Ramsey Theory 1: A Motivating Example

Part of a series of videos by Kaj Hansen on Ramsey Theory. He's an undergraduate mathematics student at the University of Georgia. He's working to make Ramsey Theory more accessible to a broader audience.

[Cid]

This is great! Keep up the good work. We need more videos online of people explaining things other than how to integrate and/or solve systems of equations. From a teacher, I just wanted to suggest one or two things for teaching practice:

Give your viewer/lecturee a bit more guidance for remember some stuff. For example, when you said what colors you would use for friendship/non-friendship you showed the colors. Why not write on the board the word "friends" in Color A. This will help you keep track in case you lose the flow and the same for your viewers. [I know in this case, it doesn't actually matter -- but it's presentation ;) ]

For definitions, make sure you write them down or have them pop up on the video (personally, I'd rather have them on the board...) --- or put them in the video description since you have the ability in a non-classroom setting!

Keep going strong and keep practicing teaching by making these kinds of videos!

[sunilrampuria]

Further one can see that if the red lines were drawn to the other vertices, it would lead to the same result. So without loss of generality we can choose any three vertices on which we are connecting our main vertices with red line.

[robertschlesinger]

A nice first lecture on Ramsey Theory.

[hiteshramkotha]

Good and simple explanation, thanks a lot Kaj Hansen

[RexGalilae]

1953 Math Exam Questions : Simple, yet profound
2016 Math Exam Questions : Complicated, yet Shallow

[Steffonomy]

Great video! It's very helpful to see a walkthrough and visualization! Well done :)

[EquuleusPictor]

This is now a classic and I've seen it proposed in math competitions for kids as young as 11, but I wonder how was this problem viewed back then ?

[puiminyap]

Great video. Can you do a tutorial on R(4, 4) as well?

[sinisamilisavljevic]

If two of them are mutual enemies, they are neither friends nor strangers. (kekeke)