Textbook: R. Lidl, H. Niederreiter, Finite Fields, 2nd ed., Cambridge University Press, Cambridge, 1997 (also see Links).

Lecture notes (in Estonian, in progress)

Schedule

1. A primer on group theory.
2. A primer on ring theory, irreducible polynomials.
3. Field extensions, splitting fields of polynomials.
4. Finite fields, their properties, existence and uniqueness. Properties of irreducible polynomials.
5. Trace and norm of an element. Normal Basis Theorem.
6. Effective computation in finite fields, optimal normal bases.
7. Roots in finite fields.
8. Cyclotomic polynomials, Wedderburn's little theorem.
9. Order of a polynomial, primitive polynomials.
10. Properties of irreducible polynomials.
11. Linearized polynomials.
12. Elliptic curves over finite fields.