Math 336 - Schedule

Math 336, Schedule of lectures

Week 1 (1/22-1/26)

3ABC: Greatest common divisors
4A: Unique factorization (fundamental theorem of arithmetic)

Week 2 (1/29-2/2)

4B: Consequences of the FTA
5ABDE: Congruences

Week 3 (2/5-2/9)

6ABCDE: The integers mod m
13E: Error-correcting codes (application of arithmetic mod 2)

Week 4 (2/12-2/16)

8ABC: Rings

Prelim 1, February 22

Week 5 (2/19-2/23)

9ABCE: Multiplicative orders; theorems of Fermat and Euler

Week 6 (2/26-3/2)

10B: RSA codes
11A: Subgroups

Week 7 (3/5-3/9)

11BDE: Cosets, homomorphisms, permutation groups, Cayley's theorem

Week 8 (3/12-3/16)

12AB: Chinese remainder theorem
Applications (distributed arithmetic, spare keys for RSA)

Spring break; Prelim 2, March 29

Week 9 (3/26-3/30)

12C: Square roots of 1 mod m
14: Polynomials
15AC: Greatest common divisors for polynomials

Week 10 (4/2-4/6)

15D: Unique factorization for polynomials
20A: Congruences for polynomials
20B: Chinese remainder theorem for polynomials; Lagrange interpolation
21A: Application of Lagrange interpolation to factorization

Week 11 (4/9-4/13)

23A: Primitive roots
28AB: Congruence classes of polynomials

Week 12 (4/16-4/20)

28C: Orders of elements mod m(x)
28D: Splitting fields
Hill, Chapters 1 and 2: Hamming distance and error correction

Week 13 (4/23-4/27)

Hill, Chapters 5, 6, and 7: Linear codes

Week 14 (4/30-5/4)

Hill, Chapters 11 and 12: BCH codes, cyclic codes

Back to course home page.

Last modified: Thu May 10 09:03:11 EDT 2001