Group Theory: Review of basic Group Theory, Direct sum and direct product of groups, Group Actions, Cayley's Theorem, The Class Equation, Sylow's Theorems (15 lectures) Ring Theory: Review of basic Ring Theory, Properties of Ideals, Prime and Maximal Ideals, Two-sided ideals and Quotient Rings, Chinese Reminder Theorem, Euclidean Domain, Euclidean Algorithm, Principal Ideal Domain, Euclidean Domain is a Principal Ideal Domain, UFD, PID implies UFD. (20 lectures) Field Theory: Field extensions, basic properties of degree of field extensions. (5 lectures)
Reference Books
University Algebra (N S Gopalakrishnan)
Abstract Algebra (Gallian)
Abstract Algebra (Dummit & Foote)
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