Math 3360, Spring 2009
Schedule of lectures
Note: "CS" below refers to the coding
supplement by Sarah Spence. For example, CS2 is Chapter 2 of the coding
supplement. And "RSA" refers to the RSA
paper.
Week 1 (1/19-1/23)
2ABD: Induction, division theorem
3ABC: Greatest common divisors
4A: Unique factorization (fundamental theorem of arithmetic)
Week 2 (1/26-/30)
4B,C(I): Consequences of the FTA
5ABDE: Congruences
Week 3 (2/2-2/6)
6ABCDE: The integers mod m
8AB: Fields and rings
Week 4 (2/9-2/13)
8C: Ring homomorphisms
9ABCE: Multiplicative orders; theorems of Fermat and Euler
Week 5 (2/16-2/20)
RSA: RSA codes
11A: Subgroups
Prelim 1, Tuesday, February 17, 7:30-9:00 (covers through week 4)
Week 6 (2/23-2/27)
11B: Cosets, Lagrange's theorem
11D: Group homomorphisms
11E: Permutation groups, symmetry groups, Cayley's theorem
Week 7 (3/2-3/6)
12AB: Chinese remainder theorem
CS1: Introduction to coding theory
CS2.1-2.2:Linear codes
Week 8 (3/9-3/13)
CS2.3-2.6: Generator matrices, parity check matrices
CS2.7: Hamming codes
Spring break
Week 9 (3/23-3/27)
14: The ring of polynomials
15AC: Greatest common divisors for polynomials
15D: Unique factorization for polynomials
Week 10 (3/30-4/3)
20A: Congruences for polynomials
20B, 21A: Chinese remainder theorem for polynomials; Lagrange interpolation
Week 11 (4/6-4/10)
15B, 23A: Primitive roots
28AB: Congruence classes of polynomials
Prelim 2, Thursday, April 9, 7:30-9:00 (covers through week 10)
Week 12 (4/13-4/17)
28C: Orders of elements mod m(x)
28D: Splitting fields
CS3.1: Introduction to cyclic codes
Week 13 (4/20-4/24)
CS3.2:Ideals in rings
CS3.3-3.4:More on cyclic codes
Week 14 (4/27-5/1)
CS4: Minimal polynomials; BCH and Reed-Solomon codes
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Last modified: Feb 6, 2009