Syllabus and Schedule

Course page: http://www.math.msu.edu/~magyar/Math481 .

The dates below are tentative. Changes will be announced in class and on our course page.

Section numbers refer to Harris, Hirst, Mossinghoff, Combinatorics and Graph Theory. We will cover Part 2 of the book, then selections from Part 1. Homework will be assigned weekly on the Course page.

Date Section: Topic
1/7 2: Introduction
1/9 2.1: Three basic problems n!, n^k, (n | k); examples
1/11 Fourth problem: multi-sets ((n | k)), correspondences, (n | k) = (n | n-k)
Last day for computer/phone registration, and to change pass/fail grading option
1/14 Quiz: Four basic problems
2.2: Properties of binomial coeffs, Pascal's Triangle
1/16 2.2: Binomial theorem, generating function proof
1/18 2.3: Principle of Inclusion-Exclusion
1/21 ML King Day, no class
1/23 Quiz: Binomial coefficients
2.3: PIE examples
1/25 2.4.1: Generating function for double decks
2.4.2: Generating function for multi-sets: ∑_k≥0 ((n | k)) x^k = 1/(1-x)ⁿ
1/28 Quiz: PIE
2.4.2, 2.4.3: Counting with repetition, changing money
1/30 Review
2/1 Test 1
Last day to drop a course with refund

2/4 2.4.4: Fibonacci numbers
2/6 2.4.5: Recurrence relations
2/8 2.4.6: Catalan numbers and convolution

2/11 Quiz: Recurrences
2.5.1: Groups
2/13 2.5.2: Burnside lemma
2/15 2.5.2: Counting with symmetry

2/18 Quiz: Counting with symmetry

2/20 Counting on solids
2/22 Counting on solids
2/25 Review
2/27 Test 2
Mid-semester: last day to drop a course with no grade reported
2/29 1.1.1: Graph definitions
3/3−7 Spring Break

3/10 1.1.2: Connectedness
3/12 1.1.3: Bipartite graphs
3/14 1.2.1 & 1.2.2: Tree basics
3/17 Quiz: Graphs
1.2.4: Counting trees, Cayley theorem n^n-2
3/19 1.2.4: Prufer codes
3/21 1.3.1: Planar graphs

3/24 Quiz: Trees
1.3.2: Euler's formula
3/26 1.3.4: Kuratowski theorem
3/28 1.3.3: Platonic solids
3/31 Quiz: Planar graphs
Review
4/2 Review
4/4 Test 3
4/7 1.4.1, 1.4.2: Coloring
4/9 1.4.3: Four Color Theorem
4/11 1.4.4: Chromatic polynomial
4/14 Quiz: Graph coloring
Unlabelled trees
4/16 Unlabelled trees
4/18 Unlabelled trees
4/21 Review
4/23 Review
4/25 Review, Evaluation
5/2 Final Exam 10am-12noon, Wells C-305

Date	Section: Topic

1/7	2: Introduction
1/9	2.1: Three basic problems n!, n^k, (n \| k); examples
1/11	Fourth problem: multi-sets ((n \| k)), correspondences, (n \| k) = (n \| n-k) Last day for computer/phone registration, and to change pass/fail grading option

1/14	Quiz: Four basic problems 2.2: Properties of binomial coeffs, Pascal's Triangle
1/16	2.2: Binomial theorem, generating function proof
1/18	2.3: Principle of Inclusion-Exclusion

1/21	ML King Day, no class
1/23	Quiz: Binomial coefficients 2.3: PIE examples
1/25	2.4.1: Generating function for double decks 2.4.2: Generating function for multi-sets: ∑_k≥0 ((n \| k)) x^k = 1/(1-x)ⁿ

1/28	Quiz: PIE 2.4.2, 2.4.3: Counting with repetition, changing money
1/30	Review
2/1	Test 1 Last day to drop a course with refund

2/4	2.4.4: Fibonacci numbers
2/6	2.4.5: Recurrence relations
2/8	2.4.6: Catalan numbers and convolution

2/11	Quiz: Recurrences 2.5.1: Groups
2/13	2.5.2: Burnside lemma
2/15	2.5.2: Counting with symmetry

2/18	Quiz: Counting with symmetry
2/20	Counting on solids
2/22	Counting on solids

2/25	Review
2/27	Test 2 Mid-semester: last day to drop a course with no grade reported
2/29	1.1.1: Graph definitions

3/3−7	Spring Break

3/10	1.1.2: Connectedness
3/12	1.1.3: Bipartite graphs
3/14	1.2.1 & 1.2.2: Tree basics

3/17	Quiz: Graphs 1.2.4: Counting trees, Cayley theorem n^n-2
3/19	1.2.4: Prufer codes
3/21	1.3.1: Planar graphs

3/24	Quiz: Trees 1.3.2: Euler's formula
3/26	1.3.4: Kuratowski theorem
3/28	1.3.3: Platonic solids

3/31	Quiz: Planar graphs Review
4/2	Review
4/4	Test 3

4/7	1.4.1, 1.4.2: Coloring
4/9	1.4.3: Four Color Theorem
4/11	1.4.4: Chromatic polynomial

4/14	Quiz: Graph coloring Unlabelled trees
4/16	Unlabelled trees
4/18	Unlabelled trees

4/21	Review
4/23	Review
4/25	Review, Evaluation

5/2	Final Exam 10am-12noon, Wells C-305