| MTH 482 | Discrete Mathematics II | Spring 2014 |
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
| |