Modern Algebra and Number Theory

Code: MA727 | L-T-P-C: 4-0-0-8

MA727 Modern Algebra and Number Theory [4-0-0-8] Prerequisites: Nil

Modern Algebra: Group theory - normal series, solvable groups, nilpotent groups; Ring theory - rings and modules, prime ideals, nil and Jacobson radicals, finitely generated modules, exact sequences, tensor products, primary decomposition, Noetherian rings, Artin rings; Field theory - field extensions, automorphism groups, Galois theory.

Number Theory: congruences, residue systems, Chinese remainder theorem; quadratic residues, reciprocity law; arithmetic functions-Euler function, Mobius function; continued fractions; quadratic forms; Diophantine equations; partitions; Riemann zeta function.

Texts/References:

1. D. S. Dummit and R. M. Foot, Abstract Algebra, John Wiley & Sons, Inc., II Edition, 1999.
2. S. Lang, Algebra, III edition, Springer, 2004.
3. C. Musili, Introduction to Rings and Modules, Narosa Publishing Company, 1997.
4. I. Stewart, Galois Theory, Academic Press, 1989.5. M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison Wesley, 1969.
5. D M. Burton, Elementary Number Theory, WC Brown Publishers, 1994.
6. T. M. Apostol, Introduction to Analytic Number Theory, Narosa Publishing House, 1995 (or Springer, 1976).
7. A. Baker, A Concise Introduction to the Theory of Numbers, Cambridge University Press, 1984.