Combinatorics (WI26)

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Math 118: Combinatorics
Meetings: Kemeny 004 MWF 10:10-11:15
X-hour: Th 12:15-1:05
I'm not planning to use the X-hour except for making up classes that are missed due to travel
Instructor: Foster Tom
Office: Kemeny 318
Office hours: TuTh 10-11 (starting Jan 13)
Course summary:
I'm not planning on a single unifying theme, but we will explore some topics in combinatorics that I hope you will enjoy. We will talk about:
  • Combinatorial species and generating functions
  • Symmetric functions and permutation enumeration
  • Graph colouring and polynomials
  • (Possibly) chip firing, cops and robbers

Evaluation:

We will have biweekly homework assignments. You are encouraged to collaborate but you must write your responses on your own and understand what you are submitting. 

There will be presentations and a term paper near the end of the term. Please select a research paper to study and give a 20-30 minute talk on. Also, please write an expository paper of 4-10 pages summarizing the ideas and providing background context. I'll provide a list of potential papers to study, and you are encouraged to seek your own as well.

As this is a graduate course, evaluation for the graduate students will be much more informal. I won't give much feedback on the homework by default, but feel free to meet me in office hours to discuss it in further depth if you like. 

Textbook:

There is no required textbook and everything you need to know will be in the lectures. Here are several useful references that you may enjoy for further reading:

  • Enumerative Combinatorics by Richard Stanley
  • Introduction to the Theory of Species of Structures by Bergeron, Labelle, and Leroux
  • Proofs from THE BOOK by Aigner and Zeigler
  • Counting with Symmetric Functions by Mendes and Remmel

Course schedule:

Date Topic Homework
M Jan 5 Cayley's formula for the number of trees
W Jan 7 Generating functions
F Jan 9 Generating functions and partitions

 
M Jan 12 Combinatorial Species (Part 1)
W Jan 14

Combinatorial Species (Part 2)
F Jan 16 Operations on Species (Part 1) Homework 1
M Jan 19 MLK Day - no class
W Jan 21 Operations on Species (Part 2)
F Jan 23 Symmetric functions (Part 1)
M Jan 26 Symmetric functions (Part 2)
W Jan 28
F Jan 30 Homework 2
M Feb 2
W Feb 4
F Feb 6 Presentation topic proposal
M Feb 9
W Feb 11
F Feb 13 Homework 3
M Feb 16
W Feb 18
F Feb 20
M Feb 23
W Feb 25
F Feb 27 Presentations Homework 4
M Mar 2 Presentations
W Mar 4 Presentations
F Mar 6 Presentations
M Mar 9 Presentations

 

Course Summary:

Course Summary
Date Details Due