Speaker and affiliation

Number of Lectures

Detailed Syllabus

Manoj Kummini

CMI

6

Vector spaces, bases and dimension, linear trans- formations and matrices, linear operators, eigen- values, characterstic polynomials.

Clare D’Cruz

CMI

3

Groups: subgroups, cyclic groups, homomor- phisms, cosets, modular arithmetic.

Purusottam Rath

CMI

3

Groups : product groups, normal subgroups, quo- tient groups, symmetric group, symmetries of plane figures.

Krishna Hanumanthu

CMI

6

Ring theory: polynomial rings, prime and maxi- mal ideals, homomorphisms, quotient rings, eu- clidean domains, UFDs.

Sukhendu Mehrotra

CMI

6

Fields: examples of fields, algebraic elements, de- gree of field extensions, ruler and compass con- structions, algebrically closed fields and algebraic closure, adjoining roots and splitting fields, finite fields.