josephus, recurrence, generalized 13—16 79—81
Josephus, subset 20
Jouaillec, Louis Maurice 601
Jungen, R. 590 604
Kafkaesque scenario 260
Kaplansky, Irving 8 589
Karlin, Anna Rochelle 601
Kaucky, Josef 590 604
Kellogg, Oliver Dimon 582
Kent, Clark (= Kal-El) 358
Kernel functions 356
Ketcham, Henry King 148
Kilometers 287 296
Kilroy, James Joseph vii
Kipling, Joseph Rudyard 246
Kissinger, Henry Alfred 365
Klamkin, Murray Seymour 590 602 603
Klarner, David Anthony 601
Knockout tournament 418—419
Knopp, Konrad 590 605
Knuth, Donald Ervin iii—vi viii ix 102 253 397 492 531 588 590—591 601 605 625
Knuth, John Martin 605
Knuth, Nancy Jill Carter ix
Knuth, numbers 78 97 100
Kramp, Christian 111 591
Kronecker, Leopold, delta notation 24
Kummer, Ernst Eduard 206 514 591—592 603
Kummer, formula for hypergeometrics 213 217
Kurshan, Robert Paul 487 592
Lagny, Thomas Fantet de 290 592
Lagrange (= de la Grange), Joseph Louis, comte 592 604
Lagrange, identity 64
Lah, Ivo 592 603
Landau, Edmund Georg Hermann 429 434 592 603 605
Laplace, Pierre Simon, marquis de 452 580 592
Last but not least 132 455
Law of Large Numbers 377
LCM see “Least common multiple”
Least common multiple 103 107
Least integer function see “Ceiling function”
Least upper bound 57 61
LeChiffre, Mark Well 148
Left-to-right maxima 302
Legendre, Adrien Marie 548 592 602
Lehmer, Derrick Henry 592 602 604
Leibniz, Gottfried Wilhelm, Freiherr von vii 168 588 593
Lekkerkerker, Cornelius Gerrit 593
Levels of exercises viii 72—73 95 497
Levine, Eugene 584 604
Lexicographic order 427
lg: Binary logarithm 70
Liang, Franklin Mark 601
Lieb, Elliott Hershel 593 605
Lies, and statistics 195
Lincoln, Abraham 387
Lines in the plane 4—8 17 19
Little oh notation 434
ln: Natural logarithm 262
log: Common logarithm 435
Logan, Benjamin Franklin (= Tex), Jr. 273 593 602—604
Logarithmico-exponential functions 428—429
Logarithms 53—54 70 262 435
Long, Calvin Thomas 593 1603
Lottery 373—374 422—423
Lower index 154
Lower parameters 205
Loyd, Samuel 536 593
Lucas, numbers 298 302
Lucas, Prangois Edouard Anatole 1 278 593 602—604
Lyness, Robert Cranston 487 593 602
Lytton, Edward George Bark Lytton Bulwer, baron v
L’Hospital, Guillaume Prangois Antoine de, marquis de Sainte Mesme, rule 326 382
Maclaurin, Colin 455 593
MacMahon, Maj. Percy Alexander 140 593
Macsyma 42 525
Magic tricks 279
Mallows, Colin Lingwood 492
Markov, Andrei Andreevich (the elder), processes 391
Martian DNA 363
Mathematical induction 3 7 10—11 17 43
Mathematical induction, backwards 18
Mathematical induction, basis of 3 306—307
Mathematical induction, failure of 550
Mathematical induction, important lesson about 494 526
Mathews, Edwin Lee (= 41) 8 21 94 105 106 329
Matiiasevich (= Matijasevich), Iurii (= Yuri) Vladimirovich 280 593 603
| Maxfield, Margaret Waugh 599 604
Mayr, Ernst ix 601 602
McEliece, Robert James 71
McGrath, James Patrick 601
McKellar, Archie Charles 586 603
Mean (average) of a probability distribution 370—381
Median 370 371 423
Mediant 116
Melzak, Zdzislaw Alexander vi 594
Mendelsohn, Nathan Saul 594 603
Merchant, Arif Abdulhussein 601
Merging 79 175
Mersenne, Marin 109 131 585
Mersenne, numbers 109—110 151 278
Mersenne, primes 109—110 127 507
Miles 287 296
Mills, Stella 593
Mills, William Harold 594 603
Minimum 65 237 363
Mirsky, Leon 604
Mixture of probability distributions 414
Mobius, August Ferdinand 136
Mobius, function 136—139 357 448—449 501
mod 0 82—83 500
mod: binary operation 81—85
mod: congruence relation 123—126
MODE 370 371 423
Modular arithmetic 123—129
Modulus 82
Moessner, Alfred 594 604
Moments 384—385
Montgomery, Peter Lawrence 594 603
Moriarty, James 162
Morse, Samuel Finley Breese, code 288 310
Moser, Leo 594 602
Motzkin, Theodor Samuel 533 539 590 594
Mountain ranges 345 541
Mozzochi, Charles Jeffrey 594
Mu function 136—139 357 448—449 501
Multinomial coefficients 168 171—172 240 545
Multiple of a number 102
Multiple sums 34—41 61
Multiple-precision numbers 127
Multiplicative functions 134—136 357
Multisets 77 256
Mumble function 83 84 492 499
Mumble-fractional part 88
Murdock, Phoebe James viii
Murphy’s Law 74
Myers, Basil Roland 594 604
n-notation 64 106
Name and conquer 2 32 88 139
National Science Foundation ix
Natural logarithm 53—54 262
Naval Research ix
Navel research 285
Nearest integer 95
Necessary and sufficient condition 72
Necklaces 139—141 245
Negating the upper index 164—165
Negative binomial distribution 388—389 414
Negative factorial powers 52 63 188
Newman, James Roy 600
Newman, Morris 604
Newton, series 189—192
Newton, Sir Isaac 189 263 594
Newtonian generating function 364
Niven, Ivan Morton 318 594 602
Nontransitive paradox 396
Normal distribution 424
Notation x—xi 2 21—25 48—49 67—70 73 81 102 111 115 123—124 194 243
Notation, extension of 49 52 154 210—211 252 257 297
Notation, ghastly 67 175
Notation, need for new 83 115 253
Nu function 12 114 146 529
Null case 2 306—307 335 541
Number system 107 119
Number system, binomial 234
Number system, Fibonacci 282 296 303
Number system, prime-exponent 107 116
Number system, radix 11 16 109 146 148 195 233 446 511
Number system, residue 126—129 144
Number system, Stern — Brocot 119—123 146 292 504 527
Number theory 102—152
o, considered harmful 434—435
o-notation 76 429—435
Obvious, clarified 403 511
Odds 396
Odlyzko, Andrew Michael 81 540 588 605
Office of Naval Research ix
One-way equalities 432—433
Open interval 73—74 96
Operators 47 55 219
Optical illusions 278 279 536
Organ-pipe order 509
Pacioli, Luca 586
Palais, Richard Sheldon viii
Paradoxes 279 396 515
Paradoxical sums 57
Parallel summation 159 174 208—209
Parentheses 343—345
Parenthesis conventions xi
Partial fraction expansions 64 189 284—285 324—327 360 362 462 490 535
Partial quotients 292 304 540
Partial sums 48—49 55—56 161 165—166 223—230 233
Partial sums, required to be positive 345—348
Partition into nearly equal parts 83—85
Partitions, of a number 316
Partitions, of a set 244—245
Partitions, of the integers 77—78 99 101
Pascal, Blaise 155 156 594 602
Pascal’s triangle 155
Pascal’s triangle extended upward 164
Pascal’s triangle, extended upward 164
Pascal’s triangle, row products 231
Pascal’s triangle, row sums 163 165
Pascal’s triangle, variant of 238
Patashnik, Amy Markowitz ix
Patashnik, Oren iii iv vi ix 102 492 588 601
Patil, Ganapati Parashuram 594 605
Peirce, Charles Santiago Sanders 510 595 603
Peirce, sequence 151
Penney ante 394—396 416 423 424
Penney, Walter Francis 394 595
Pentagon 300 (exercise 46) 416 420
Pentagonal numbers 366
Percus, Jerome Kenneth 595 604
Perfect powers 66
Periodic recurrences 179
permutations 111—112 193—196
Permutations, ascents in 253—254 256
Permutations, up-down 363
Personal Computer 109
Perturbation method 32—33 43—44 64 179 270—271
Pfaff, Johann F’riedrich 207 217 595 603
Pfaff, reflection law 217 235
pgf see “Probability generating function”
Phages 420 424
Phi (= Golden ratio) 70 97 285—287 296 530
Phi function (= Totient function) 133—135 137—144 357 448—449
Phidias 285
Philosophy vii 11 16 46 71 72 75 91 170 181 194 317 453 489 494 577
Phyllotaxis 277
PI 26 70 146 232 471 540 570
Pig, Porky 482
Pigeonhole Principle 130
Pincherle, Salvatore 589
Pisano, Leonardo 585 (see also “Fibonacci”)
Pittel, Boris Gershon 552
Pizza 4 409
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