Kevin Milans : Teaching : Fall 2019 Math571: Combinatorial Analysis 1

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 2:30pm-3:20pm, Thurs 11:30am-12:30pm, and by appointment
Class Meetings: MWF 11:30am-12:20pm in Armstrong Hall 120
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Section(s) Comments
1 Jan 7 Introduction; Survey of some combinatorial problems 1 -
2 Jan 9 Principles of Sum and Product 2 -
3 Jan 11 Double Counting I; Sets, Cartesian Product 2.6,2.7 HW1 assigned.
4 Jan 14 Double Counting II; Subsets; Bijections 2.6,3.1
5 Jan 16 Words; Binomial Coefficients 3.1,3.2 -
6 Jan 18 Identities and Combinatorial Stories 3.2 -
7 Jan 21 Permutations 3.5
8 Jan 23 Selections; Integral solutions to equations; Stars and Bars 3.7 -
9 Jan 25 Binomial Theorem and Pascal's Triangle 3.3 -
10 Jan 28 Binomial Theorem Applications 3.3 -
- Jan 30 Class canceled (weather) - -
- Feb 1 Class canceled (weather) - HW2 assigned.
11 Feb 4 Asymptotics and Bounds 3.6 -
12 Feb 6 Trees; Cayley's Theorem 3.10 -
13 Feb 8 Bell Numbers; Bounds 3.11 -
14 Feb 11 Recurrences; Fibonacci Numbers 4.1 -
15 Feb 13 Characteristic Equation Method 4.3 -
16 Feb 15 Generating Function Method I 4.1 HW2 due. HW3 assigned.
17 Feb 18 Generating Functions II 4.1 -
18 Feb 20 Generating Functions III; Extended Binomial Thm 4.1 -
19 Feb 22 Balanced parentheses; Catalan Numbers I 4.5 -
20 Feb 25 Catalan Numbers II; Lattice paths 4.5 -
21 Feb 27 Ballot lists; Exponential Generating Functions 4.5 -
22 Mar 1 EGFs II; Derangements; Bell numbers 4.4 HW3 due. HW4 assigned.
23 Mar 4 Inclusion/Exclusion I 5.1 -
24 Mar 6 Inclusion/Exclusion II 5.1 -
25 Mar 8 Latin squares; Systems of distinct representatives 6.1,6.2 -
- - Spring Break: March 11-March 15 - -
26 Mar 18 Partial Latin squares 6.2 -
27 Mar 20 Orthogonal Latin squares I 6.6 -
28 Mar 22 Orthogonal Latin squares II 6.6 HW4 due.
29 Mar 25 Extremal set theory; intersecting families 7.1 -
30 Mar 27 Intersecting families II; Erdos--Ko--Rado 7.1 HW5 assigned.
- Mar 29 Class rescheduled - -
31 Apr 1 Sperner Families 7.2 -
32 Apr 2 Steiner Triple Systems I 8.1 -
33 Apr 3 Steiner Triple Systems II 8.2 -
34 Apr 5 Projective Planes 9.5 -
35 Apr 8 Projective Planes: Construction 9.3 -
36 Apr 10 Induction; Pigeonhole Principle - -
37 Apr 12 Ramsey Theory: Graphs 10.4 HW5 due.
38 Apr 15 - - HW6 assigned.
milans@math.wvu.edu