Abstract Algebra I

An introduction to Group Theory. Includes the study of plane symmetry groups, modular number systems, and permutation groups, as well as general group structure: subgroups, cyclic groups, Lagrange’s Theorem, homomorphism and isomorphism theorems, and the fundamental theorem of finite Abelian groups. Emphasizes writing mathematical proofs. May include additional topics such as Cayley graphs, Burnside’s Theorem, or introductory ring theory; and/or applications such as error-correcting codes or permutation puzzles.

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