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Gill A. — Applied Algebra for the Computer Sciences
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Название: Applied Algebra for the Computer SciencesАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1976Количество страниц: 445Добавлена в каталог: 12.11.2014Операции: Положить на полку |
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Предметный указатель
Modular lattice 151 MODULO 41 107 112 Monic polynomial 302 Monoid 266 Monomorphism 107 Multigraph 364 Multiple 84 305 Multiplicative group 271 299 Multiplicative identity 288 Multiplicative inverse 297 Multiplicative order 299 Mutually exclusive propositions 123 NAND gate 206 Natural language 232 Natural number 1 Necessity 127 129 Negation laws 131 Negation, arithmetic 92 Negation, logical 122 Nelson, R.J. 263 Nering, E.D. 337 Network, combinational 180 Network, logic 180 Network, maxterm normal combinational 196 Network, minterm normal combinational 196 Network, sequential 211 Network, standard combinational 185 Network, switching 180 Next-state function 215 241 NIM 415 Node 360 Noise 339 Nondeterministic finite-state automaton 243 Nondeterministic recognizer 260 Nondirected graph 395 Nonplanar graph 387 Nonsingular matrix 332 Nonterminal 236 Nontransitivity 36 NOR gate 207 Normal subgroup 281 NOT gate 184 Null laws 14 103 132 161 188 Null matrix 331 Null set 2 Null space 336 Null string 230 Null vector 327 Nullity 336 Number, complex 2 319 Number, cyclotomic 375 Number, Fibonacci 78 Number, natural 1 Number, prime 2 Number, rational 2 65 100 Number, real 2 66 One 144 One-to-one mapping 52 One-way recognizer 260 Onto mapping 52 Open path 364 Operation 91 Operation table 92 Operation, associative 96 Operation, binary 91 Operation, commutative 96 Operation, distributive 97 Operation, elementary 332 Operation, order of 91 Operation, regular 249 Operation, unary 91 Optimal code 354 Optimal path 406 Optimality 407 OR gate 180 184 Order of cycle 62 Order of element 276 Order of group 271 Order of operation 91 Order of set 2 Order(ing), additive 299 Order(ing), linear 43 Order(ing), multiplicative 299 Order(ing), partial 43 Order(ing), total 43 Order(ing), well 43 Ordered tuple 25 Ordering diagram 43 Ore, O. 415 Output alphabet 214 Output function 215 Output symbol 214 pair 26 Paley, H. 24 48 Paradox 3 5 Parity check matrix 343 Parity checker 219 Parsing 234 Partial ordering 43 Partition 15 151 Partition, coset 284 Partition, equivalence 39 Partition, lattice of 151 Partition, left coset 284 Partition, right coset 281 Partition, trivial 40 Path 28 363 Path, directed 396 Path, Euler 370 Path, length of 28 241 364 Path, open 364 Path, optimal 406 Path, proper 364 Path, proper spanning 400 Path, solution 403 Peano postulates 71 Peano's successor function 71 Perfect code 352 Permissible move 403 Permutation 61 78 Permutation group 272 Peterson, W.W. 325 359 Phrase-structure grammar 236 Phrase-structure language 236 Pigeonhole Principle 65 Planar graph 387 Point 360 Polish notation 92 Polygon 391 Polygonal graph 391 Polynomial 157 302 305 Polynomial ideal 308 Polynomial residue class 309 POSET 142 Post's correspondence problem 261 Post-order traversal 378 Postulate 94 Power 96 267 276 Power set 4 Pre-order traversal 377 Premise 134 Prime factorization 76 Prime factorization theorem 87 314 Prime ideal 295 Prime number 2 Primitive element 325 Primitive polynomial 325 Principal diagonal 36 331 Principal ideal ring 292 Problem, committee chairmanship 386 Problem, Koenigsberg bridge 370 Problem, marriage 383 Problem, Post's correspondence 261 Problem, recursively unsolvable 261 Problem, traveling salesman 371 PRODUCT 271 303 Production 236 Projection 26 51 Proof by contradiction 137 Proof by induction 72 Proof, indirect 137 Proper ideal 292 Proper path 364 Proper refinement 15 Proper spanning path 400 Proper subfield 316 Proper subgraph 363 Proper subgroup 279 Proper subring 290 Proper subset 4 Proper subsystem 95 Proposition 121 Proposition, compound 123 Proposition, converse of 130 Proposition, equivalence of 128 Proposition, existential 139 Proposition, generated 133 Proposition, inverse of 130 Proposition, mutually exclusive 123 Proposition, universal 139 Proposition, valid 134 Propositional calculus 131 Propositional laws 131 Pseudograph 364 Pushdown automaton 260 Puzzles 79 414 Quantifier 139 Quasi-perfect code 352 Quasi-universal gate 209 Quotient 84 306 Quotient algebra 112 Quotient ring 293 Quotient set 40 RADIX 88 RANGE 27 Rank of matrix 332 Rank of relation 40 Rational number 2 65 100 Real number 2 66 Realization of transmission function 195 Received encoded message 339 Received message 339 Received vector 342 Received word 340 Recognition algorithm 232 Recognition quasi-algorithm 233 Recognizer 259 Recognizer, deterministic 260 Recognizer, nondeterministic 260 Recognizer, one- and two-way 260 Recursive definition 77 Recursive function 261 Recursive language 232 Recursive procedure 83 Recursively enumerable language 233 Recursively unsolvable problem 261 Reducible polynomial 305 Reductio ad absurdum 137 refinement 15 Reflexive transitive closure 37 Reflexivity 36 Regular grammar 237 Regular graph 363 Regular language 237 Regular operation 249 Regular set 249 Relation 26 Relation matrix 28 Relation on set 28 Relation, binary 27 Relation, circular 42 Relation, composite 30 Relation, composition of 30 Relation, congruence 111 115 116 Relation, equivalence 39 Relation, identity 28 Relation, rank of 40 Relation, universal 28 Relatively prime 87 Relatively prime in pairs 87 Remainder 84 306 Residue class 41 Restriction 51 Right coset 281 Right coset partition 284 Right identity 264 Right inverse of element 270 Right inverse of matrix 337 Right subtree 376 Right zero 265 Right-invertible element 270 Ring 288 Ring of polynomials 304 Ring, boolean 291 Ring, commutative 288 Ring, extension 317 Ring, factor 293 Ring, principal idea 292 Ring, quotient 293 Ring, subring 290 Rogers, H. 263 Root of polynomial 307 Root of tree 78 376 Rooted tree 78 376 Row equivalence 332 Row rank 332 Row space 332 Row vector 331 Row-reduced echelon canonical form 333 Rules 136 Russell's paradox 3 Rutherford, D.E. 178 Saaty, T.L. 415 scalar 327 Self-complementary graph 365 Self-dual graph 392 Self-dual set 105 Self-dual transmission function 295 Semigroup 266 Separating edge 364 Sequential network 211 Serial adder 212 Set 1 Set laws 13 14 Set, accepted 241 244 260 Set, cardinality of 2 64 Set, complementary vertex 382 Set, countable 65 Set, denumerable 65 Set, disjoint 6 Set, edge 360 Set, empty 2 Set, equality of 3 Set, falsity 122 Set, finite 2 64 Set, generated 7 82 Set, index 4 Set, infinite 2 64 Set, maxset 19 20 Set, message 339
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