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Beskrivning
This text introduces students to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.
Chapter 1: Number Theory Induction Binomial Coefficients Greatest Common Divisors The Fundamental Theorem of Arithmetic Congruences Dates and Days Chapter 2: Groups I Some Set Theory Permutations Groups Subgroups and Lagrange's Theorem Homomorphisms Quotient Groups Group Actions Counting with Groups Chapter 3: Commutative Rings I First Properties Fields Polynomials Homomorphisms Greatest Common Divisors Unique Factorization Irreducibility Quotient Rings and Finite Fields Officers, Magic, Fertilizer, and Horizons Chapter 4: Linear Algebra Vector Spaces Euclidean Constructions Linear Transformations Determinants Codes Canonical Forms Chapter 5: Fields Classical Formulas Insolvability of the General Quintic Epilog Chapter 6: Groups II Finite Abelian Groups The Sylow Theorems Ornamental Symmetry Chapter 7: Commutative Rings III Prime Ideals and Maximal Ideals Unique Factorization Noetherian Rings Varieties Grobner Bases Hints for Selected Exercises Bibliography Index
