Author: Timothy Gowers
This is the first video of a course entitled Topics in Combinatorics, which is given as part of the Part III Mathematics course at Cambridge University in the Michaelmas term of 2020. Because of the pandemic, all courses are online this year, and since we are allowed to post our lectures on YouTube, I felt strongly that if there is anybody outside Cambridge who might be interested, they should have the opportunity to watch them. Please bear in mind that the videos are created principally for a one-off teaching purpose, and just as when lecturing normally I have moments where I make small slips and have to correct myself, so I do in these videos, and I have not edited them out. I also have occasional technical glitches and have left those in too. My reasoning is that anybody truly interested in the material will not mind too much that an actual human being is trying to explain it.
I assume a background in basic undergraduate mathematics: discrete probability, linear algebra, standard definitions from graph theory, and so on. But compared with most graduate courses, there are very few prerequisites.
The videos are designed to be accompanied by printed notes, which can be found at this link:
A first question sheet can be found here:
This first video begins with some remarks about the running of the course, mainly aimed at Cambridge students taking it in 2020 and of limited interest to anyone else. The second half consists of a few general remarks about combinatorics, which start at 13:30.
Video source Youtube