Read Intransitive Dice by Conrey, Gabbard, Grant, Liu and Morrison. Don't worry about bits you don't understand.
Try to narrow down the range of possible values for the chromatic number of the plane.
Read about counting. Choose a chapter called something like that from a book and get stuck in. Good words/phrases to look for: permutations, combinations, binomial coefficients, inclusion/exclusion, pigeonhole principle. Also good words, but mostly more advanced topics: asymptotics, recurrence relations, generating functions, derangements, catalan numbers, stirling numbers,... Come to class with one exercise that you've done to share with everyone. Aim for something at the trickier end of the ones you tried.
Same as 28th, but further on from where you've reached. Perhaps other things TBD depending on how Monday goes.
Counting wrap-up. Like last Monday, come with a problem and solution (and maybe some theory) to share.
Intro to Graph Theory. No prep, but you the counting assignment due on Friday.
No specific prep, but you should be working through a graph theory chapter or two, ready for...
Come with a graph theory result/exercise to show off.
Come with another graph theory result/exercise to show off.
Just for a change, come with a graph theory result/exercise to show off.
There's a cardinal in that tree! An arboro-ornithological introduction to infinite graph theory. (No prep required, but remember to have submitted the second assignment, due on the 22nd.)
Critical Sets in Latin Squares: Finite and Infinite. This will set the scene for the first possible group research project that we have in mind.
First set of meetings (more details in class). Schedule:
Welcome back. We'll plan for the second half of the semester.
Work on whatever topic you selected on Monday. Come with something to share.
Mix of students presenting and group work on the infinite latin square project. Assignment due on Friday.
Infinite latin squares and other combinatorial adventures. You should be working on your topics outside class, but nothing to prep for the classtime itself (except possibly some small bits between Monday and Wednesday, depending on exactly what we do in class on Monday).
Kaethe and Matt will ask you to prepare to present problems, but in fact will hijack both sessions for their own nefarious ends and edit this page afterwards to make it look like that was the plan all along.
Have problems to present for real this time, on Monday at least. On Thursday (1.50pm, Sci217) we'll Zoom in to the Northeast Combinatorics Network's webcast talk by Peter Cameron. Part of Wednesday will be Kaethe and/or Matt prepping some material to help us understand that, but there might be time for one of you to share work then too.
If you didn't present anything last week, there will be time to do so this week. As well as this, polishing up your final submissions is a good idea. Draft due on Wednesday and Matt and Kaethe will get you some feedback by Friday.
Meetings in Sci217, May 7th.
Aaron: 12.30pm w/Miha Della: 10am w/Onur Kat: 1.30pm w/Miha Kenny: 11am w/Sara William: 9am w/Onur