Kevin Milans : Teaching : Spring 2025 Math378

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: M,Thurs 12:00pm-1:00pm, 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 13 Introduction; Induction/Recursion/No Minimum Counter Example 1.1 - - HW1 posted.
2 Jan 15 Induction Examples 1.1,1.2 - - -
3 Jan 17 Fibonacci Numbers; Game of Nim 1.1,1.2 - - -
- Jan 20 MLK Day: no class - - - -
4 Jan 22 Game of Nim 1.2 - - Workshop: 4pm
5 Jan 24 Recurrence relations: examples 1.3,1.4 - - HW1 due 12pm (Crowdmark); HW2 assigned.
6 Jan 27 Characteristic Equation Method, Special Case - quiz1.pdf quiz1-soln.pdf Quiz 1 in class
7 Jan 29 Recurrence Relations: tiling, words without substrings 2.1 - - -
8 Jan 31 Char Eqn Method, Homogeneous Eqns; Pigeonhole Principle 2.1 - - HW2 due 12pm (Crowdmark) HW3 assigned.
9 Feb 3 Pigeonhole II: no rigid tiling of 6 by 6 grid; sum - - - -
10 Feb 5 Test 1: 1.1-1.4, 2.1(partial) - test1.pdf test1-soln.pdf -
11 Feb 7 Pigeonhole III: Groupwork (Erdos problem) 2.1 - - HW3 due. HW4 posted.
12 Feb 10 Erdos divisibility problem; Erdos--Szekeres 2.1 quiz3.pdf quiz3-soln.pdf Quiz 3 in class.
13 Feb 12 Erdos--Szekeres II 2.1 - - -
14 Feb 14 Graphs; Degree-Sum Theorem 2.2 - - HW4 due. HW5 posted.
15 Feb 17 Review Quiz 3 (Pigeonhole Principle) - quiz4.pdf quiz4-soln.pdf Quiz 4 in class.
16 Feb 19 Handshake corollary; Graph isomorphism 2.2 - - -
17 Feb 21 Bipartite graphs; Graph isomorphism 2.2 - - HW5 due. HW6 posted.
18 Feb 24 Ramsey Theory 2.3 quiz5.pdf quiz5-soln.pdf Quiz 5 in class
19 Feb 26 Edge colorings with few monochromatic triangles - - - -
20 Feb 28 Ramsey Theory II 2.3 - - HW6 due. HW7 posted.
21 Mar 3 Ramsey Theory III 2.3 - - -
22 Mar 5 Test 2: 2.1--2.3, lectures 9--20 - test2.pdf test2-soln.pdf -
23 Mar 7 Schur, Van der Waerden Numbers 2.4 - - HW7 due. HW8 posted.
24 Mar 10 Open problems; Counting: Addition, Multiplication Principles 2.5,3.1 quiz7.pdf quiz7-soln.pdf Quiz 7 in class
25 Mar 12 Counting: Addition, Multiplication Principles 3.1 - - -
26 Mar 14 Probability; random variables; expected value 3.2 - - HW8 due.
27 Mar 24 Linearity of Expectation; Permutations 4.1 - - HW9 posted.
28 Mar 26 Combinations 4.2 - - -
29 Mar 28 Combinations of multisets; counting solutions 4.4 - - HW9 due. HW10 posted.
30 Mar 31 Combinatorial proofs I 5.1.1 quiz9.pdf quiz9-soln.pdf Quiz 9 in class.
31 Apr 2 Combinatorial proofs II; Pascal's Triangle 5.1.1,5.1.2 - - -
32 Apr 4 Multinomial coefficients; binomial coefficient bounds 5.1.2,5.1.3 - - HW10 due. HW11 posted.
33 Apr 7 Ramsey Numbers: quantitative lower bounds 5.1.4 - - -
34 Apr 9 Test 3: Lectures 23-31; Sections 2.4,2.5,3.1,3.2,Ch4,5.1.1-5.1.3, and Multinomials (part of 5.3) - test3.pdf test3-soln.pdf -
35 Apr 11 Binomial, Multinomial Theorem 5.2,5.3 - - HW11 due. HW12 posted.
36 Apr 14 Inclusion/Exclusion 8.1 quiz11.pdf quiz11-soln.pdf Quiz 11 in class
37 Apr 16 Graphic Sequences 10.1 - - -
- Apr 18 Fall Break: No class - - - -
38 Apr 21 Walks, trails, paths, and cycles 10.2.1 - - HW12 due. HW13 posted.
39 Apr 23 Forests and Trees 10.2 quiz12.pdf quiz12-soln.pdf Quiz 12 in class.
40 Apr 25 Closed odd walks; bipartite graphs 10.3 - - HW13 due. HW14 posted.
41 Apr 28 Hall's Theorem 10.3, 11.3 - - -
42 Apr 30 Graph coloring, clique and independence number 10.7 - - -
43 May 2 Mycielski's Construction - - - HW14 due.
- May 3 Final Exam: Tues May 6, 11:00am-1:00pm - - - -
milans@math.wvu.edu