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

Majority circuit      99
Majority circuit, partial      97
Malton, Andrew      xi
Manipulating ranges      152
Map coloring      448
Marktoberdorf      17
Marr, country of      106
Mathematical induction      see "Induction"
Mathematical model      1
Mathematician's license      242
MAX      355
Maximum $\uparrow$       311
McIlroy, Doug      xi 349
McKeeman, Bill      xi
Median      191
Membership $\in$       141 197 212
Membership $\in$ in a cross product      266
Membership $\in$ in a relation      269
Membership $\in$ in a sequence      254
Merchant of Venice      86
Mersenne numbers      323
Mersenne primes      323
Mersenne, Father Marin      323
Message Encryption and Authentication      284
Metatheorem      45
Method of the bridge      58
Minimal element      228 292
Minimum $\downarrow$       311
Minkowski, Hermann      111
Misra, Jay      xi xii
MIT      93
ML      141
Mod mod      316
Model for a logic      128
Model theory      127
Model, mathematical      1
Modern algebra      387
MODULO      325
Modulus      325
modus ponens      58 114 119 120
Monoid      143 396
Monoid, Abelian      143 396
Monotonicity      70 308
Monotonicity of $\exists$       165
Monotonicity of $\forall$       160
Mont Blanc      183
Moriarity      348
Morphing      388
Most significant digit      328
Multigraph      425
Multigraph, connected      428
Multiple assignment      19
Multiplexor      108
Multiplication $\cdot$       303
Multiplicity, of a root      364
Multiset      211
Mutual associativity      46 256
Mutual implication      58 59 76 120
Mutual interchangeability      46
Mux (multiplexor)      108
Myers, Paul      xi
Named tuple      267
NAND      27
Nand-gate      102
National Science Foundation      xii
Natural deduction      113
Natural deduction, hallmark of      114
Natural deduction, inference rules for      114
Natural deduction, proof formats for      118
Natural deduction, reason for inventing      121
Natural join $\bowtie$       297 298
Natural numbers $\mathbb{N}$       139
Natural numbers $\mathbb{N}$ , representations of      327
nd      113
NDE      371
NDE, generating function for      381
Negation $\neg$       26 45
Negative integers $\mathbb{Z}^{-}$       139
Neptune      2 3
Nesting axiom      150
Newton, Isaac      2 9 16
Nobel prize      79 212
Node      233
Noether, Emmy      230 231
Noetherian      230
Nondeterminism      180 189 242
Nonhomogeneous difference equation      371
NOR      27
Nor-gate      103
Normal form, conjunctive      67 135
Normal form, disjunctive      67
Not $\neg$       26 45
Not $\neg$ , translation of      33
Not-gate      91
Notational surprises      30
Nullary operator      387
NUPRL      xi 131
Occurs      146
Octal number system      328 329
OED (Oxford English Dictionary)      25
Office of Naval Research      xii
Ohio State      129
One pair      353
One-point rule      148
One-to-one      282
Onto      282
Open expression      162
Operator precedence      7
Operator, associative      29
Operator, binary      7
Operator, Boolean      25
Operator, closed      391
Operator, commutative      12
Operator, conjunctional      29
Operator, idempotent      49
Operator, infix      7
Operator, prefix      7
Operator, symmetric      12
Operator, unary      7
Operators and $\wedge$       27
Operators, absolute value abs      283 314
Operators, addition +      303
Operators, alter      261
Operators, append $\triangleright$       255
Operators, at least $\geq$       308
Operators, at most $\leq$       308
Operators, cardinality #      201 212
Operators, catenation ^      256
Operators, ceiling, $\lceil x\rceil$       320
Operators, complement ~      202 270
Operators, conjunction $\wedge$       27
Operators, consequence $\Leftarrow$       27
Operators, count #      259
Operators, difference —      203 213 270
Operators, disjunction $\vee$       27
Operators, divides |      315
Operators, division /      316
Operators, equality =      11 27 141 197 212
Operators, equality modulo m $^{m}_{=}$       325
Operators, equivalence $\equiv$       27
Operators, floor, $\lfloor x\rfloor$       320
Operators, function composition $\bullet$       281
Operators, greater >      308
Operators, implication $\Rightarrow$       27
Operators, inequality $\neq$       27
Operators, inequivalence $\not{\equiv}$       27 45
Operators, integer division $\div$       316
Operators, intersection $\cap$       203 213 270
Operators, inverse      270
Operators, length #      258

Operators, less <      308
Operators, maximum $\uparrow$       311
Operators, membership $\in$       141 197 212 254 269
Operators, minimum $\downarrow$       311
Operators, mod mod      316
Operators, multiplication $\cdot$       303
Operators, nand      27
Operators, natural join $\bowtie$       297 298
Operators, negation $\neg$       26
Operators, nor      27
Operators, not $\neg$       26 45
Operators, or $\vee$       27
Operators, power set $\mathcal{P}$       203
Operators, prepend $\triangleright$       251
Operators, product $\circ$       271
Operators, product $\Pi$       145 310
Operators, projection $\pi$       297
Operators, proper subbag $\subset$       212
Operators, proper subsequence $\subset$       257
Operators, proper subset $\subset$       201
Operators, proper superset $\supset$       201
Operators, relatively prime $\bot$       318
Operators, selection $\sigma$       297
Operators, size #      234 461
Operators, subbag $\subseteq$       212
Operators, subsequence $\subseteq$       257
Operators, subset $\subseteq$       201
Operators, subtraction —      306
Operators, summation $\sum$       142 144 145 310
Operators, superset $\supseteq$       201
Operators, unary minus —      306
Operators, union $\cup$       203 213 270
Operators, universal quantification $\forall$       145 158
Opportunity-driven proof      166
Or $\vee$       27 49
Or $\vee$ , translation of      33 34
or-gate      91
Order of a group element      399
Order of Merit      212
Order, linear      287 307
Order, partial      285
Order, quasi      287
Order, strict partial      287
Order, total      287 307
Ordered domain      307
Ordered pair      265
Ordering, lexicographic      235
Outdegree of a vertex      425
Overloading      141
Oxford English Dictionary      27 251
Oxford University      19
P(n,r)      338
pair      265
Palindrome      264 359
Paradox      54 210
Parent      234
parent relation      269
Parentheses, avoiding      29
Paris Academy of Sciences      144
Partial function      280
Partial majority circuit      97
Partial order      285
Partial order, strict      287
Partial-fraction decomposition      379
Partially ordered set      285
Partition of a set      209
Partition of a set versus equivalence relation      276
Pascal      4 25 141 146 262 267 347
Pascal's triangle      346
Pascal, Blaise      346 403
Patashnik, Oren      318 474
Patents      289
Path      426
Path, edge-path representation      427
Path, Euler path      430
Path, Hamilton circuit      439
Path, Hamilton path      439
Path, length of      427
Path, shortest      449
Path, simple      427
pdiv (proper divisor)      229
Peano arithmetic      227
Peano, Giuseppe      227
Percentage of Relatively Prime Pairs      321
perm (Permutation)      191
Permutation      410
Permutation of a bag      339
Permutation of a sequence      264 338
Permutation of a set      338
Permutation with repetition      339
Permutation, cyclic      410
Permutation, disjoint permutations      411
Permutation, groups of      410
PERT      286
Phidean      225
Pigeonhole Principle      355
Pigeonhole principle, generalized      355
PL/1      30
Planar graph      445
Plus +      303
Poincare, Henri      131
Poker      353
Polar coordinates      369
Polish notation      5
Polymorphism      142
Polynomial, characteristic      364
Polynomial, degree of      364
Polynomial, root of      364
Pomerania      116
Portia's suitor's dilemma      86
pos      307
POSET      285 292
Positive integers $\mathbb{Z}^{+}$       139
Positive reals $\mathbb{R}^{+}$       139
Postcondition      2 179
Potter, Walt      xi
Potz-Hoeffner, Arnd      xi
Power set $\mathcal{P}$       203
Power-set algebra      413 414
Powers of a function      281
Powers of a relation      272
Powers of group elements      399
PQ-L      126
Prague, German University of      116
precedence of operators      7
Precedence of operators of boolean operators      28
Precondition      2 179
Precondition, weakest      182
pred relation      269
Predicate      157
Predicate calculus      157
Predicate calculus, first-order      245
Predicate calculus, second-order      245
Predicate symbol      157
Prefix      257
prefix operator      7
Premise      10 114 125
Prepend $\triangleright$       251
Prependant      251
Prim's algorithm      456
Prim, Robert Clay      456
Primality testing      323
Prime number      322
Prime number, facts about      323
Princeton University      403
Principal diagonal      390
Principia Mathematica      212
Principle of comprehension      200
Principles, minimize rabbits      51
Principles, structure proofs to avoid repetition      48

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