Modern Algebra

Week – I
1. Groups - Introduction2. Subgroups3. Elementary Properties of Abelian Groups4. Elementary Properties of Non Abelian Groups
Week – II
5. The group of Integer Modulo n6. Complex Roots of Unity7. Cyclic Group8. General Linear Group
Week – III
9. The Group of Symmetries10.Subgroups Generated by a Subset11.Cosets and Index of Subgroups12.Properties of Group Homomorphism and Isomorphism
Week – IV
13.Normal Subgroups14.Quotient Groups15.Class Equation16.Direct Product of a Finite Number of Groups
Week – V
17.Fundamental Theorem of Finite Abelian Groups18.Cayley's Theorem and Problems in Group Theory19.Rings - Introduction20.Class of Rings
Week – VI
21.Rings from Number System22.The Ring of Real Quaternion's and Rings of Continuous Functions23.Ring of Matrices24.Polynomial Rings
Week – VII
25.Subrings and Ideals26.Zero - Divisor and Group of Units27.Properties of Ring Homomorphism28.Operations on Ideals
Week – VIII29.Integral Domains and Fields30.Maximal Ideals and Prime Ideals31.Euclidean Domains and Principal Ideal Domain32.Unique Factorization Domains