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Gilbert W.J., Nicholson W.K. — Modern Algebra with Applications
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Название: Modern Algebra with ApplicationsАвторы: Gilbert W.J., Nicholson W.K. Аннотация: As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing—with extensive use in computing science, physics, chemistry, and data communications as well as in areas of mathematics such as combinatorics.
Язык: Рубрика: Математика /Алгебра /Учебники /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 352Добавлена в каталог: 12.03.2005Операции: Положить на полку |
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Abel, N.H. 1 47 48 Abelian group 48 Abelian group, finite 92 Absorption laws 15 Abstract algebra 2 Action of a group 96 Adder, full 35 Adder, half 34 Adder, modulo 2 28 Adder, serial 152 Addition modulo m 84 Adjoining an element 220 Affine plane 242 Algebra of sets 7 Algebra, abstract 2 Algebra, boolean 7 14 25 Algebra, classical 1 Algebra, modern 2 Algebraic numbers 221 233 Algebraic structure 4 Alternating group 70 81 85 88 AND gate 36 Angle trisection 251 257 Antisymmetry 23 Archimedean solids 121 Archimedes 258 Associativity 3 14 48 137 155 atom 26 Automorphism 75 151 Automorphism, Frobenius 235 Axiomatic method 295 Axioms 295 Axis of symmetry 51 BCH code 284 benzene 126 Biconditional 18 Bijective 50 63 Binary code 266 Binary operation 2 Binary symmetric channel 266 Binomial theorem 178 Binomial theorem, coefficients 129 Boole, G. 7 Boolean algebra 7 14 25 Boolean algebra, isomorphism 39 Boolean algebra, morphism 39 Boolean algebra, representation theorem 39 Boolean expression 26 Boolean ring 158 176 Bose, R.C. 242 284 Bridge circuit 43 Burnside, W. 125 Burnside’s theorem (lemma) 125 Cancellation 53 Cantor’s theorem 41 Carrol, L. 41 Casting out lines 288 Cauchy sequences 6 Cayley's theorem 71 Cayley, A. 47 71 CD 264 Center of a group 74 Characteristic of a ring 226 Check digit 266 Chinese remainder theorem 198 Circle group 88 98 Circle squaring 251 259 Circuit see Switching circuits Classical algebra 1 Closed switch 19 Closure of an operation 3 48 Code 264 Code rate 267 Code word 266 Code, (n, k)- 266 Code, BCH 284 Code, binary 266 Code, cyclic 292 Code, error-correcting 265 Code, error-detecting 264 Code, linear 276 Code, parity check 267 274 Code, polynomial 270 Code, repeating 268 Coefficient 166 Colorings 128 Common divisor 184 299 Common divisor, multiple 184 303 Commutativity 3 14 48 148 167 Commutator 101 Complement 8 14 complex numbers 4 223 Complex roots 191 Composition of functions 49 Composition of relations 150 Concatenation 140 Conclusion 293 Conditional 17 Cone, n-agonal 116 Congruence 77 79 145 Congruence class 77 145 Congruence, linear 197 conjugate 191 Conjunctive normal form 45 Constant polynomial 167 Constructible number 252 Constructible point 252 Construction of polygons 259 Contradiction 17 Contradiction, proof by 294 CONVERSE 295 Convolution fraction 175 Convolution of functions 173 Convolution of sequences 168 Coset 79 82 Coset leader 280 Countable 221 Counterexample 295 Cross-ratio 101 Crystalline lattice 120 Crystallographic group 120 Cube, duplication of 251 256 Cube, rotation group of 114 CYCLE 64 Cycle, disjoint 66 Cyclic code 291 Cyclic group 56 Cyclic monoid 139 150 Cyclic subgroup 57 Cyclotomic polynomial 195 Cylinder, n-agonal 116 Da Vinci, L. 109 De Morgan's laws 15 Decode 280 Dedekind cuts 6 Degree, of a polynomial 166 Degree, of an extension 219 Delta function 172 Derivative 292 Detecting errors 280 Determinant 110 112 287 Diagram, state 143 Diagram, tree 148 Diagram, Venn 8 32 Difference 9 Difference, symmetric 9 Dihedral group 58 90 Dirac delta function 172 Direct product 2 91 164 Direct sum 91 Disjoint cycles 66 Disjunctive normal form 30 Distributions 175 Distributivity 4 14 156 Division 184 299 Division algorithm 180 181 298 Divisor of zero 159 dodecahedron 112 Dodecahedron, rotation group 114 Domain 172 Domain, integral 159 Domain, left Ore 172 Duality in boolean algebras 15 Duality of regular solids 112 Duerer, A. 246 Duplication of the cube 251 256 DVD 264 Eigenvalue 108 109 111 Eigenvector 108 110 Eisenstein’s Criterion 194 Element of a set 7 Empty set 7 Encode 266 280 Encoding matrix 276 Endomorphism ring 178 Equivalence class 77 Equivalence relation 5 77 Equivalence, logical 295 Equivalent circuits 20 Error polynomial 275 Error-correcting code 264 Error-detecting code 264 Euclidean algorithm 185 300 Euclidean group 104 Euclidean ring 181 Euclid’s lemma 302 Euclid’s theorem 298 Euler 103 Euler, L. 103 236 242 260 Even permutation 68 Exclusive OR 10 29 Extension field 218 Extension field, degree of 219 Extension field, finite 219 Factor 184 see Factor Theorem 182 Faithful action of a group 96 Faithful representation 109 Feedback shift register 231 272 Fermat primes 260 Fermat, P. 103 260 Fermat’s Last Theorem 305 Field 4 160 Field extension 218 Field of fractions 170 Field of quotients 170 Field of rational functions 172 221 Field of, convolution fractions 175 Field, finite 6 45 225 Field, Galois 6 227 Field, primitive element in 229 Field, skew 172 Fifteen puzzle 74 Finite, abelian group 92 Finite, extension 219 Finite, field 6 45 225 Finite, geometry 242 Finite, group 56 Finite, groups in three dimensions 116 Finite, groups in two dimensions 109 Finite-state machine 142 First isomorphism theorem 87 210 Fixed points 125 Flip-flop 46 Formal power series 169 Fractional differentiation and integration 175 Fractions, field of 170 Fractions, left 172 Free monoid 140 Free semigroup 140 Free, group 75 Frobenius automorphism 235 Full adder 35 Function, bijective 50 63 Function, composition of 49 Function, delta 172 Function, generalized 175 Function, Heaviside 175 Function, impulse 172 Function, injective 49 Function, inverse 49 Function, one-to-one 49 Function, onto 50 Function, surjective 49 Function, transition 142 Fundamental Theorem of Arithmetic 187 Fundamental theorem of, algebra 6 190 Galois field 6 227 Galois theory 47 Galois, E. 6 47 225 Gate 36 Gauss' lemma 193 Gauss, C.F. 6 190 260 Gaussian integers 72 183 General linear group 107 Generalized function 175 Generator idempotent 292 Generator matrix 276 Generator of a monoid 139 Generator polynomial 270 Generator, group 56 Geometry 242 Goldbach conjecture 304 Graeco-Latin square see Orthogonal latin squares Greatest common divisor 21 184 299 Greatest lower bound 25 Group 48 Group acting on a set 96 Group factor 83 Group generator 56 Group isomorphism 60 Group matrix 107 Group morphism 60 Group of a polynomial 80 Group of a rectangle 53 55 Group of a square 89 Group of low order 94 Group of prime order 80 Group order 56 Group permutation 50 Group quaternion 73 95 107 Group quotient 83 Group translation 49 104 Group, abelian 48 Group, alternating 70 82 86 88 Group, automorphism 75 Group, center 74 Group, circle 88 98 Group, commutative 48 Group, crystallographic 120 Group, cyclic 56 Group, dihedral 58 90 Group, euclidean 104 Group, finite 56 Group, free 75 Group, general linear 107 Group, icosahedral 115 Group, infinite 56 Group, Klein 52 90 Group, metabelian 102
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