March Lectures

Week of March 3-7

Mar 3: Transpositions. Conjugates.
Mar 5: Cosets. Left coset partition.
Tutorial: Test #3.

Week of March 10-14

Mar 10: Lagrange's theorem. Primality testing and public key cryptography.
Mar 12: Normal subgroups.
Tutorial: Extended Euclidean algorithm, greatest comon divisor of polynomials.

Week of March 17-21

Mar 17: Quotient groups. Homomorphism theorem.
Mar 19: Example of homomorphism theorem. Rings.
Tutorial: Test #4.

Week of March 24-28

Mar 24: Subrings. Inverse elements. Fields. Examples of fields. Ideals.
Mar 26: Quotient rings. Ring homomorphisms.
Tutorial: Polynomial factorization, rings and fields.

Week of March 31-April 4

Mar 31: Maximal ideals and fields. Constructing a field of 256 elements. Efficient multiplication and inversion.
Apr 2: Advanced Encryption Standard. Revision of course.
Tutorial: no tutorial this day

To February lectures.