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

Graph, complete bipartite      437
Graph, degree of      426
Graph, directed      423
Graph, dual      448
Graph, homeomorphic      438
Graph, isomorphism      438
Graph, planar      445
Graph, spanning tree of      453
Graph, subgraph of      437
Graph, undirected      424
Greater >      308
Greatest common divisor gcd      316
Greatest common divisor gcd and Fibonacci numbers      320
Greatest lower bound      292
Gries, David      xii 17 27 268 285 388
Gries, Elaine W.      v 268
Gries, Paul      xi
Group      397
Group, abelian      397
Group, commutative      397
Group, cyclic      405
Group, identity of      397
Group, permutation group      410
Group, symmetric      397
Groups of transformations      406
Groups, additive of integers      400
Groups, additive of integers mod n      397 400
guard      189 236
Guarded command      189
Haken, W.      449
half-adder      92 96
Halle, University of      464
Halloween      328
Halting problem      78 79
HAMILTON CIRCUIT      439
Hamilton path      439
Hamilton, William Rowan      439 440
Hartmanis, Juris      xi
Harvard      212
Hasse diagram      286
HDE      363
Head of a sequence      254
Hehner, Eric C.R.      xi 474
Height of a binary tree      234
Henry VIII      32—34
Henzinger, Tom      xi xii
Herigone      16
Heterogeneous set      198
Heuristics, definition elimination      48
Heuristics, parse theorems in different ways      56
Heuristics, to prove $P\equiv Q$ , transform one to the other      50
Heuristics, use shape of expressions      47
Hexadecimal number system      328 329
Heyting      131 132
Hidden variables and textual substitution      10
Hilbert style of proof      109
Hilbert's unsolved problems      111 469
Hilbert, David      3 79 111 116 129 132 231 403 469
Historical notes, Abel, Niels Henrik      144
Historical notes, Boole, George      26
Historical notes, Cantor, Georg F.L.P.      464
Historical notes, Cayley, Arthur      409
Historical notes, constructive mathematics      131
Historical notes, de Morgan, Augustus      54
Historical notes, Descartes, Rene      268
Historical notes, Dijkstra, Edsger W.      183
Historical notes, Encryption and Authentication      284
Historical notes, Euclid      319
Historical notes, Euler, Leonhard      431
Historical notes, Fermat, Pierre      403
Historical notes, Fibonacci numbers      224
Historical notes, Gentzen, Gerhard      116
Historical notes, Goedel, Kurt      129
Historical notes, golden ratio      225
Historical notes, Hamilton, William Rowan      440
Historical notes, Hilbert, David      111
Historical notes, Hoare, Charles Anthony R.      19
Historical notes, Kronecker, Leopold      132
Historical notes, Leibniz's Def. of Equality      13
Historical notes, Leibniz, Gottfried Wilhelm      9
Historical notes, morphing      388
Historical notes, Noether, Emmy      231
Historical notes, notational surprises      30
Historical notes, Pascal, Blaise      347
Historical notes, Peano, Giuseppe      227
Historical notes, percentage of relatively prime pairs      321
Historical notes, rigor      3
Historical notes, Russell, Bertrand A.W.      212
Historical notes, Shannon, Claude E.      93
Historical notes, software patents      289
Historical notes, starting with Zero      6
Historical notes, symbols for equality      16
Historical notes, the fascinating prime numbers      323
Historical notes, Turing, Alan M.      79
Historical notes, Webster and Hilbert on Rigor      3
Hoare triple      17 179
Hoare, Charles Anthony R.      xi 17 19 474
Hodges, Andrew      474
Hofstadter, Douglas R.      126 474
Homeomorphic graphs      438 447
Homogeneous difference equation      363
Homomorphic image      395
Homomorphism      388 395
Homosexuality      79
Hopcroft, John E.      448
Horgan, John      474
Hypothesis      10 125
i      369
Idempotency      49
Idempotency of $\cap$       205
Idempotency of $\cup$       205
Idempotency of $\downarrow$       311
Idempotency of $\uparrow$       311
Idempotency of $\vee$       49
Idempotency of $\wedge$       51
Idempotency of gcd      317
Identifiers, short versus long      34
Identity      44 389
Identity function      281 283
Identity of $\cap$ (U)      205
Identity of $\cdot$ (1)      304
Identity of $\cup$ ( $\emptyset$ )      205
Identity of $\equiv$ (true)      44
Identity of $\vee$ (false)      49
Identity of $\wedge$ (true)      51
Identity of +(0)      304
Identity of a group      397
Identity of gcd (0)      317
Identity of ^ ( $\epsilon$ )      256
Identity relation      269
Identity, left      389
Identity, right      389
if fi (alternative statement)      189
If-then, translation of      33 35
If-then-else (conditional statement)      188
iff (if and only if)      11
Ill-defined set      210
Imaginary part, of a complex number      369
implementation      94 95
Implementation of a specification      94 95
Implication $\Rightarrow$       27 56
Implication $\Rightarrow$ versus equivalence      35
Implication $\Rightarrow$ , dealing with      35
Implicit use of instantiation      161
incident      424
Inclusion/exclusion principle      362
Incompleteness theorem      128
Inconsistent      88 126
Indegree of a vertex      425
Indentation of a subproof      112

INDEX      401
Induction for inductive definitions      232
Induction over $<\mathbf{U}, \prec>$       228
Induction over sequences      252
Induction over the naturals      217 218
Induction, base case      218
Induction, hints on proving by      221
Induction, inductive case      219
Induction, inductive hypothesis      219
Induction, strong      219
Induction, weak      219
Inductive case      219 222
Inductive definition      222
Inductive definition, base case      222
Inductive definition, finding closed-form solution of      366
Inductive definition, inductive case      222
Inductive hypothesis      219
Inductive hypothesis, exposing      221
Inequality $\neq$       27
Inequivalence $\not{\equiv}$       27 45
Inference rule      10 125
Inference rule for natural deduction      114
Inference rule, Leibniz      12 14 22 148
Inference rule, substitution      11
Inference rule, transitivity of equality      12
Inference-rule scheme      11
Infinite algebra      387
Infinite set      461
Infix operator      7
Information theory      93
Injective      282
Instant Insanity      433
Instantiation      161
Instantiation, concealed      161
Instantiation, implicit use of      161
Institute for Advanced Study      129
Integer division $\div$       316
Integer type $\mathbb{Z}$       139
Integral domain      303
Intensionality      197
Interchange of dummies      150
Interchange of quantification      166
Interior region      445
Internal node      233
Interpretation      127
Interpretation, BHK, of constructive mathematics      132
Interpretation, standard, for expressions      127
Intersection $\cap$       203 213 270
Introduction rule      113
Intuitionistic mathematics      131
Invariant of a loop      237
Inverse of a function      45 282
Inverse of a relation      270
Inverse, additive      304
Inverse, left      389
Inverse, right      389
Inverter      91
Irrational number      130 463
Irreflexive relation      273
Isolated vertex      425
Isomorphic graphs      438
Isomorphic image      392
Isomorphism      388 392
isprefix      254 257
isseg      254 258
istail      252
Jacobi, Karl Gustav Jacob      144
Jeng, Jacqueline      xii
jokes      see "Amusements jokes"
Jones, Cliff B.      474
Journal fuer die reine und angewandte Mathematik      144
Kepler, Johannes      2 224
Klein, Felix      111 231
Knight's Tour      441
Knights and knaves      105
Knuth, Donald E.      289 318 474
Koenigsberg      426
Koenigsberg bridges problem      430
Kolmogorov      132
Kosztolnyik, Karen      xii
Kozen, Dexter      xi
Kronecker, Leopold      131 132 464
Kruskal's algorithm      457
Kruskal, Joseph Bernard      457
Kummer, Ernst Eduard      464
Kuratowski, Kasimir      447
Lame, G.      224
Lamport, Leslie      xi 474
Language of a logic      125
Language, strongly typed      141
Language, untyped      141
LCM      317
Leaf      233
League for Programming Freedom      289
Least common multiple lcm      317
Least element      292
Least significant digit      328
Lebesgue, Henri Leon      131
Left      389
Left identity      44 389
Left identity of $\Rightarrow$ (true)      57
Left identity of ^ ( $\epsilon$ )      256
Left inverse      389
Left inverse of a function      283
Left subtree      233
Left zero      50 389
Leibniz inference rule      12 22 148
Leibniz's rule as an axiom      60
Leibniz, Gottfried Wilhelm      7 9 12 16 111 474
Leifer, Jamey      xi
Lemma      53
Length, of a path      427
Length, of a sequence      258
Less <      308
Lewis, Clarence I.      474
Lexicographic ordering      235
LHS (Lefthand side)      20
Liars and truars      106
Linear order      287 307
Linearly ordered set      287
Lisp      25 141 254 262
Logic      125
Logic as the glue that binds      vii
Logic, completeness of      128
Logic, consistent      126
Logic, constructive      130
Logic, E      41 125
Logic, equational      41 125
Logic, equational, advantages of      viii
Logic, extension of      128
Logic, inconsistent      88 126
Logic, model for      128
Logic, ND      113
Logic, PQ-L      126
Logic, soundness of      128
Logical system, formal      125
Loop      236
Loop invariant      237
Loop, bound function of      241
Loop, checklist for proving correctness of      238
Loop, invariant of      237
Loop, proving termination of      240
Loop, repetend of      236
Loop-free digraph      424
Lotus      289
Lower bound      292
Lucas, E.      224
MacMillan, Paul      xi
Magnitude, of a complex root      369
Maintain      20

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