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Modern algebra with applications

Modern algebra with applications (Loan 4 times)

Material type
단행본
Personal Author
Gilbert, William J., 1941-
Title Statement
Modern algebra with applications / William J. Gilbert.
Publication, Distribution, etc
New York :   Wiley,   [c1976].  
Physical Medium
xii, 348 p. : ill. ; 24 cm.
ISBN
0471298913
General Note
"A Wiley-Interscience publication."  
Includes index.  
Bibliography, Etc. Note
Bibliography: p. 319-323.
Subject Added Entry-Topical Term
Algebra, Abstract.
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001 000000110667
005 19980706141717.0
008 760623s1976 nyua b 001 0 eng
010 ▼a 76022756
020 ▼a 0471298913
040 ▼a DLC ▼c DLC
049 1 ▼l 422389789 ▼f 과학 ▼l 422425892 ▼f 과학
050 0 ▼a QA162 ▼b .G53
082 0 0 ▼a 512/.02
090 ▼a 512.8 ▼b G466m
100 1 ▼a Gilbert, William J., ▼d 1941-
245 1 0 ▼a Modern algebra with applications / ▼c William J. Gilbert.
260 ▼a New York : ▼b Wiley, ▼c [c1976].
300 ▼a xii, 348 p. : ▼b ill. ; ▼c 24 cm.
500 ▼a "A Wiley-Interscience publication."
500 ▼a Includes index.
504 ▼a Bibliography: p. 319-323.
650 0 ▼a Algebra, Abstract.

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No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Education Reserves3/ Call Number 512.8 G466m Accession No. 412610307 Availability Available Due Date Make a Reservation Service B M
No. 2 Location Main Library/Education Reserves(Large Size)/ Call Number 512.8 G466m Accession No. 412610306 Availability Available Due Date Make a Reservation Service B M
No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.8 G466m Accession No. 422389789 Availability Available Due Date Make a Reservation Service B M
No. 2 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.8 G466m Accession No. 422425892 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

CONTENTS
1. Introduction = 1
  Classical Algebra = 1
  Modern Algebra = 2
  Binary Operations = 2
  Algebraic Structures = 5
  Extending Number Systems = 6
2. Boolean Algebras = 8
  Algebra of Sets = 8
  Number of Elements in a Set = 13
  Boolean Algebras = 15
  Switching Circuits = 23
  Posets and Lattices = 25
  Normal Forms and Simplification of Circuits = 28
  Transistor Gates = 39
  Representation Theorem = 42
  Exercises = 44
3. Groups = 51
  Groups and Symmetries = 52
  Subgroups = 58
  Cyclic Groups and Dihedral Groups = 60
  Morphisms = 64
  Permutation Groups = 67
  Even and Odd Permutations = 73
  Cayley's Representation Theorem = 77
  Exercises = 78
4. Quotient Groups = 82
  Equivalence Relations = 82
  Cosets and Lagrange's Theorem = 85
  Normal Subgroups and Quotient Groups = 88
  Morphism Theorem = 93
  Direct Products = 98
  Groups of Low Order = 102
  Action of a Group on a Set = 104
  Exercises = 108
5. Symmetry Groups in Three Dimensions = 112
  Translations and the Euclidean Group = 112
  Matrix Groups = 115
  Finite Groups in Two Dimensions = 117
  Proper Rotations of Regular Solids = 119
  Finite Rotation Groups in Three Dimensions = 124
  Crystallographic Groups = 129
  Exercises = 130
6. P o ´ lya-Burnside Method of Enumeration = 133
  Burnside's Theorem = 134
  Necklace Problems = 135
  Coloring Polyhedra = 138
  Counting Switching Circuits = 140
  Exercises = 145
7. Monoids and Machines = 147
  Monoids and Semigroups = 147
  Finite-State Machines = 152
  Quotient Monoids and the Monoid of a Machine = 155
  Exercises = 160
8. Rings and Fields = 166
  Rings = 166
  Integral Domains and Fields = 171
  Subrings and Morphisms of Rings = 173
  New Rings from Old = 176
  Field of Fractions = 182
  Convolution Fractions = 184
  Exercises = 188
9. Polynomial and Euclidean Rings = 193
  Division Algorithm = 193
  Euclidean Algorithm = 198
  Unique Factorization = 202
  Factoring Real and Complex Polynomials = 205
  Factoring Rational and Integral Polynomials = 207
  Factoring Polynomials over Finite Fields = 211
  Linear Congruences and the Chinese Remainder Theorem = 212
  Exercises = 217
10. Quotient Rings = 221
  Ideals and Quotient Rings = 221
  Computations in Quotient Rings = 225
  Morphism Theorem = 227
  Quotient Polynomial Rings that are Fields = 228
  Exercises = 232
11. Field Extensions = 235
  Field Extensions = 235
  Algebraic Numbers = 238
  Galois Fields = 243
  Primitive Elements = 246
  Exercises = 252
12. Latin Squares = 255
  Latin Squares = 255
  Orthogonal Latin Squares = 258
  Finite Geometries = 262
  Magic Squares = 266
  Exercises = 269
13. Geometrical Constructions = 272
  Constructible Numbers = 273
  Duplicating the Cube = 278
  Trisecting an Angle = 278
  Squaring the Circle = 281
  Constructing Regular Polygons = 281
  A Nonconstructible Number of Degree Four = 283
  Exercises = 284
14. Error-Correcting Codes = 286
  The Coding Problem = 287
  Simple Codes = 290
  Polynomial Representation = 293
  Matrix Representation = 299
  Error Correcting and Decoding = 304
  BCH Codes = 309
  Exercises = 314
Bibliography and References = 319
Answers to the Odd-Numbered Exercises = 324
Glossary of Symbols = 337
Index = 341

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