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Gill A. — Applied Algebra for the Computer Sciences
Gill A. — Applied Algebra for the Computer Sciences

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Название: Applied Algebra for the Computer Sciences

Автор: Gill A.

Аннотация:

The purpose of this book is to cover, in a mathematically precise manner, a variety of concepts, results, techniques, and applications of modern algebra that are of particular use to beginning students in the computer sciences. Abstract topics such as sets, relations, functions, Boolean algebras, groups, rings, and fields are interspersed in this book with computer-oriented applications such as combinational and sequential networks, formal languages, automata, and codes. The object of this interspersal is to provide the beginner with motivation for delving into abstract mathematics, and to lay the groundwork for a number of applied areas which, as a computer-sciences major, the student will pursue in the future.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 445

Добавлена в каталог: 12.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abbott, J.C.      178
Abelian group      271
Absorption laws      14 104 132 149 161 188
Abstract algebra      94
Accepted set      241 244 260
Accepting state      241 260
Ackerman's Function      83
Addition      92
Additive group      271 298
Additive identity      288
Additive inverse      297
Additive order      299
Adjacency matrix      361 396
Adjacent edges      362
Adjacent faces      392
Adjacent vertices      361
Adjoining of root      317
Algebra of propositions      131
Algebra of sets      101
Algebra, abstract      94
Algebra, binary      264
Algebra, boolean      161
Algebra, cardinality of      94
Algebra, extension of      95
Algebra, isomorphism of      107
Algebra, quotient      112
Algebra, switching      189
Algebraic system      94
Algorithm      94 261
Algorithm, Euclidean      85 312
Algorithm, generating      233
Algorithm, recognition      232 233
Alphabet      229
Ambiguous language      235
AND gate      184
Antisymmetry      36
Arbib, M.A.      262
ARC      360
Argument      50 67 134
Argumental      134
Artin, E.      337
Associative laws      13 96 99 131 148 161 188 266 271 288 327
Associative operation      96
Assymmetry      36
atom      165
Automaton      233
Automaton, connected finite-state      247
Automaton, finite-state      240 260
Automaton, linear bounded      260
Automaton, nondeterministic finite-state      243
Automaton, pushdown      260
Automorphism      109
Auxiliary head      260
Auxiliary memory      260
Axiom      94
Base      88
Base field      317
Basis of induction      71 72
Basis of vector space      329
Berge, C.      415
Binary code      339
Binary operation      91
Binary relation      27
Binary scaler      219
Binary symmetric channel      341
Binary tree      376
Bipartite graph      382
Birkhoff, G.      24 48 90 178 286 337
Block      15
Block code      339
Boolean algebra      161
Boolean arithmetic      31
Boolean expression      173
Boolean function      173
Boolean ring      291
Booth, J.L.      227 262
Branch      360
Burnside, W.      286
Busacker, R.G.      415
Cancellation law      99 275 288
Canonical factorization      57
Cantor's paradox      5
Cardinality classes      64
Cardinality of algebra      94
Cardinality of set      2 64
Carmichael, R.D.      286
Cartesian product      26
cell      259
Chain      158
Chain rule      136
Channel      338
Characteristic      323
Characteristic function      68
Check symbol      346
Chevalley, C.      286
Chord      375
Church's thesis      261
Circular relation      42
Classes, cardinality      64
Classes, equivalence      39
Classes, polynomial residue      309
Classes, residue      41
Closure      93
Code vector      342
Code word      339
Code, binary      339
Code, block      339
Code, distance in      341
Code, equivalence of      395
Code, generalized Hamming      359
Code, Hamming      353
Code, linear      342
Code, linear binary      343
Code, optimal      354
Code, perfect      352
Code, quasi-perfect      352
Code, systematic      346
Codomain      50
Coefficient      302
Column equivalence      332
Column rank      332
Column space      332
Column vector      331
Column-reduced echelon canonical form      333
Combinational network      180
Committee chairmanship problem      386
Common divisor      84 311
Common multiple      88
Communication channel      338
Commutative laws      13 96 99 131 148 161 188 267 271 288
Commutative operation      96
Commutative ring      288
Comparator gate      226
Complement laws      13 161 188
Complement of element      6 92 159
Complement of graph      362
Complementary transmission functions      201
Complementary vertex sets      382
Complementation      92
Complemented lattice      159
Complete directed graph      398
Complete graph      362
Complex number      2 319
Component      364
Composite function      54
Composite relation      30
Composition of functions      54
Composition of relations      30
Compound proposition      123
Computable function      261
Concatenation      230
Conclusion      126
Conditional rules      136
Congruence relation      111 115
Conjunction      123
Conjunctive normal form      133
Conjunctive simplification      136
Connected component      364
Connected finite-state automaton      247
Connected graph      364
Consequence      134
Consequent      126
Constant polynomial      302
Context-free grammar      237
Context-free language      237
Context-sensitive grammar      237
Context-sensitive language      237
Contractible graph      389
Contradiction      122
Contrapositive      130
Contrapositive inference      136
Converse of proposition      130
Converse of relation      27
Coordinate      26
Coset      281
Coset leader      350
Coset partition      284
Countable set      65
Counterexample      138
Crossover      387
CYCLE      62 367 371
Cycle rank      375
Cyclic group      274
Cyclic monoid      267
Cyclotomic number      375
Dagger      207
Davis, M.      262
De Morgan's laws      14 75 104 132 159 161 188
Decision graph      406
Decoder      339
Decoding      341
Decoding table      340
Defining condition      2
Definition      94
Degree of polynomial      302
Degree of vertex      362
Delay unit      211
Denumerable set      65
Derivation      237
Derivative      304 314
descendent      29
Destination      338
Detachment      136
Deterministic recognizer      260
Diagonalization argument      67
Diagram, Hasse      43
Diagram, ordering      43
Diagram, transition      215
Diagram, Venn      7
Dickson, L.E.      286
DIMENSION      329
Direct descendent      29
Direct product      118
Directed graph      78 364 395
Directed path      396
Disjoint sets      6
Disjunction      122
Disjunctive addition      136
Disjunctive normal form      133
Disjunctive simplification      136
Distance in code      341
Distance in graph      367
Distributive lattice      156
Distributive laws      13 97 99 131 156 161 188 288 327
Distributive operation      97
Diversity condition      384
Division theorem      83 305
Divisor      84 305
Domain      27 50 94
Double induction      74
Double-error correction      341
Double-error detection      341
Draw configuration      409
Dual      103 132 148
Dual graphs      392
Dual transmission functions      202
Duality      103 132 148
Economy subgraph      378
EDGE      28 360
Edge matrix      372
Edge set      360
Edge, adjacent      362
Edge, matrix      372
Edge, separating      364
Element      1
Element, complement of      6 92 159
Element, exponent of      96
Element, greatest      144
Element, inverse of      97 270
Element, least      43 72 144
Element, minimal      170
Element, order of      276
Element, primitive      325
Element, right inverse of      270
Elementary contraction      389
Elementary operation      332
Empty set      2
Empty string      230
Encoder      338
End-order traversal      378
Endmarker      259
Endomorphism      109
Entry      28 331
Epimorphism      107
Equality of functions      50
Equality of sets      3
Equality of transmission functions      187
Equivalence class      39
Equivalence kernel      57 111
Equivalence of codes      395
Equivalence of combinational networks      180
Equivalence of grammars      237
Equivalence of propositions      128
Equivalence partition      39
Equivalence relation      39
Equivalence rules      136
Error correction      340
Error detection      340
Error pattern      349
Euclidean algorithm      85 312
Euler graph      369
Euler loop      368
Euler path      370
Exclusive OR gate      210
EXCORgate      210
Existential proposition      139
Existential quantifier      139
Expansion theorem      194
Exponent of element      96
Exponent of group      278
Extended next-state function      218 241
Extension field      317
Extension of algebra      95
Extension of function      51
Extension ring      317
Face      391 392
Factor      84 305
Factor ring      293
Factorial      77
Fallacy      138
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