Introductory Modern Algebra

Saul Stahl 지음

Wiley 2013년 09월 30일 출간

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Praise for the First Editionquot;Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra.quot;m-CHOICEIntroductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pivotal algebraic ideas.The author provides a clear, precise, and accessible introduction to modern algebra and also helps to develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can inform us about such diverse items as multivariate functions and the 15-puzzle. Featuring new sections on topics such as group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, and the fundamental theorem of algebra, the Second Edition also includes:An in-depth explanation of the principles and practices of modern algebra in terms of the historical development from the Renaissance solution of the cubic equation to Dedekind's idealsHistorical discussions integrated with the development of modern and abstract algebra in addition to many new explicit statements of theorems, definitions, and terminologyA new appendix on logic and proofs, sets, functions, and equivalence relationsOver 1,000 new examples and multi-level exercises at the end of each section and chapter as well as updated chapter summariesIntroductory Modern Algebra: A Historical Approach, Second Edition

Preface ix1 The Early History 11.1 The Breakthrough 12 Complex Numbers 92.1 Rational Functions of Complex Numbers 92.2 Complex Roots 172.3 Solvability by Radicals I 232.4 Ruler and Compass Constructibility 262.5 Orders of Roots of Unity 362.6 The Existence of Complex Numbers* 383 Solutions of Equations 453.1 The Cubic Formula 453.2 Solvability by Radicals II 493.3 Other Types of Solutions* 504 Modular Arithmetic 574.1 Modular Addition, Subtraction, and Multiplication 574.2 The Euclidean Algorithm and Modular Inverses 624.3 Radicals in Modular Arithmetic* 694.4 The Fundamental Theorem of Arithmetic* 705 The Binomial Theorem and Modular Powers 755.1 The Binomial Theorem 755.2 Fermat's Theorem and Modular Exponents 855.3 The Multinomial Theorem* 905.4 The Euler φ-Function* 926 Polynomials Over a Field 996.1 Fields and Their Polynomials 996.2 The Factorization of Polynomials 1076.3 The Euclidean Algorithm for Polynomials 1136.4 Elementary Symmetric Polynomials* 1196.5 Lagrange's Solution of the Quartic Equation* 1257 Galois Fields 1317.1 Galois's Construction of His Fields 1317.2 The Galois Polynomial 1397.3 The Primitive Element Theorem 1447.4 On the Variety of Galois Fields* 1478 Permutations 1558.1 Permuting the Variables of a Function I 1558.2 Permutations 1588.3 Permuting the Variables of a Function II 1668.4 The Parity of a Permutation 1699 Groups 1839.1 Permutation Groups 1839.2 Abstract Groups 1929.3 Isomorphisms of Groups and Orders of Elements 1999.4 Subgroups and Their Orders 2069.5 Cyclic Groups and Subgroups 2159.6 Cayley's Theorem 21810 Quotient Groups an

“This book is an excellent book for an upper-level, undergraduate, one or two semester course, in modern algebra, for a typical University student population that is not especially strong in proofs.”& (MAA Reviews, 13 January 2014)

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저자(글) Saul Stahl

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SAUL STAHL, PhD, is Professor in the Department of Mathematics at the University of Kansas. In addition to authoring six previous books and more than thirty papers in the field of geometry, Dr. Stahl has twice been the recipient of the Carl B. Allendoerfer Award from the Mathematical Association of America.

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