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portada A First Course in Abstract Algebra: With Applications
Type
Physical Book
Publisher
Author
Topic
álgebra
Collection
matemáticas
Year
2005
Language
English
Pages
581
Format
Paperback
ISBN
0131862677
ISBN13
9780131862678
Edition No.
3
Categories

A First Course in Abstract Algebra: With Applications

Joseph J. Rotman (Author) · Pearson · Paperback

A First Course in Abstract Algebra: With Applications - Joseph J. Rotman

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Synopsis "A First Course in Abstract Algebra: With Applications "

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.

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