First Course in Abstract Algebra, A
A clear, structured introduction to abstract algebra that guides readers from basic set theory through groups, rings, fields, and linear algebra with applications to codes and geometry.
About This Book
This text introduces the core structures of abstract algebra, beginning with set theory and progressing through groups, subgroups, and homomorphisms.
Readers explore rings, polynomials, and fields, including unique factorization and finite fields.
Linear algebra concepts such as vector spaces, linear transformations, and determinants are developed in algebraic context.
Advanced topics include canonical forms, Sylow theorems, and applications to coding theory and geometric constructions.
The book concludes with discussions of finite abelian groups, prime ideals, and Grobner bases.
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