Kevin Milans : Teaching : Spring 2013 Math571

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MWF 2:30pm-3:30pm, and by appointment
Class Meetings: MWF 1:30pm-2:20pm in Armstrong Hall 415
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Section(s) Quiz Quiz Soln Comments
1 Jan 14 Introduction; Elementary Principles 1.1 - - HW1 assigned.
2 Jan 16 Words; Binomial Coefficients and Theorem 1.1 - - -
3 Jan 18 Stars and Bars Model; Lattice Path Model 1.1,1.2 - - -
4 Jan 23 Elementary Identities; Extended Binomial Theorem 1.2 - - -
5 Jan 25 Sums of Polynomials; Delannoy Numbers 1.2 - - -
6 Jan 28 Delannoy Numbers and Taxi Balls 1.2 - - HW1 due; HW2 assigned.
7 Jan 30 Aztec Diamond; Cayley's Formula 1.3 - - -
8 Feb 1 Cayley's Formula; Multinomial Coefficients 1.3 - - -
9 Feb 4 Ballot Problem; Catalan Numbers 1.3 - - -
10 Feb 6 Catalan Numbers 1.3 - - -
11 Feb 8 Recurrence Relations: Fibonacci Numbers, Derangements 2.1 - - -
12 Feb 11 Catalan Recurrence; Multiparameter Recurrences; Systems of Recurrences 2.1 - - HW2 due; HW3 assigned.
13 Feb 13 Recurrences on Graphs; Characteristic Equation Method 2.1,2.2 - - -
14 Feb 15 Recurrences: Generating Function Method I 2.2 - - -
15 Feb 18 Recurrences: Generating Function Method II 2.2 - - -
16 Feb 20 Recurrences: Substitution and Asymptotics 2.3 - - -
17 Feb 22 Recurrences: Sterling's Formula 2.3 - - -
18 Feb 25 Ordinary Generating Functions 3.1 - - HW3 due.
19 Feb 27 OGFs: Permutation Statistics 3.1 - - -
20 Mar 1 Midterm Exam: Ch. 1 and 2 - - - -
21 Mar 4 OGFs: Permutations by number of cycles 3.1 - - HW4 assigned.
22 Mar 6 OGFs; Eulerian Numbers: Permutations by number of runs 3.1 - - -
23 Mar 8 Inclusion/Exclusion: Basics 4.1 - - -
24 Mar 11 Combinatorial Proofs via Inclusion/Exclusion 4.1 - - -
25 Mar 13 Inclusion/Exclusion: Eulerian numbers and the chromatic polynomial 4.1 - - -
26 Mar 15 Pigeonhole Principle Applications I 10.1 - - -
27 Mar 15 Pigeonhole Principle Applications II (Makeup Class) 10.1 - - -
- Mar 18 No Class; Makeup on Fri, Mar 15 - - - -
28 Mar 20 Pigeonhole Principle Applications III 10.1 - - -
29 Mar 22 Erdős--Szekeres Theorem 10.1 - - HW4 due.
30 Apr 1 Ramsey Theory: Introduction 10.2 - - HW5 assigned.
31 Apr 3 Ramsey Theory for Graphs 10.2 - - -
32 Apr 5 Ramsey's Theorem I 10.2 - - -
33 Apr 8 Ramsey's Theorem II 10.2 - - -
34 Apr 10 Ramsey's Theorem: Applications 10.2 - - -
35 Apr 12 Graph Ramsey Theory 10.2 - - -
36 Apr 15 Turán's Theorem; Erdős--Stone 11.1 - - HW5 due.
37 Apr 17 Kruskal--Katona I 11.2 - - -
38 Apr 19 Kruskal--Katona II 11.2 - - HW6 assigned.
39 Apr 22 Sperner's Theorem; Erdős's extension 11.2 - - -
40 Apr 24 Intersecting Families; Erdős--Ko--Rado 11.2, 12.1 - - -
41 Apr 26 Posets 12.1 - - -
42 Apr 29 Dilworth's Theorem 12.1 - - HW6 due.
43 May 1 Ranked and Graded Posets; Symmetric Chain Decompositions 12.2 - - -
44 May 3 Strong Sperner Property; Inductive Sym. Chain Decomp. of Boolean Lattice 12.2 - - -
- May 10 Final Exam - - - -
milans@math.wvu.edu