First Course in Abstract Algebra With Applications
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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 nbsp 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 39 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 nbsp For all readers interested in abstract algebra
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