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Gilbert W.J., Nicholson W.K. — Modern Algebra with Applications
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Название: Modern Algebra with Applications
Авторы: 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.
Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject—effectively holding your interest and creating a more seamless method of instruction.
Incorporating the applications of modern algebra throughout its authoritative treatment of the subject, this book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back of the text.
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Рубрика: Математика /Алгебра /Учебники /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2004
Количество страниц: 352
Добавлена в каталог: 12.03.2005
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Предметный указатель
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 -function 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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