Introduction to Abstract Algebra (inbunden)
Fler böcker inom
Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
560
Utgivningsdatum
2012-04-10
Upplaga
4 ed
Förlag
John Wiley & Sons Inc
Medarbetare
Nicholson
Illustrationer
Illustrations
Dimensioner
257 x 180 x 33 mm
Vikt
1067 g
Antal komponenter
1
Komponenter
68:B&W 7 x 10 in or 254 x 178 mm Case Laminate on White w/Gloss Lam
ISBN
9781118135358

Introduction to Abstract Algebra

av W Keith Nicholson
Inbunden,  Engelska, 2012-04-10
1866
Köp
Spara som favorit
  • Skickas från oss inom 5-8 vardagar.
  • Fri frakt över 249 kr för privatkunder i Sverige.
Finns även som
Visa alla 1 format & utgåvor
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.
Visa hela texten

Passar bra ihop

  1. Introduction to Abstract Algebra
  2. +
  3. The Anxious Generation

De som köpt den här boken har ofta också köpt The Anxious Generation av Jonathan Haidt (inbunden).

Köp båda 2 för 2155 kr

Kundrecensioner

Har du läst boken? Sätt ditt betyg »

Fler böcker av W Keith Nicholson

  • Modern Algebra with Applications

    Modern Algebra with Applications

    William J Gilbert, W Keith Nicholson

    Praise for the first edition "This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generall...

    2306
    Köp
    Skickas inom vardagar.

Recensioner i media

This could also be an excellent adjunct to more theoretically oriented textbooks used in more intensive courses. (Computing Reviews, 5 November 2012)

Övrig information

W. KEITH NICHOLSON, PhD, is Professor in the Department of Mathematics and Statistics at the University of Calgary, Canada. He has published extensively in his areas of research interest, which include clean rings, morphic rings and modules, and quasi-morphic rings. Dr. Nicholson is the coauthor of Modern Algebra with Applications, Second Edition, also published by Wiley.

Innehållsförteckning

PREFACE ix ACKNOWLEDGMENTS xvii NOTATION USED IN THE TEXT xix A SKETCH OF THE HISTORY OF ALGEBRA TO 1929 xxiii 0 Preliminaries 1 0.1 Proofs / 1 0.2 Sets / 5 0.3 Mappings / 9 0.4 Equivalences / 17 1 Integers and Permutations 23 1.1 Induction / 24 1.2 Divisors and Prime Factorization / 32 1.3 Integers Modulo n / 42 1.4 Permutations / 53 1.5 An Application to Cryptography / 67 2 Groups 69 2.1 Binary Operations / 70 2.2 Groups / 76 2.3 Subgroups / 86 2.4 Cyclic Groups and the Order of an Element / 90 2.5 Homomorphisms and Isomorphisms / 99 2.6 Cosets and Lagranges Theorem / 108 2.7 Groups of Motions and Symmetries / 117 2.8 Normal Subgroups / 122 2.9 Factor Groups / 131 2.10 The Isomorphism Theorem / 137 2.11 An Application to Binary Linear Codes / 143 3 Rings 159 3.1 Examples and Basic Properties / 160 3.2 Integral Domains and Fields / 171 3.3 Ideals and Factor Rings / 180 3.4 Homomorphisms / 189 3.5 Ordered Integral Domains / 199 4 Polynomials 202 4.1 Polynomials / 203 4.2 Factorization of Polynomials Over a Field / 214 4.3 Factor Rings of Polynomials Over a Field / 227 4.4 Partial Fractions / 236 4.5 Symmetric Polynomials / 239 4.6 Formal Construction of Polynomials / 248 5 Factorization in Integral Domains 251 5.1 Irreducibles and Unique Factorization / 252 5.2 Principal Ideal Domains / 264 6 Fields 274 6.1 Vector Spaces / 275 6.2 Algebraic Extensions / 283 6.3 Splitting Fields / 291 6.4 Finite Fields / 298 6.5 Geometric Constructions / 304 6.6 The Fundamental Theorem of Algebra / 308 6.7 An Application to Cyclic and BCH Codes / 310 7 Modules over Principal Ideal Domains 324 7.1 Modules / 324 7.2 Modules Over a PID / 335 8 p-Groups and the Sylow Theorems 349 8.1 Products and Factors / 350 8.2 Cauchys Theorem / 357 8.3 Group Actions / 364 8.4 The Sylow Theorems / 371 8.5 Semidirect Products / 379 8.6 An Application to Combinatorics / 382 9 Series of Subgroups 388 9.1 The JordanHolder Theorem / 389 9.2 Solvable Groups / 395 9.3 Nilpotent Groups / 401 10 Galois Theory 412 10.1 Galois Groups and Separability / 413 10.2 The Main Theorem of Galois Theory / 422 10.3 Insolvability of Polynomials / 434 10.4 Cyclotomic Polynomials and Wedderburns Theorem / 442 11 Finiteness Conditions for Rings and Modules 447 11.1 Wedderburns Theorem / 448 11.2 The WedderburnArtin Theorem / 457 Appendices 471 Appendix A Complex Numbers / 471 Appendix B Matrix Algebra / 478 Appendix C Zorns Lemma / 486 Appendix D Proof of the Recursion Theorem / 490 BIBLIOGRAPHY 492 SELECTED ANSWERS 495 INDEX 523

Du kanske gillar