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Gilbert W.J., Nicholson W.K. — Modern Algebra with Applications
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.


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\phi$-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
1 2 3
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