Introductory modern algebra : a historical approach / / Saul Stahl

• Autore: Stahl Saul
• Pubblicazione: Hoboken, New Jersey : , : Wiley, , 2013; ©2013
• Edizione: Second edition.
• Descrizione fisica: 1 online resource (691 p.)
• Disciplina: 512/.02
• Soggetto topico: Algebra, Abstract
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Half Title page; Title page; Copyright page; Preface; Chapter 1: The Early History; 1.1 The Breakthrough; Chapter 2: Complex Numbers; 2.1 Rational Functions of Complex Numbers; 2.2 Complex Roots; 2.3 Solvability by Radicals I; 2.4 Ruler-and-Compass Constructibility of Regular Polygons; 2.5 Orders of Roots of Unity; 2.6 The Existence of Complex Numbers; Chapter 3: Solutions of Equations; 3.1 The Cubic Formula; 3.2 Solvability by Radicals II; 3.3 Other Types of Solutions; Chapter 4: Modular Arithmetic; 4.1 Modular Addition, Subtraction, and Multiplication ; 4.2 The Euclidean Algorithm and Modular Inverses4.3 Radicals in Modular Arithmetic; 4.4 The Fundamental Theorem of Arithmetic; Chapter 5: The Binomial Theorem and Modular Powers; 5.1 The Binomial Theorem; 5.2 Fermat's Theorem and Modular Exponents; 5.3 The Multinomial Theorem; 5.4 The Euler φ-Function; Chapter 6: Polynomials Over A Field; 6.1 Fields and Their Polynomials; 6.2 The Factorization of Polynomials; 6.3 The Euclidean Algorithm for Polynomials; 6.4 Elementary Symmetric Polynomials; 6.5 Lagrange's Solution of the Quartic Equation; Chapter 7: Galois Fields ; 7.1 Galois's Construction of His Fields7.2 The Galois Polynomial; 7.3 The Primitive Element Theorem; 7.4 On the Variety of Galois Fields; Chapter 8: Permutations; 8.1 Permuting the Variables of a Function I; 8.2 Permutations; 8.3 Permuting the Variables of a Function II; 8.4 The Parity of a Permutation; Chapter 9: Groups; 9.1 Permutation Groups; 9.2 Abstract Groups; 9.3 Isomorphisms of Groups and Orders of Elements; 9.4 Subgroups and Their Orders; 9.5 Cyclic Groups and Subgroups; 9.6 Cayley's Theorem; Chapter 10: Quotient Groups and Their Uses; 10.1 Quotient Groups; 10.2 Group Homomorphisms ; 10.3 The Rigorous Construction of Fields10.4 Galois Groups and the Resolvability of Equations; Chapter 11: Topics in Elementary Group Theory; 11.1 The Direct Product of Groups; 11.2 More Classifications; Chapter 12: Number Theory; 12.1 Pythagorean Triples; 12.2 Sums of Two Squares; 12.3 Quadratic Reciprocity; 12.4 The Gaussian Integers; 12.5 Eulerian Integers and Others; 12.6 What Is the Essence of Primality?; Chapter 13: The Arithmetic of Ideals; 13.1 Preliminaries; 13.2 Integers of a Quadratic Field; 13.3 Ideals; 13.4 Cancelation of Ideals; 13.5 Norms of Ideals ; 13.6 Prime Ideals and Unique Factorization13.7 Constructing Prime Ideals; Chapter 14: Abstract Rings; 14.1 Rings; 14.2 Ideals; 14.3 Domains; 14.4 Quotients of Rings; A. Excerpts from Al-Khwarizmi's Solution of the Quadratic Equation1; B. Excerpts from Cardano's Ars Magna1; C. Excerpts from Abel's A Demonstration of the Impossibility of the Algebraic Resolution of General Equations Whose Degree Exceeds Four1; D. Excerpts from Galois's On the Theory of Numbers1; E. Excerpts from Cayley's The Theory of Groups1; F. Mathematical Induction; G. Logic, Predicates, Sets, and Functions ; G.1 Truth Tables
• Sommario/riassunto: Praise for the First Edition ""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.""-CHOICE Introductory 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
• Titolo autorizzato: Introductory modern algebra
• ISBN: 1-118-83752-5; 1-118-55203-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910462709003321
• Lo trovi qui: Univ. Federico II