Algebra I

This course introduces basic concepts in group theory such as the notion of subgroups, permutation groups, cyclic groups, cosets, Lagrange’s theorem, quotient groups and isomorphism theorems. Major topics: Divisibility, congruences. Permutations. Binary operations. Groups. Examples of groups including finite abelian groups from the study of integers and finite non-abelian groups constructed from permutations. Subgroups. Cyclic groups. Cosets. Theorem of Lagrange. Fermat’s Little Theorem and Euler's Theorem. Direct products of groups. Normal subgroups. Quotient groups. Isomorphism Theorems

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