Kevin Milans : Teaching : Spring 2022 Math378

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 2:30pm-3:30pm, and by appointment
Class Meetings: MWF 1:30pm-2:30pm in Armstrong Hall 121
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Section(s) Quiz Quiz Soln Comments
1 Jan 10 Introduction; A proof involving sqrt and floor - - - -
2 Jan 12 Induction 1.1,1.2 - - HW1 posted.
3 Jan 14 Tromino Tilings 1.1,1.2 - - -
- Jan 17 MLK Day: no class - - - HW2 posted.
4 Jan 19 More tilings; Recurrence relations 1.3 - - -
5 Jan 21 Recurrence relations II 1.3 quiz1.pdf quiz1-soln.pdf Quiz 1 in class
6 Jan 24 Bad proof example; unrolling a recurrence 1.3 - - HW2 due. HW3 posted.
7 Jan 26 Pigeonhole principle 2.1 quiz2.pdf quiz2-soln.pdf Quiz 2 in class.
8 Jan 28 Erdos--Szekeres Theorem; Groupwork 2.1 - - -
9 Jan 31 Groupwork (continued) 2.1 - - HW3 due. HW4 posted.
10 Feb 2 Graphs and Multigraphs 2.2 - - -
11 Feb 4 Test 1: Classes 1 through 9; Sec. 1.1-1.3, 2.1 - test1.pdf test1-soln.pdf -
12 Feb 7 Bipartite graphs; graph isomorphism; Ramsey Theory 2.2,2.3 - - HW4 due. HW5 posted.
13 Feb 9 Ramsey Numbers r(n,m) 2.3 quiz4.pdf quiz4-soln.pdf Quiz 4 in class.
14 Feb 11 Handshaking lemma; r(3,4) at most 9 2.3 - - -
15 Feb 14 Multicolor Ramsey numbers; Graph Ramsey Theory 2.3,2.4 - - HW5 due. HW6 posted.
16 Feb 16 Schur, Van der Waerden Numbers 2.4 quiz5.pdf quiz5-soln.pdf Quiz 5 in class.
17 Feb 18 r(C_4,C_4); Counting: Addition, Multiplication Principles 2.4,3.1 - - -
18 Feb 21 Counting examples; Subtraction Principle 3.1 - - HW6 due. HW7 posted.
19 Feb 23 Probability: Introduction 3.2 quiz6.pdf quiz6-soln.pdf Quiz 6 in class.
20 Feb 25 Group Activity: Max Run of Heads 3.2.1 - - -
21 Feb 28 Permutations; Falling Factorials 4.1 - - HW7 due.
22 Mar 2 Combinations; Binomial Coefficients 4.2 - - -
23 Mar 4 Test 2: Classes 10 through 21; 2.2-2.4; 3.1, 3.2, 4.1 - test2.pdf test2-soln.pdf -
24 Mar 7 Binomial coefficient examples; decks of cards 4.2 - - HW8 posted.
25 Mar 9 Group activity: probability of all aces in one hand 4.2 - - -
26 Mar 11 Multinomial coefficients 4.3 - - -
27 Mar 21 Combinations of multisets 4.4 - - HW8 due. HW9 posted.
28 Mar 23 Counting solutions; combinatorial proofs 4.4,5.1 quiz8.pdf quiz8-soln.pdf Quiz 8 in class
29 Mar 25 Combinatorial proofs II 5.1 - - HW8 due. HW9 posted.
30 Mar 28 Pascal's Triangle; binomial coefficient bounds 5.1.2-5.1.3 - - HW9 due. HW10 posted.
31 Mar 30 Ramsey Numbers: quantitative upper bounds 5.1.4 quiz9.pdf quiz9-soln.pdf Quiz 9 in class.
32 Apr 1 Ramsey Numbers: quantitative lower bounds 5.1.4 - - -
33 Apr 4 Ramsey Numbers: quantitative lower bounds II; Binomial Theorem 5.1.4, 5.2 - - HW10 due. HW11 posted.
34 Apr 6 Inclusion/Exclusion 8.1 - - -
35 Apr 8 Test 3: Classes 22 through 33; 4.2-4.4, 5.1, 5.2, 8.1 - test3.pdf test3-soln.pdf -
36 Apr 11 Ordinary Generating Functions 9.1 - - HW11 due. HW12 posted.
37 Apr 13 OGFs and Recurrence Relations 9.2 quiz11.pdf quiz11-soln.pdf Quiz 11 in class.
38 Apr 18 Fibonacci Formula Derivation 9.2 - - HW12 due. HW13 posted.
39 Apr 20 Graph Coloring 10.7 quiz12.pdf quiz12-soln.pdf Quiz 12 in class.
40 Apr 22 Graph Coloring II 10.7 - - -
41 Apr 25 Group Activity: Mycielski's Construction 10.7 - - HW13 due.
42 Apr 27 Large girth, large chromatic number; Degeneracy; Chromatic polynomial 10.7 - - -
43 Apr 29 Review - - - -
- May 3 Final Exam: Tues May 3, 11:00am-1:00pm - - - -
milans@math.wvu.edu