Gries D. — A Logical Approach to Discrete Math :: Электронная библиотека попечительского совета мехмата МГУ

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Gries D. — A Logical Approach to Discrete Math

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Название: A Logical Approach to Discrete Math

Автор: Gries D.

Аннотация:

This text attempts to change the way logic and discrete mathematics are taught. While many books treat logic simply as another topic of study, this book treats logic as a basic tool to be applied in essentially every other area. The book is organized so that selected chapters can either be studied together or used as a reference. The core of the book consists of textual substitution, equality and assignment, Boolean expressions, propositional calculus, quantification and predicate calculus. The remaining chapters can be selected according to individual course outlines.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-rd edition

Год издания: 1993

Количество страниц: 520

Добавлена в каталог: 23.01.2014

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Предметный указатель

# (Size)      201 212 234 258 259 461
$(^{n}_{r})$ (n choose r)      341 343
$\aleph$ (Cardinality of $\mathbb{N}$ )      464
$\bot$ (Relatively prime)      318
$\bullet$ (Function composition)      281
$\cap$ (Intersection)      203 213 270
$\cdot$ (Multiplication)      303
$\circ$ (Product)      271 281
$\cup$ (Union)      203 213 270
$\div$ (Integer division)      316
$\downarrow$ (Minimum)      311
$\emptyset$ (Empty set)      197
$\epsilon$ (Empty sequence)      251
$\equiv$ (Equivalence)      27 53
$\exists$ (Exists)      145 163
$\forall$ (Forall)      145 158
$\geq$ (At least)      308
$\in$ (Membership)      141 197 212 254 269
$\LaTeX$       xii
$\lceil x \rceil$ (Ceiling)      320
$\Leftarrow$ (Consequence)      27 56
$\leq$ (At most)      308
$\lfloor x \rfloor$ (Floor)      320
$\mathbb{B}$       139
$\mathbb{C}$       139
$\mathbb{N}$       139
$\mathbb{Q}$       139
$\mathbb{R}$       139
$\mathbb{R}^{+}$       139
$\mathbb{Z}$       139
$\mathbb{Z}^{+}$       139
$\mathbb{Z}^{-}$       139
$\mathcal{P}$ (Power set)      203
$\neg$ (Not)      26 45
$\neq$ (Inequality)      27
$\not{\equiv}$ (Inequivalence)      27 45
$\pi$ (pi)      130 297 321
$\Pi$ (Product)      145 310
$\rightarrow$       189
$\Rightarrow$ (implication)      27 56
$\sigma$ (sigma)      297
$\subset$ (Proper subsequence)      257
$\subset$ (Proper subset)      201
$\subseteq$ (Subsequence)      254 257
$\subseteq$ (subset)      201
$\sum$ (Summation)      142 144 145 310
$\supset$ (Proper superset)      201
$\supseteq$ (Superset)      201
$\TeX$       xii
$\triangleleft$ (Append)      254
$\triangleright$ (Prepend)      251
$\uparrow$ (Maximum)      311
$\vdash$ (Turnstile)      114
$\vee$ (Disjunction)      27
$\wedge$ (Disjunction)      27
$^{m}_{=}$ Equivalence mod m      325
+ (addition)      303
- (Difference)      203 213 270
- (negation)      306
- (subtraction)      306
/ (division)      316
01 $\diamond$ -calculus      135
< (Less)      308
= (Equality)      11 27 141
> (Greater)      308
Aaron, Eric G.      xi
Abel, Niels Henrik      143 144 396
Abelian group      397
Abelian monoid      143 396
abort      189
abs      283 314
Absolute value      283 314
Absorption      52 344 413
Accademia Militare      227
Ada      141
Adder, binary      99
Adder, full      100 101
Adder, half      92 96
Adder, three-bit      102
Additive group of integers      400
Additive group of integers mod n      397 400
Additive inverse      304
Adjacency list      429
Adjacency matrix      429
Adjacent      424
Admit induction      228
Aggregate      7
Aleph $\aleph$       464
Algebra      387
Algebra, boolean      412
Algebra, carrier of      387
Algebra, finite      387
Algebra, infinite      387
Algebra, power-set algebra      413 414
Algebra, signature of      388
Algol      30 146
Allen, L.E.      473
Almstrum, Vicki      xi
Altdorf University      9
ALTER      261
Alternative statement      189
Amusements, jokes      3 6 17 19 36 53 54 179 224 225 289 328 334 338 348 349 388 431
Anagram      338
Ancestor      275
And $\wedge$       27 51
And $\wedge$ , translation of      33
and-gate      91
Angle, of a complex number      369
Antecedent      27
Antecedent, assuming the antecedent      71
Antisymmetric relation      273
Antisymmetry      59
Antisymmetry of $\leq$       308
Antisymmetry of $\subseteq$       207
Appel, K.      449
Append $\triangleright$       254 255
Argument, of a function application      13
Arguments in mathematics      171
Arity      387
Ascending      191
assignment statement      17
Assignment statement, calculating      186
Assignment statement, hoare triple for      18
Assignment statement, multiple assignment      19
Assignment statement, reasoning about      181
Assignment statement, sequences of      185
Associativity      29
Associativity of $\bullet$       281
Associativity of $\cap$       205
Associativity of $\cdot$       303
Associativity of $\circ$       271
Associativity of $\cup$       205
Associativity of $\downarrow$       311
Associativity of $\equiv$       43
Associativity of $\not{\equiv}$       46
Associativity of $\uparrow$       314
Associativity of $\vee$       49
Associativity of $\wedge$       51
Associativity of +      303
Associativity of gcd      317
Assuming the antecedent      71
Asymmetric relation      273
At least $\geq$       308
At most $\leq$       308
AT&T      93
Athens      225
atoms      415
Automata theory      387
Automorphism      388 392
av (average)      355

Axiom      41 125
Axiom of Choice      209
Backhouse, Roland C.      83 473
Bag      211
Bag comprehension      211
Bag enumeration      211
Bag equality =      212
Bag membership $\in$       212
Bag, permutation of      339
Barshatsky, Harry M.      xi
Base b system      328
base case      218 222
Bees      224
behavior      94
Bell Labs      93
Bell, E.T.      x 231 268 347 403 431 473
Berlin, University of      132 144 464
BHK interpretation      132
Bijective      282
Binary adder      99
Binary number system      329
Binary operator      7 387
Binary relation      267
Binary tree      233
Binary tree, complete      234
Binary tree, height of      234
Binary tree, internal node of      233
Binary tree, leaf of      233
Binary tree, left subtree of      233
Binary tree, node of      233
Binary tree, right subtree of      233
Binary tree, root of      233
Binary tree, size of      234
Binary unit (bit)      93 328
Binet formula      245
Binomial coefficient      341
Binomial theorem      346
Bipartite graph      436
Bipartite graph, complete      437
Bishop of Cloyne      440
Bishop, Errett      131 473
Bit      93 328
Blaise Pascal      347
Body of a quantification      143
Bolyai prize      111
Boole, George      16 25 26 54 93 111 473
Boolean      16
Boolean algebra      412
Boolean expression      25
Boolean expression versus circuit diagram      91
Boolean expression, evaluation of      28
Boolean operator      25
Boolean type $\mathbb{B}$       139
Boolean value      25
Boolean variable      25
Boolian      25
Borel, Emile      131
Bound function      241
Bound occurrence      145 146
Bound variable      143
Boundary case      363
Box principle      355
Breadth-first algorithm      455
Bridge, method of      58
Bridges, Douglas      473
Brouwer, L.E.J.      131 132
Bryn Mawr College      231
budget      54
Building blocks, universal set of      102
Bush, George      338
Bussan, Mimi      v 268
C      16 25
Cajori, Florian      x 16 473
Calculating an assignment      186
Calculus      41
Calculus, 01 $\diamond$ -calculus      135
Calculus, predicate      157
Calculus, propositional      41
California problem      334
Cambridge University      79 403
Cancellation      304 398
Cantor diagonalization      463
Cantor, Georg F.L.P.      131 132 210 463 464 469
cardinal number      464
Cardinality #      201 461
Cardinality # of an infinite set      462
Carrier      387
Cartesian product      266
Case analysis      58 73—75 120
Catenation ^      254 256
Catherine I      431
Catherine the Great      431
Cauchy, Augustin Louis      144
Cayley, Arthur      408 409
Ceiling of x, $\lceil x \rceil$       320
Celebrity problem      435
Cesaro, E.      321
Chain      287
Change of dummy      151
Character type $\mathbb{C}$       139
Characteristic polynomial      364
Characteristic predicate      200
Checklist for proving a loop correct      238
Cheng, Betty H.C.      xi
Chess board      441
Child      234
child relation      269
Choice, axiom of      209
choose      242
Christina, Queen of Sweden      268
Christmas      328
Circuit diagram      90
Circuit diagram versus boolean expression      91
City of New York, College of      212
Classes of relations      273
Cleopatra      32—34
Closed expression      162
Closed operator      391
Closed-form solution      366
Closure of a relation      274
Coding theory      387
Cohen, Paul      470
Combinational digital circuit      90
Combinations of a set      340
Combinations of a set with repetition      341
Combinatorial argument      344
Commutative      12 397
Commuting diagram      392
Complement ~      202 270
complete      111
Complete binary tree      234
Complete digraph      442
Complete graph      436
Complete logic      128
Complex number      369
Composite number      322
Computable function      79
Concatenation      see "Catenation"
Conclusion      10 125
Conditional expression      190
Conditional statement      188
Congruence      325
Congruent modulo n      325
Conjunct      27
Conjunction $\wedge$       27 51
Conjunctional operator      29
Conjunctive normal form      67 135
Connected digraph      428
Connected multigraph      428
Connective      27

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