Graham R.L., Knuth D.E., Patashnik O. — Concrete mathematics :: Электронная библиотека попечительского совета мехмата МГУ

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Graham R.L., Knuth D.E., Patashnik O. — Concrete mathematics

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Название: Concrete mathematics

Авторы: Graham R.L., Knuth D.E., Patashnik O.

Аннотация:

This book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's primary aim is to provide a solid and relevant base of mathematical skills. It is an indispensable text and reference for computer scientists and serious programmers in virtually every discipline.

Язык:

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 625

Добавлена в каталог: 12.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

      162
$n^{th}$ difference      267
$\gamma$       see “Euler’s constant”
$\Leftrightarrow$ (if and only if)      68
$\mathcal{J}$ : Imaginary part      64
$\mu$       see “Mobius function”
$\nu$       see “Nu function”
$\Phi$       see “Phi”
$\pi$       26 70 146 232 471 540 570
$\Rightarrow$ (implies)      71
$\Sigma$       374
$\sqrt{2}$       100
$\sqrt{3}$       364
$\theta$       see “Big Theta notation”
$\varphi$       see “Euler’s totient function”
$\vartheta$       see “Theta operator”
... (ellipsis)      21 50 108
6      see “Finite calculus”
A      see “Difference operator”
A-notation      65
Aaronson, Bette Jane      ix
Abel, Niels Henrik      578 603
Abramowitz, Milton      42 578
Absolute convergence      60—61 64
Absolute error      438 441
Absolute value of complex number      64
Absorption identities      157—158 247
Acton, John Emerich Edward Dalberg, baron      66
Adams, William Wells      578 604
Addison-Wesley      ix
Addition formula      158—159 245 247
Additional Stirling number identities      251
Aho, Alfred Vaino      578 602
Ahrens, Wilhelm Ernst Martin Georg      8 578 602
Akhiezer, Naum Il’ich      578
Alfred [Brousseau], Brother Ulbertus      580 602
Algebraic integers      147
Algorithms, analysis of      138 399—412
Algorithms, divide and conquer      79
Algorithms, Euclid’s      103 123 289—290
Algorithms, Fibonacci’s      95 101
Algorithms, Gosper’s      224—226 519
Algorithms, greedy      101 281
Algorithms, self-certifying      104
ALICE      31 394—396 416
Allardice, Robert Edgar      2 5 78
American Mathematical Society      viii
AMS Euler      ix 625
Analysis of Algorithms      138 399—412
Analytic functions      196
Ancestor      117 277
Andre, Antoine Desire      578 604
Andrews, George W. Eyre      215 316 515 579 603 604
Answers, notes on      viii 483 606
Anti-difference operator      48 54 456—457
Approximation      8 76 87—89 110 114 425—482
Approximation of sums by integrals      45 262—263 455—461
Archibald, Raymond Clare      581
Argument of hypergeometric      205
Arithmetic progression      26 30 362
Armageddon      85
Armstrong, Daniel Louis      80
Ascents      253—254 256
Askey, Richard Allen      603
Associative law      30 61 64
Asymptotic approximations      438
Asymptotics      8 76 110 114 425—482
Asymptotics for sums      87—89 452—482
Atkinson, Michael David      579 602
Austin, A. K.      581
Automaton      391
Automorphic numbers      505
Average of a reciprocal      418
Average, defined      370
Average, variance      409—411
Bachmann, Paul Gustav Heinrich      429 448 579
Bailey, Wilfrid Norman      223 579 603
Ball, Walter William Rouse      579 602
Banach, Stefan      419
Barlow, Peter      579 603
Barton, David Elliott      577 582
BASEBALL      73 148 195 616 620 621
BASIC      173 432
Basic fractions      134 138
Basic Stirling number identities      250
Basis of induction      3 10—11 306—307
Bateman, Harry      595
Baum, Lyman Frank      556
Beatty, Samuel      579 602
Bee trees      277
Beeton, Barbara Ann Neuhaus Friend Smith      viii
Bell, Eric Temple      318 579 604
Bell, numbers      359 479
Bender, Edward Anton      579 605
Bernoulli numbers      269—276 301 303 353 456
Bernoulli numbers, calculation of      274
Bernoulli numbers, generalized      see “Stirling polynomials”
Bernoulli numbers, generating function for      271 337 351
Bernoulli, Jakob (=Jacobi=Jacques=James)      269 456 579
Bernoulli, Johann (=Jean)      593
Bernoulli, numbers      see “Bernoulli numbers”
Bernoulli, polynomials      353 456—458
Bernoulli, trials      388 (see also “Coins flipping”)
Bernshtein (=Bernstein), Sergei Natanovich      605
Bertrand, Joseph Louis Frangois      145 579 602
Bertrand, postulate      145 487 528
Bessel, Friedrich Wilhelm, function      206 512
Beyer, William Hyman      579
Biased coin      387
Bicycle      246 486
Bieberbach, Ludwig      589
Bienayme, Irenee Jules      580
Big Ell notation      430
Big Oh notation      76 429—435
Big Omega notation      434
Big Theta notation      434
Bijection      39
Bill      394—396 416
Binary logarithm      70
Binary notation (radix-z)      11—13 15 70 113
Binary partitions      363
Binary search      121 183
Binary trees      117
Binet, Jacques Philippe Marie      285 289 580
Binomial coefficients      153—242
Binomial coefficients, combinatorial interpretation      153 158 160 169—170
Binomial coefficients, definition      154 211
Binomial coefficients, dual      515
Binomial coefficients, indices of      154
Binomial coefficients, middle      187 242
Binomial coefficients, reciprocal of      188
Binomial coefficients, top ten identities of      174
Binomial coefficients, wraparound      238 (exercise 75) 301
Binomial convolution      351 353
Binomial distribution      387—388 401 414 418
Binomial distribution, negative      388—389 414
Binomial number system      234
Binomial series, generalized      200—204 232 240 349
Binomial theorem      162—163 199 206 221
Blom, Gunnar      580 605
Bloopergeometric series      232
Boas, Ralph Philip, Jr.      viii 574 580 605
Boggs, Wade Anthony      195
Bohl, Piers Paul Felix      87 580
Bois-Reymond, Paul David Gustav du      426 580 589
Boncompagni, Prince Baldassarre      585
Bootstrapping      449—452
Borchardt, Carl Wilhelm      589
Borel, Emile Felix Edouard Justin      580 605
Borwein, Jonathan Michael      580 604

Borwein, Peter Benjamin      5130 604
Bound variables      22
boundary conditions      24—25 75 86 159
Bowling      6
Box principle      95 130 497
Brahma, Tower of      1 4 264
Brent, Richard Peirce      292 510 540 580
Bricks      299 360
Brillhart, John David      580 602
Brocot, Achille      116 580
Broder, Andrei Zary      ix 601
Brooke, Maxey      580 603
Brousseau, Brother Alfred      580 602
Brown University      ix
Brown, Mark Robbin      601
Brown, Morton      487 580
Brown, Roy Howard      ix
Brown, Thomas Craig      581 602
Brown, Trivial      581
Brown, William Gordon      344 581
Browning, Elizabeth Barrett      306
Bubblesort      434
Buckholtz, Thomas Joel      593.
Burr, Stefan Andrus      581 604
Calculators      67 330
Calculus      vi 33
Calculus, finite and infinite      47—56
Candy      36
Canfield, Earl Rodney      577 581 605
Cards, shuffling      423
Cards, stacking      259—260 295
Carlitz, Leonard      604
Carroll, Lewis (=Dodgson, Rev. Charles Lutwidge)      31 279 581 582 599
Carry      70 233 283 537
Cassini, identity      278—279 286 289 296 300
Cassini, Jean Dominique      278 581
Catalan numbers      181 203 303
Catalan numbers, combinatorial interpretations      344—346 541
Catalan numbers, generalized      347
Catalan numbers, table of identities      203
Catalan, Eugene Charles      203 347 581
Cauchy, Augustin Louis      581 602
Cauchy, inequality      64
Cech, Eduard      vi
Ceiling function      67—69
Center of gravity      259—260
Certificate of correctness      104
Chace, Arnold Buffum      581 602
Chaimovich, M.      581
Chain rule      54 469
Change      313—316 360
Change, large amounts of      330—332 478
Changing the index of summation      30—31 39
Changing the tails of a sum      452—455
Cheating      viii 158 309 374 387
Chebyshev, inequality      376—377 414 416 555
Chebyshev, Pafnutil Lvovich      38 145 581 602
Chebyshev, summation inequalities      38
Cheese slicing      19
Chen, Pang-Chieh      601
Chinese remainder theorem      126 146
Chu Shih-Chieh      169
Chung, Fan-Rong King      ix
Clausen, product identities      241
Clausen, Thomas      582 603 604
Clearly, clarified      403 556
Cliches      166 310
Closed form      3 7 108 317 548
Closed interval      73—74
Cobb, Tyrus Raymond      195
Coins      313—316
Coins, biased      387
Coins, fair      387 416
Coins, flipping      387—396
Coins, spinning      387
Collingwood, Stuart Dodgson      279 582
Collins, John      594
Colombo, Cristoforo (=Columbus, Christopher)      74
Colors      482
Columbia University      ix
Combinations      153
Common logarithm      435
Commutative law      30 61 64 308
Commutative law, relaxed      31
Complete graph      354
Complex factorial powers      211
complex numbers      64
Complex numbers, roots of unity      149 204 361 530 550 572
Composite numbers      105
Composition of generating functions      414
Concrete Math Club      74
Concrete mathematics, defined      vi
Conditional convergence      59
Conditional probability      402—405 410—411
Confluent hypergeometric series      206
Congruences      124—126
Connection Machine      131
Contiguous hypergeometrics      514
Continuants      287—295 298 300 487
Continued fractions      287 290—295 304 540
Convergence      206 317 517
Convergence, absolute      60—61 64
Convergence, conditional      59
Convex regions      5 20 483
Convolution      197 319 339—350
Convolution, binomial      351 353
Convolution, identities for      202 258
Conway, John Horton      396 566 582
Cotangent function      272 303
Counting, combinations      153
Counting, cycle arrangements      247—248
Counting, derangements      193—196 199—200
Counting, integers in intervals      73—74
Counting, necklaces      139—141
Counting, parenthesized formulas      343—345
Counting, permutations      111 253—254
Counting, set partitions      245
Counting, spanning trees      335 354
Counting, with generating functions      306—316
Coupon collecting      558
Cover, Thomas Merrill      605
Coxeter, Harold Scott Macdonald      579
Cramer, Carl Harald      510 582 603
Cray X-MP      109
Crelle, August Leopold      582 602
Cribbage      65
Crispin, Mark Reed      598
Crowe, Donald Warren      582 602
Crudification      433
Cubes, sum of consecutive      51 63 269 275 353
Cumulants      383—387 414 415 424
CUNY (= City University of New York)      ix
Curtiss, David Raymond      582 603
Cycles      139 245 248 486
Cyclic shift      12
Cyclotomic polynomial      149
D      see “Derivative operator”
David, Florence Nightingale      577 582
Davison, John Leslie      293 578 582 604
de Branges, Louis      589
de Bruijn, cycle      486
de Bruijn, Nicolaas Govert      430 433 486 582 604 605
De Moivre, Abraham      283 467 582
Definite sums, analogous to definite integrals      49—50
Degenerate hypergeometric series      210 216 222 235
Derangements      193—196 199—200 379—380 386—387 414
Derivative operator      33 47 1191 219—221 296 319 350—351 456—457
Descents      see “Ascents”
dgf      see “Dirichlet generating function”
Dice      367—370 413 415

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