Syllabus and Schedule

Course Page: http://www.math.msu.edu/~magyar/Math482 .

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

Reference: [W] Herbert Wilf, Generatingfunctionology (2nd ed).

Homework will be assigned daily on the Course Page.

Lect	Date	Section: Topic
1	1/6	Snow day, no classes
2	1/8	Twelvefold Way (1). f : [k]→[n] dist (marked bins); problems, formulas, recurrences
3	1/10	Twelvefold Way (2). f : [k]→[n] indist (unmarked bins); Sirling set partitions, number partitions
4	1/13	Other sequences: Stirling cycle, Fibonacci, Catalan, trees
5	1/15	Review: Method of Generating Functions
6	1/17	[W] Ch 1: Generating functions and recurrences (1)
	1/20	M.L. King Day, no classes
7	1/22	[W] Ch 1: Generating functions and recurrences (2)
8	1/24	[W] Ch 2.1: Formal power series
9	1/27	[W] Ch 2.2: Rules connecting sequences and generating functions
10	1/29	[W] Ch 2.3: Exponential generating functions
11	1/31	[W] Ch 2.3: Exponential generating functions Last day to drop with tuition refund
12	2/3	[W] Ch 3: Cards, decks, and hands (1)
13	2/5	[W] Ch 3: Cards, decks, and hands (2)
14	2/7	[W] Ch 3: Cards, decks, and hands (3)
15	2/10	[W] Ch 3: Cards, decks, and hands (4)
16	2/12	[W] Ch 5: Analytic theory (1)
17	2/14	[W] Ch 5: Analytic theory (2)
18	2/17	Review (1)
19	2/19	Review (2)
20	2/21	Midterm Exam
21	2/24	[W] Ch 5.1: Lagrange inversion, Cayley formula (1)
22	2/26	[W] Ch 5.1: Lagrange inversion, Cayley formula (2) Last day to drop with no grade reported
23	2/28	Integer partitions and Euler's Pentagonal Number Formula
	3/1-9	Spring Break
24	3/10	Rooted unlabeled trees, x Dlog Method
25	3/12	Unrooted unlabeled trees
26	3/14	Unrooted unlabeled trees, Otter's Lemma
27	3/17	Unrooted unlabeled trees, Otter's Formula
28	3/19	Polyhedra review: definitions, basic facts, examples, drawings
29	3/21	Polyhedra: vertex and face constructions
30	3/24	Polyhedra: f-vectors
31	3/26	Steinitz Lemma Steinitz Theorem: Statement, pictures, 3-connected graphs
32	3/28	Balinski's Theorem
33	3/31	Connectivity, Menger's Theorem
34	4/2	Summary of polyhedral graph properties
35	4/4	Rubber-band model
36	4/7	Rubber-band model
37	4/9	Rubber-band model
38	4/11	Finish rubber-band model
39	4/14	Maxwell realization
40	4/16	Maxwell realization
41	4/18	Finish Steinitz proof: canonical form
42	4/21	Review
43	4/23	Review
44	4/25	Review
	4/28	Final exam Mon Apr 28, 10:00am−12:00 noon, Wells A-136