Ramsey coloring of K5 Kevin Milans : Teaching : Spring 2026 Math378

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: M,Th 1:00pm-2:00pm in ARM 408H, and by appointment
Class Meetings: MWF 2:30pm-3:20pm in ARM 315
Home | Course Syllabus (PDF) | Homework | Quizzes | Tests

Course Schedule

No. Date Class Summary Section(s) Comments
1 Jan 12 Introduction; Induction/Recursion/No Minimum Counter Example 1.1 HW1 posted.
2 Jan 14 Induction Examples 1.1,1.2 -
3 Jan 16 Fibonacci Numbers 1.1,1.2 -
4 Jan 21 Game of Nim 1.2 Workshop: 4:30pm, Hodges Hall 221
5 Jan 23 Game of Nim Analysis 1.2 HW1 due 1:30pm (Crowdmark); Quiz 1 in class; HW2 assigned.
6 Jan 26 Class canceled (WVU snow day) - -
7 Jan 28 Recurrences: regions in the plane separated by lines 1.3,1.4 -
8 Jan 30 Tilings; recurrences; Characteristic Equation Method I 1.3,1.4 HW2 due; HW3 assigned.
9 Feb 2 Characteristic Equation Method II 1.4 -
10 Feb 4 Domino Tilings: how to show a tiling does not exist 1.3,1.4 Quiz 2 in class
11 Feb 6 Pigeonhole Principle I: no rigid tiling of a 6x6 board, handshaking 2.1 HW3 due. HW4 posted.
12 Feb 9 Pigeonhole Principle II: sum; Erdos--Szekeres 2.1 -
13 Feb 11 Test 1: 1.1-1.4, 2.1(partial) - -
14 Feb 13 Pigeonhole Principle III: Erdos--Szekeres 2.1 HW4 due. HW5 posted.
13 Feb 13 Erdos--Szekeres II; Erdos divisibility problem 2.1 -
14 Feb 16 Erdos divisibility problem II 2.1 -
15 Feb 18 Intro to Graphs; degree sum formula - Quiz 4 in class
16 Feb 20 Handshake corollary; Graph isomorphism 2.2 HW5 due. HW6 posted.
17 Feb 23 Subgraphs; edge-colorings of graphs 2.2,2.3 -
18 Feb 25 Ramsey Theory I 2.3 Quiz 5 in class
19 Feb 27 Ramsey Theory II: upper bound on $r(3,4)$ 2.3 HW6 due. HW7 posted.
20 Mar 2 Ramsey Theory III: General Ramsey Upper Bound 2.3 -
21 Mar 4 Ramsey Theory IV: Extensions: multicolor, general graph targets 2.3 Quiz 6 in class
22 Mar 6 Schur's Theorem; Open Problems 2.4,2.5 HW7 due. HW8 posted.
23 Mar 9 Principles of Counting 3.1 -
24 Mar 11 Test 2: lectures 12 to 22, sections 2.1-2.5 - -
25 Mar 13 Principles of Counting II 3.1 HW8 due. HW9 posted.
26 Mar 23 Probability 3.2 -
27 Mar 25 Permutations and factorials 4.1 Quiz 8 in class.
29 Mar 27 Double counting: rule of division; combinations 4.1,4.2 HW9 due.
30 Mar 30 Binomial coefficients; lattice paths 4.2 HW10 posted.
31 Apr 1 Combinations of multisets 4.4 Quiz 9 in class.
- Apr 3 Spring recess - -
32 Apr 6 Multionomial coefficient examples 4.4 HW10 due. HW11 posted.
33 Apr 8 The birthday paradox - Quiz 10 in class.
34 Apr 10 Combinatorial proofs and identities 5.1 HW11 due. HW12 assigned.
35 Apr 13 Binomial, Multinomial Theorem 5.2,5.3 -
36 Apr 15 Test 3: Lectures 23 to 34, Ch3, Ch4, 5.1 - -
37 Apr 17 Graphic Sequences 10.1 HW12 due. HW13 assigned.
milans@math.wvu.edu