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

Principles, use lemmas      53
Private-key cryptography      284
Product $\circ$       271
Product $\circ$ of functions      281
Product $\Pi$       145 310
Program specification      179
Programs, uncountable number of      470
Projection $\pi$       297
PROLOG      141
proof      15
Proof by case analysis      73
Proof by contradiction      77 117
Proof by contrapositive      79
Proof by mutual implication      76
Proof format      14
Proof format for case analysis      120
Proof format for contradiction      120
Proof format for implication      69
Proof format for Modus Ponens      119 120
Proof format for mutual implication      120
Proof format for natural deduction      118
Proof of a theorem in a logic      125
Proof, Hilbert style      109
Proof, opportunity driven      166
Proof, subproof      110 116
Proper subbag $\subset$       212
Proper subsequence $\subset$       257
Proper subset $\subset$       201
Proper superset $\supset$       201
Proposition      32
Proposition, translation to expressions      33
Propositional calculus      41
Propositional variable      33 41
Ptolemy I      319
Public-key cryptography      284
Quadratic formula      364
Quantification      143
Quantification for $\cdot$       310
Quantification for $\downarrow$       313
Quantification for $\uparrow$       313
Quantification for +      310
Quantification, existential $\exists$       145 163
Quantification, existential $\exists$ , making use of      167
Quantification, general form of      143
Quantification, interchange of      166
Quantification, textual substitution in      147
Quantification, universal $\forall$       145 158
Quantified variable      142
Quasi order      287
Queens College      26
Query      296
Quicksort      19
Quotient      316
Rabbit      50 71
Ran      270
Range of a quantification      143
Range of a relation      270
Range split      149
Range, manipulation of      152
Range, need for finite range      149
Rational function      377
Rational numbers $\mathbb{Q}$       139
Real numbers $\mathbb{R}$       139
Real part, of a complex number      369
Reasoning about assignment      181
Reasoning, styles of      120
Recorde, Robert      16 475
Recursion      222
Referencing a segment      260
Referencing sequence elements      259
Reflexive closure      274
Reflexive reduction      287
Reflexive relation      273
Reflexivity of $\equiv$       44
Reflexivity of $\leq$       308
Reflexivity of $\Rightarrow$       57
Reflexivity of $\subseteq$       207
Reflexivity of =      12
Region      445
Reid, Constance      111 475
Reinfelds, Juris      xi
Relation      267
Relation, antisymmetric      273
Relation, asymmetric      273
Relation, binary      267
Relation, classes      273
Relation, determinate      280
Relation, domain of      270
Relation, equivalence      276
Relation, identity      269
Relation, inverse of      270
Relation, irreflexive      273
Relation, operations on      270
Relation, powers of      272
Relation, product of      271
Relation, range of      270
Relation, reflexive      273
Relation, reflexive closure of      274
Relation, symmetric      273
Relation, symmetric closure of      274
Relation, transitive      273
Relation, transitive closure of      274
Relational database      295
Relational scheme      295
Relations, ancestor      275
Relations, at least $\geq$       308
Relations, at most $\leq$       308
Relations, child      269
Relations, empty      269
Relations, grandparent      272
Relations, greater >      308
Relations, less <      308
Relations, parent      269
Relations, pred      269
Relations, sister      269
Relations, succ      269
Relatively prime $\bot$       318
Remainder      316
Repetend      236
replacement      52
Reverse of a sequence      263
Reverse Polish notation      5
RHS (Righthand side)      20
Right identity      44 389
Right identity of ^( $\epsilon$ )      256
Right inverse      389
Right inverse of a function      283
Right subtree      233
Right zero      50 389
Right zero of $\Rightarrow$ (true)      57
Rigid variable      181
Rigor      3
Ring-of-lights problem      246
Roman numerals      328
Room with a view      19
Root of a polynomial      364
Root of a tree      233
Royal flush      353
Rucklidge, William      xi
Rule of difference      337
Rule of product      337
Rule of sum      337
Runge, Carl D.T.      111
Russell, Bertrand A.W.      26 210—212 475
Russell, John      212
Samuelson, Pamela      475
Satisfiable      31 128
Satisfied      31
Scheme      25 141 254
Schneider, Fred B.      xii 17 27 268 285 388

Scholten, Carel S.      xi 473
Schroeder — Bernstein theorem      465
Scope      145
Scope in proofs      113
Scope of a dummy      145
Second-order predicate calculus      245
Segment      257
Segment, reference to      260
Selection $\sigma$       297
Self-loop      424
Semantics      7
Semigroup      396
Sequence, empty, $\epsilon$       251
Sequence, length of      258
Sequence, membership in      254
Sequence, permutation of      264 338
Sequence, prefix of      257
Sequence, referencing elements of      259
Sequence, reverse of      263
Sequence, segment of      257
Sequence, singleton sequence      252
Sequent      114
Set comprehension      195
Set comprehension, traditional      198
Set enumeration      195
Set equality      197
Set membership $\in$       141 197
Set, average of      355
Set, cardinality of      461
Set, characteristic predicate of      200
Set, combinations of      340
Set, countable      466
Set, denumerable      466
Set, finite      461
Set, heterogeneous      198
Set, ill-defined      210
Set, infinite      461
Set, maximum of      355
Set, partially ordered      285
Set, partition of      209
Set, permutation of      338
Set, size of      461
Set, uncountable      466
Set, well founded      309
Shakespeare, William      86
Shannon      61
Shannon, Claude E.      61 91 93 474 475
Sherlock Holmes      348
Short variable names      34
Shortest path      449
Shunting      57
Shute, Graham      474
Sibling      234
Side effect      279
Sieve of Eratosthenes      323
Signature      388
Simple path      427
Simultaneous substitution      8
Singleton      197 252
Sir Gowers, Ernest      ix
sister relation      269
Size #      201 212 461
skip      188
Slide rule      393 394
Smullyan, Raymond M.      83 475
Software patents      289
Sound logic      128
Spanning tree      453
Specification      94
Specification of a combinational circuit      94
Specification of a program      179
Specification, implementation of      94 95
Spreadsheet      288
St. Petersburgh Academy      431
Stallman, Richard M.      475
Standard interpretation for expressions      127
Start vertex      424
Starting with zero      6
State      8
Straight      353
Straight flush      353
Strengthening      58 160 165
Strict partial order      287
Strong induction      219
Strong induction, equivalence with weak induction      244
Stronger predicate      58
Strongly typed      141
Styles of reasoning      120
Subalgebra      391
Subbag $\subseteq$       212
Subbag $\subseteq$ , proper $\subset$       212
Subexpression, type of      140
Subgraph      437
Subgroup      400
Submonoid      396
Subproof      110 116
Subproof, indentation of      112
Subsemigroup      396
Subsequence $\subseteq$       254 257
Subsequence $\subseteq$ , proper $\subset$       257
Subset $\subseteq$       201
Subset $\subseteq$ , proper $\subset$       201
Substitution      11 61
Substitution, simultaneous      8
Substitution, textual      8 141
Subtraction —      306
succ relation      269
Summation $\sum$       142 144 145 310
Superman puzzle      37 88
Superset $\supseteq$       201
Superset $\supseteq$ , proper $\supset$       201
Surjective      282
Symmetric closure      274
Symmetric group      397
Symmetric operator      12
Symmetric relation      273
Symmetries of the square      407
Symmetry of $\cap$       205
Symmetry of $\cdot$       304
Symmetry of $\cup$       205
Symmetry of $\downarrow$       311
Symmetry of $\equiv$       43
Symmetry of $\not{\equiv}$       46
Symmetry of $\uparrow$       311
Symmetry of $\vee$       49
Symmetry of $\wedge$       51
Symmetry of +      304
Symmetry of a geometric figure      407
Symmetry of gcd      317
Syntactic sugar      29
Syntax      7
Szabo, M.E.      475
Tail of a sequence      254
Tally systems      328
Tardy bus problem      106
Tarjan, Robert      448
Tautology      31
Teacher's manual      ix
Term      157
Termination of a loop      240
Ternary number system      329
Ternary operator      387
Texas at Austin, University of, xii      183
Textual substitution      8 141
Textual substitution and hidden variables      10
Textual substitution in a quantification      147
Textual substitution, simultaneous      8
Theorem      42 45
Theorem as a formal friend      42
Theorem of a logic      125

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