## MAT 2001: Algebra 1

Syllabus

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.

References:

1. M. Artin: Algebra, Second Edition, Pearson Prentice-Hall of India, New Delhi, 2011.

2. D. S. Dummit and Richard M. Foote: Abstract Algebra, Third Edition, Wiley, 2005.

3. J. A. Gallian: Contemporary Abstract Algebra, Eighth Edition, BROOKS/COLE Cenage Learning, 2013

4. Yvette Kosmann-Schwarzbach: Groups and Symmetries: From Finite Groups to Lie Groups by Springer, 2010.

5. I. S. Luthar and I. B. S. Passi.  Algebra Vols I & 2, Narosa, 1996, 1999.

#### Study at Ashoka

[current_url]