Introductory Modern Algebra A Historical Approach.

Detalles Bibliográficos
Autor principal: Stahl, Saul
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2013.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • 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
  • 6.5 Lagrange's Solution of the Quartic Equation
  • Chapter 7: Galois Fields
  • 7.1 Galois's Construction of His Fields
  • 7.2 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 Fields
  • 10.4 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 Factorization
  • 13.7 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

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