Kevin Milans : Teaching : Spring 2015 Math773

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: TuWThMW 11:30am-12:30pm, and by appointment
Class Meetings: TuTh 10:00am-11:15am in Armstrong Hall 313

Home | Course Syllabus (PDF) | Homework

Course Schedule

References are as follows:

No. Date Class Summary Comments
1 Jan 13 Graphs with small clique and independence numbers; useful inequalities -
2 Jan 15 Discrete probability spaces; union bound; runs of heads HW1 assigned.
3 Jan 20 Independence of events; random variables; expected value -
4 Jan 22 Linearity of expectation; k-uniform hypergraphs that are not 2-colorable -
5 Jan 27 Convexity; Jensen's inequality -
6 Jan 29 Analysis tricks; sum-free subset example HW1 due; HW2 assigned.
7 Feb 3 Conditional probabilities and expectations; random walks -
8 Feb 5 Alterations: dominating sets; derandomization -
9 Feb 10 Erdos--Ko--Rado; the random graph; randomness as a resource -
10 Feb 12 Markov's inequality; Large girth and large chromatic number HW2 due; HW3 assigned.
11 Feb 17 Bollobas's Thm; List chromatic number; degeneracy -
12 Feb 19 Alon: List chromatic number grows with degeneracy -
13 Feb 24 Second moment; sets with distinct sums -
14 Feb 26 Mutual independence; Local Lemma I HW3 due; HW4 assigned.
15 Mar 3 Local Lemma II (general case and proof) -
16 Mar 5 Linear forests; linear arboricity of graphs with large girth -
17 Mar 10 Chernoff-type bounds I -
18 Mar 12 Chernoff-type bounds II HW4 due.
19 Mar 17 Hadwiger conjecture; refutation of the Hajos conjecture I -
20 Mar 19 Refutation of the Hajos conjecture II -
21 Mar 31 The polynomial method; eventown and oddtown -
22 Apr 2 Matrix criterion for independence; k-distance sets I HW5 due.
23 Apr 7 k-distance sets II; Multilinear reduction; Frankl--Wilson Thm -
24 Apr 9 Combinatorial Nullstellensatz I; Cauchy--Davenport Thm -
25 Apr 14 Combinatorial Nullstellensatz II; Chevalley--Warning Thm -
26 Apr 16 Alon--Tarsi Thm -
27 Apr 21 Alon--Tarsi Application: List chromatic number of (Cn)2 -
28 Apr 23 - HW6 due.

milans@math.wvu.edu