A First Course in Abstract Algebra

  • Pearson Education (US)
  • 2005
  • Paperback
  • 640
  • Sproget er ikke defineret
  • 3
  • 9780131862678

This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each. Number Theory: Induction; Binomial Coefficients; Greatest Common Divisors; The Fundamental Theorem of Arithmetic Congruences; Dates and Days. Groups I: Some Set Theory; Permutations; Groups; Subgroups and Lagrange's Theorem; Homomorphisms; Quotient Groups; Group Actions; Counting with Groups. Commutative Rings I: First Properties; Fields; Polynomials; Homomorphisms; Greatest Common Divisors; Unique Factorization; Irreducibility; Quotient Rings and Finite Fields; Officers, Magic, Fertilizer, and Horizons. Linear Algebra: Vector Spaces; Euclidean Constructions; Linear Transformations; Determinants; Codes; Canonical Forms. Fields: Classical Formulas; Insolvability of the General Quintic; Epilog. Groups II: Finite Abelian Groups; The Sylow Theorems; Ornamental Symmetry. Commutative Rings III: Prime Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases. For all readers interested in abstract algebra.

871,00 kr.