My Library

University LibraryCatalogue

     
Limit search to items available for borrowing or consultation
Result Page: Previous Next
Can't find that book? Try BONUS+
 
Look for full text

Search Discovery

Search CARM Centre Catalogue

Search Trove

Add record to RefWorks

PRINTED BOOKS
Author Durbin, John R.

Title Modern algebra : an introduction / John R. Durbin.

Published Hoboken, N.J. : John Wiley & Sons, [2009]
©2009

Copies

Location Call No. Status
 UniM Bund  512 DURB {Bund89 20200519}    AVAILABLE
Edition 6th ed.
Physical description xiii, 335 pages : illustrations ; 26 cm
Notes Previous ed.: 2005.
Bibliography Includes bibliographical references and index.
Contents I Mappings and Operations 9 -- 1 Mappings 9 -- 2 Composition. Invertible Mappings 15 -- 3 Operations 19 -- 4 Composition as an Operation 25 -- II Introduction to Groups 30 -- 5 Definition and Examples 30 -- 6 Permutations 34 -- 7 Subgroups 41 -- 8 Groups and Symmetry 47 -- III Equivalence. Congruence. Divisibility 52 -- 9 Equivalence Relations 52 -- 10 Congruence. The Division Algorithm 57 -- 11 Integers Modulo n 61 -- 12 Greatest Common Divisors. The Euclidean Algorithm 65 -- 13 Factorization. Euler's Phi-Function 70 -- IV Groups 75 -- 14 Elementary Properties 75 -- 15 Generators. Direct Products 81 -- 16 Cosets 85 -- 17 Lagrange's Theorem. Cyclic Groups 88 -- 18 Isomorphism 93 -- 19 More on Isomorphism 98 -- 20 Cayley's Theorem 102 -- Appendix RSA Algorithm 105 -- V Group Homomorphisms 106 -- 21 Homomorphisms of Groups. Kernels 106 -- 22 Quotient Groups 110 -- 23 Fundamental Homomorphism Theorem 114 -- VI Introduction to Rings 120 -- 24 Definition and Examples 120 -- 25 Integral Domains. Subrings 125 -- 26 Fields 128 -- 27 Isomorphism. Characteristic 131 -- VII Familiar Number Systems 137 -- 28 Ordered Integral Domains 137 -- 29 Integers 140 -- 30 Field of Quotients. The Field of Rational Numbers 142 -- 31 Ordered Fields. The Field of Real Numbers 146 -- 32 Field of Complex Numbers 149 -- 33 Complex Roots of Unity 154 -- VIII Polynomials 160 -- 34 Definition and Elementary Properties 160 -- 35 Division Algorithm 165 -- 36 Factorization of Polynomials 169 -- 37 Unique Factorization Domains 173 -- IX Quotient Rings 178 -- 38 Homomorphisms of Rings. Ideals 178 -- 39 Quotient Rings 182 -- 40 Quotient Rings of F[X] 184 -- 41 Factorization and Ideals 187 -- X Galois Theory: Overview 193 -- 42 Simple Extensions. Degree 194 -- 43 Roots of Polynomials 198 -- 44 Fundamental Theorem: Introduction 203 -- XI Galois Theory 207 -- 45 Algebraic Extensions 207 -- 46 Splitting Fields. Galois Groups 210 -- 47 Separability and Normality 214 -- 48 Fundamental Theorem of Galois Theory 218 -- 49 Solvability by Radicals 219 -- 50 Finite Fields 223 -- XII Geometric Constructions 229 -- 51 Three Famous Problems 229 -- 52 Constructible Numbers 233 -- 53 Impossible Constructions 234 -- XIII Solvable and Alternating Groups 237 -- 54 Isomorphism Theorems and Solvable Groups 237 -- 55 Alternating Groups 240 -- XIV Applications of Permutation Groups 243 -- 56 Groups Acting on Sets 243 -- 57 Burnside's Counting Theorem 247 -- 58 Sylow's Theorem 252 -- XV Symmetry 256 -- 59 Finite Symmetry Groups 256 -- 60 Infinite Two-Dimensional Symmetry Groups 263 -- 61 On Crystallographic Groups 267 -- 62 Euclidean Group 274 -- XVI Lattices and Boolean Algebras 279 -- 63 Partially Ordered Sets 279 -- 64 Lattices 283 -- 65 Boolean Algebras 287 -- 66 Finite Boolean Algebras 291 -- A Sets 296 -- B Proofs 299 -- C Mathematical Induction 304 -- D Linear Algebra 307.
Subject Algebra, Abstract -- Textbooks.
ISBN 9780470384435 (hbk.)
0470384433 (hbk.)