October Lectures

Week of October 7-11

Oct 7: Comments about Assignment 1. Extension fields.
Oct 9: Splitting fields. Characterization of finite fields. The number of elements of a finite field. Existence and uniqueness of finite fields.

Week of October 14-18

Oct 14: No lecture this day.
Oct 16: Subfield criterion. The multiplicative group of the nonzero elements in a finite field is cyclic. Primitive elements.
[A1 handed in; A2 handed out.]

Week of October 21-25

Oct 21: Gauss' algorithm: correctness and examples.
Oct 23: Comments about Assignment 2. The number of primitive elements. The Moebius function and properties.

Week of October 28 - November 1

Oct 28: Comments about Assignment 2. The number of irreducible polynomials of certain degree. Examples.
Oct 30: Fast algorithms for testing the irreducibility of a polynomial. Examples.
[A2 handed in; A3 handed out.]

To September lectures.
To November lectures.