Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab): 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Algebra I (MAT 240)
Overview: The course continues the work done in MAT 240 on the one hand by extending the study of groups to include group actions and applications, and on the other by studying the algebraic structures of rings and fields.
- Groups – Definition, subgroups, cyclic groups, homomorphisms, normal subgroups, semi-direct products, group actions, Sylow theorems.
- Rings – Definition and examples of rings, ideals, quotient rings, maximal ideals, prime ideals, ring homomorphisms, integral domains, Euclidean domains, PID, UFD.
- Polynomial Rings and Fields – Polynomial rings, irreducible polynomials, definition and examples of fields, characteristic, field extensions, finite fields.
- I. N. Herstein, Topics in Algebra, 2/e, Wiley Eastern, 1994.
- Bhattacharya, Jain and Nagpaul, Basic Abstract Algebra, 2nd edition, CUP, 1995.
- Joseph A. Gallian, Contemporary Abstract Algebra, 4th edition, Narosa, 1999.
- M. Artin, Algebra, 2nd edition. Prentice Hall India, 2011.
- Dummit and Foote, Abstract Algebra, 3rd edition, Wiley.
- Serge Lang, Undergraduate Algebra, 2nd edition. Springer India, 2009.
- Thomas W. Hungerford, Algebra, GTM 73, Springer India, 2004.