Outline

1.

Groups

(a)

Subgroups, Cosets, Lagrange's Theorem.

(b)

Permutations, Group Actions, Burnside's Lemma.

(c)

Normal subgroups, Isomorphism Theorems.

(d)

Direct Products, Abelian groups, Fundamental Theorem of Finite Abelian Groups

2.

Rings

(a)

Subrings, Domains, Fields.

(b)

Ideals, factor rings, Isomorphism Theorems.

(c)

Prime and Maximal ideals.

(d)

Polynomial Rings, factorization, UFDs and EDs,

3.

Fields

(a)

Vector space.

(b)

Extension Fields, splitting fields, zeros of polynomials.

(c)

Algebraic Extensions, Structure and Classification of Finite fields.

References:

J.A. Gallian, Contemporary Abstract Algebra, Heath and Company, 1990.

I.N. Herstein, Abstract Algebra, Macmillan, 1986.

J.R. Durbin, Modern Algebra An Introduction, Wiley, 1992.