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

Consequence      27 56
Consequent      27
Consistent      111 126
Constable, Robert L.      xi 473
Constraint      363
Constructive logic      130
Constructive mathematics      131
Constructive mathematics and Double negation      134
Constructive mathematics and Excluded middle      132
Constructive reasoning      464
Continuum      463
Continuum Hypothesis      469
Contradiction      51 77 117 120 205
Contrapositive      56 79
Coordinate transformation      288
copyrights      289
Corbusier      225
Cornell University      x xii 17
Coset      401
Count #      259
Countable set      466
Counterexample      84
Counterexample for a boolean expression      85
Country of Marr      106
Crelle, August Leopold      144
Cross product      266
Cryptography      284
Cryptosystems      323
CSP      19
CYCLE      410 427
Cyclic group      405
Cyclic group, generator of      405
Cyclic permutation      410
Dale, Nell      xi
DARPA      xii
Data refinement      288
Database      295
DCF      230
De Morgan's law      32 52 206
De Morgan's law, generalized      164
de Morgan, Augustus      26 32 52 54 111
Decidable      111
Decimal number system      329
Decimal representation      328
Decision procedure      129
Decreasing finite chain property      230
Deduction Theorem      114
Deduction theorem, extended      72
Deg      425
Degree of a graph      426
Degree of a polynomial      364
Degree of a vertex      425
Demers, Alan      xi
DeMoivre's theorem      369
Denumerable set      466
Depth-first algorithm      456
Descartes, Rene      15 266 267 402 473
Determinate      280
Diagonal      390
Diagonalization      463
Diderot, Denis      431
Difference equation, homogeneous      363
Difference equation, nonhomogeneous      371
Difference —      203 213 270
digit      328
Digital circuit      90
Digital circuit, combinational      90
Digital Equipment Corporation      xii
Digital signature      284
Digraph      423
Digraph, complete      442
Digraph, connected      428
Digraph, representations of      429
Digraph, weighted      449
Dijkstra's shortest-path algorithm      449
Dijkstra, Edsger W.      xi 17 182 473
Directed graph      423
Dirichlet, Lejeune      355
Discourse on Method      268
Disjoint permutations      411
Disjoint sets      203
Disjunct      27
Disjunction $\vee$       27 49
Disjunctive normal form      67
Distributivity of $\cap$ over $\cup$       206
Distributivity of $\cdot$ over $\downarrow$       312
Distributivity of $\cdot$ over $\downarrow$ , $\uparrow$       314
Distributivity of $\cdot$ over $\uparrow$       312
Distributivity of $\cdot$ over +      304
Distributivity of $\cdot$ over gcd      317
Distributivity of $\circ$ over $\cap$       271
Distributivity of $\circ$ over $\cup$       271
Distributivity of $\cup$ over $\cap$       206
Distributivity of $\downarrow$ over $\uparrow$       314
Distributivity of $\neg$ over $\equiv$       45
Distributivity of $\Rightarrow$ over $\equiv$       57
Distributivity of $\Rightarrow$ over $\Rightarrow$       57
Distributivity of $\times$ over $\cap$       266
Distributivity of $\times$ over $\cup$       266
Distributivity of $\times$ over —      266
Distributivity of $\uparrow$ over $\downarrow$       314
Distributivity of $\vee$ over $\equiv$       49
Distributivity of $\vee$ over $\exists$       165
Distributivity of $\vee$ over $\forall$       159
Distributivity of $\vee$ over $\vee$       49
Distributivity of $\vee$ over $\wedge$       52
Distributivity of $\wedge$ over $\exists$       165
Distributivity of $\wedge$ over $\forall$       160
Distributivity of $\wedge$ over $\vee$       52
Distributivity of $\wedge$ over $\wedge$       51
Distributivity of + over $\downarrow$       312
Distributivity of + over $\downarrow$ , $\uparrow$       314
Distributivity of + over $\uparrow$       312
Distributivity of quantified * over *      149
Divides |      315
Divine proportion      225
Divisibility      315
Division /      316
do od loop      236
dodecahedron      439
DOM      270
Domain of a relation      270
Domain of an expression      182
Domain of discourse      127 196
Domain, integral      303
Domain, ordered      307
Domain, well ordered      309
Don't-care condition      97
Double Negation      45 46
Double negation and constructive math      134
Doyle, A. Conan      473
Dual      31 164 414
Dual graph      448
Duality      32 248
Dudley, U.      54
Dummy      142 143
Dummy renaming      150
Dummy, change of      151
Dummy, interchange of      150
e      41 125
E, consistency of      126
Edge of a digraph      423
Edge of an undirected graph      424
Edge-path representation      427
Efremidis, Sofoklis      xi
Eindhoven, Technical University of      xi
Einstein, Albert      1 4 129 231
Elements      319
Elimination rule      113
Em dash      ix

Empty range axiom      148
Empty relation      269
Empty sequence $\epsilon$       251
Empty set $\emptyset$       197
Encyclopaedia Britannica      x 473
End vertex      424
English arguments, checking      83
English arguments, formalizing      83
English to predicate logic      168
Enumeration of a set      466
Enumeration of a set with repetition      466
Epimenides      210
Equality =      11 27 141
Equality = of bags      212
Equality = of sequences      251
Equality = of sets      197
Equality = versus equivalence      29
Equality =, Leibniz's definition of      13
Equality =, symbols for      16
Equality modulo m $^{m}_{=}$       325
Equational logic      41 125
Equational logic, advantages of      viii
Equivale $\equiv$       27 53
Equivalence $\equiv$       53
Equivalence $\equiv$ in natural deduction systems      117
Equivalence $\equiv$ versus equality      29
Equivalence $\equiv$ versus implication      35
Equivalence class      277
Equivalence relation      276
Equivalence relation versus set partition      276
Equivalent      27
Eratosthenes      323
Euclid      225 318 319 323 347
Euclid's Algorithm      224 318
Euclid's Elements      347
Euler circuit      430
Euler path      430
Euler, Leonhard      426 431
Evaluation of boolean expressions      28
Evaluation of expressions      8
EWD series      183
Excluded Middle      49 205
Excluded middle and constructive math      132
Exclusion/inclusion principle      362
Exclusive NOR      36
Exclusive OR      27 36 53
Existential quantification $\exists$       3 145 163
Existential quantification, making use of      167
exponentiation      222
Exposing the inductive hypothesis      221
Expression, Boolean      25
Expression, closed      162
Expression, evaluation of      8
Expression, fully typed      140
Expression, general form of      7
Expression, open      162
Expression, standard interpretation for      127
Extended deduction theorem      72
Extension of a logic      128
Extensionality      197
Extreme and mean value      225
FALSE      25 45
Feijen, Wim H.J.      473
Fekete, Alan David      xi
Fermat numbers      403
Fermat's last theorem      403
Fermat, Pierre      403
Fibonacci numbers      224
Fibonacci numbers and gcd      320
Fibonacci, Leonardo      224
Fields, W.C.      93
finite      232
Finite algebra      387
Finite range, need for      149
Finite set      461
Finitistic mathematics      131
First versus one      6
First-order predicate calculus      245
Floor of x, $\lfloor x \rfloor$       320
flush      353
Formal languages      251 387
Formal logical system      125
FORTRAN      16 17 25 30
Foster, Alan      474
Fountain pen      183
Four of a kind      353
Four-color problem      423 449
Fowler, H.W.      ix
Frederick the Great      431
Free occurrence      145 146
Fresh variable      147 163
Full adder      100 101
Full house      353
Fully typed expression      140
Function      13 279 280
Function application      ix 13 279
Function application, type of      140
Function as a binary relation      280
Function composition $\bullet$       281
Function symbols, uninterpreted      157
Function, bijective function      282
Function, composition of      281
Function, computable function      79
Function, generating function      375
Function, identity function      281
Function, injective function      282
Function, inverse of      282
Function, one-to-one function      282
Function, onto function      282
Function, partial function      280
Function, powers of      281
Function, product of      281
Function, rational function      377
Function, surjective function      282
Function, total function      280
Function, type of      140
Fundamental invariance theorem      237
Fundamental Theorem of Arithmetic      323
Gambhir, Navindra S.      xi
Garfinkle, Simson      475
Gate      90
Gate for conjunction      91
Gate for disjunction      91
Gate for negation      91
Gate, nand      102
Gate, nor      103
Gauss, Karl Friedrich      144
GCD      316
Gebauer, Ruediger      xii
Generalized De Morgan      164
Generalized pigeonhole principle      355
Generating function      375
Generating function for an HDE      377
Generating function for an NDE      381
Generator      405
Gentzen, Gerhard      113 116 121 131 474
Gerhardt, Karl Imanuel      474
German University of Prague      116
Global reference      112
Goedel, Kurt      111 128 129 469 474
Goettingen, University of      111 116 231
Golden mean      225
Golden ratio      225 367
Golden rectangle      225
Golden Rule      51
Golden section      225
Graham, Ronald L.      318 474
Grandparent      272
Graph, bipartite      436
Graph, complete      436

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