Group theory: Binary operations and examples, Groups and their properties, Subgroups, Cyclic groups and its subgroups, cosets and Lagrange’s theorem, subgroups, normal subgroups, quotient groups, Homomorphism and Isomorphism theorems, group action and Burnside’s lemma. Sylow theorems and their applications.
Rings: basic definitions and properties, ideals, quotient rings, integral domains, Homomorphism, Isomorphism theorems, Polynomial ring, Unique factorization domain, Principal Ideal domain, Euclidean domain, Chinese remaindering over integers and polynomial rings.
Fields : basic definitions and properties. Field extensions, Finite fields, Abstract vector spaces over general fields.
- Algebra, Michael Artin, Pearson Education India; 2 edition (2015).
- Abstract Algebra, John B Fraleigh, Pearson Education India; 7 edition (2013).
- Contemporary Abstract Algebra, Joseph A Gallian, Cengage; 8 edition (2013).
- Abstract Algebra, David S Dummit and Richard M Foote, Wiley; Third edition (2011).
- Topics in Algebra, I. N. Herstein, Wiley; 2 edition (16 November 2006).