Groups: Group structure and examples. Subgroups and cosets. Normal subgroups and Quotient groups. Lagrange, Euler and Fermat’s theorem. Homomorphism, Isomorphism, Automorphism. Group actions. Class equation, Cauchy's theorem, Cayley's theorem. Simplicity of alternating groups. Sylow theorems.
Rings: Rings, Integral domains and fields. Isomorphism, homomorphism and quotient fields. Ideals - prime and maximal. Euclidean domain, division rule. Polynomials, irreducibility and Eisenstein's criterion. Chinese remainder theorem.
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