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Author:   Martyn R. Dixon (University of Alabama, Tuscaloosa) ,  Leonid A. Kurdachenko (University of Dnepropetrovsk, Ukraine) ,  Igor Ya Subbotin (National University)
Publisher:   John Wiley & Sons Inc
Imprint:   John Wiley & Sons Inc
Dimensions:   Width: 16.30cm , Height: 3.60cm , Length: 24.40cm
Weight:   0.930kg
ISBN:  

9780470496367

ISBN 10:   0470496363
Pages:   538
Publication Date:   03 September 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

Preface ix Chapter 1 Sets 1 1.1 Operations on Sets 1 Exercise Set 1.1 6 1.2 Set Mappings 8 Exercise Set 1.2 19 1.3 Products of Mappings 20 Exercise Set 1.3 26 1.4 Some Properties of Integers 28 Exercise Set 1.4 39 Chapter 2 Matrices and Determinants 41 2.1 Operations on Matrices 41 Exercise Set 2.1 52 2.2 Permutations of Finite Sets 54 Exercise Set 2.2 64 2.3 Determinants of Matrices 66 Exercise Set 2.3 77 2.4 Computing Determinants 79 Exercise Set 2.4 91 2.5 Properties of the Product of Matrices 93 Exercise Set 2.5 103 Chapter 3 Fields 105 3.1 Binary Algebraic Operations 105 Exercise Set 3.1 118 3.2 Basic Properties of Fields 119 Exercise Set 3.2 129 3.3 The Field of Complex Numbers 130 Exercise Set 3.3 144 Chapter 4 Vector Spaces 145 4.1 Vector Spaces 146 Exercise Set 4.1 158 4.2 Dimension 159 Exercise Set 4.2 172 4.3 The Rank of a Matrix 174 Exercise Set 4.3 181 4.4 Quotient Spaces 182 Exercise Set 4.4 186 Chapter 5 Linear Mappings 187 5.1 Linear Mappings 187 Exercise Set 5.1 199 5.2 Matrices of Linear Mappings 200 Exercise Set 5.2 207 5.3 Systems of Linear Equations 209 Exercise Set 5.3 215 5.4 Eigenvectors and Eigenvalues 217 Exercise Set 5.4 223 Chapter 6 Bilinear Forms 226 6.1 Bilinear Forms 226 Exercise Set 6.1 234 6.2 Classical Forms 235 Exercise Set 6.2 247 6.3 Symmetric Forms over R 250 Exercise Set 6.3 257 6.4 Euclidean Spaces 259 Exercise Set 6.4 269 Chapter 7 Rings 272 7.1 Rings, Subrings, and Examples 272 Exercise Set 7.1 287 7.2 Equivalence Relations 288 Exercise Set 7.2 295 7.3 Ideals and Quotient Rings 297 Exercise Set 7.3 303 7.4 Homomorphisms of Rings 303 Exercise Set 7.4 313 7.5 Rings of Polynomials and Formal Power Series 315 Exercise Set 7.5 327 7.6 Rings of Multivariable Polynomials 328 Exercise Set 7.6 336 Chapter 8 Groups 338 8.1 Groups and Subgroups 338 Exercise Set 8.1 348 8.2 Examples of Groups and Subgroups 349 Exercise Set 8.2 358 8.3 Cosets 359 Exercise Set 8.3 364 8.4 Normal Subgroups and Factor Groups 365 Exercise Set 8.4 374 8.5 Homomorphisms of Groups 375 Exercise Set 8.5 382 Chapter 9 Arithmetic Properties of Rings 384 9.1 Extending Arithmetic to Commutative Rings 384 Exercise Set 9.1 399 9.2 Euclidean Rings 400 Exercise Set 9.2 404 9.3 Irreducible Polynomials 406 Exercise Set 9.3 415 9.4 Arithmetic Functions 416 Exercise Set 9.4 429 9.5 Congruences 430 Exercise Set 9.5 446 Chapter 10 The Real Number System 448 10.1 The Natural Numbers 448 10.2 The Integers 458 10.3 The Rationals 468 10.4 The Real Numbers 477 Answers to Selected Exercises 489 Index 513

Reviews

However, instructors contemplating such a unified approach should give this book serious consideration. Recommended. Upper-division undergraduates through researchers/faulty. (Choice, 1 April 2011)<p>

The book is well-written and covers, with plenty of exercises, the material needed in the three aforementioned courses, albeit in a new order. (Zentralblatt MATH, 1 December 2012) However, instructors contemplating such a unified approach should give this book serious consideration. Recommended. Upper-division undergraduates through researchers/faulty. (Choice , 1 April 2011)

However, instructors contemplating such a unified approach should give this book serious consideration. Recommended. Upper-division undergraduates through researchers/faulty. (Choice , 1 April 2011)

Author Information

MARTYN R. DIXON, PHD, is Professor in the Department of Mathematics at the University of Alabama, Tuscaloosa. He has authored more than sixty published journal articles on infinite group theory, formation theory and Fitting classes, wreath products, and automorphism groups. LEONID A. KURDACHENKO, PHD, is Distinguished Professor and Chair of the Department of Algebra at the Dnepropetrovsk National University (Ukraine). Dr. Kurdachenko has authored more than 150 journal articles on the topics of infinite-dimensional linear groups, infinite groups, and module theory. IGOR YA. SUBBOTIN, PHD, is Professor in the Department of Mathematics and Natural Sciences at National University (California). Dr. Subbotin is the author of more than 100 published journal articles on group theory, cybernetics, and mathematics education.

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