Friday, April 8, 2011

Combinatorial Games: a first-year class

The past few months I have been working on some basic planning for teaching combinatorial games as a first-year college class. At Wittenberg, we have "WittSem" courses; each incoming freshman must take one. This is finally really coming together, so I will likely teach this course in the fall. Woohoo!

This is a bit of a tricky task. Last semester my course started off as too difficult because we were using a graduate-level math text and I didn't convert the book problems enough for the students. (Not to mention I was learning some of the material only slightly before teaching it.) My next batch of students will have less math background so I'm going to have to be even more careful. I will probably rely more heavily on worksheets and less on the book problems, though Lessons in Play will continue to be an excellent reference for the class.

I still plan on devoting one day per week to playing games and discovering outcome classes/values for different states. Each week we'll try to add some new evaluation tools and I'll look for great game examples of those tools.

All in all, the class will likely look a bit like the last, but without emphasis on proofs and programming. This last bit will be replaced by some discussion of cultural aspects of games throughout history. This is definitely a bigger task than I had last semester, but I'm already looking forward to it!

Once the semester starts, I'll link to the class page. Of course, if you are an incoming Wittenberg student and have any questions about how you can be allowed to play board games during class, please ask me!


  1. I'm curious, what will be the purpose of the class? I'm somewhat new to CGT, although I've studied NIM and a few other games as work for my masters. I think CGT could be very useful as an approach towards higher level mathematics and CS, especially as an introductory level course.

  2. Blake,

    this class is part of the WittSem program here, which means all students will be first-year college students. Each Wittenberg student takes one WittSem class their first year, so part of the focus of the class will be on how to handle college and turning in assignments on time, etc.

    For the math side, I plan to teach students the basics of evaluating game positions. I'll take it slowly, but I think it'll be possible without a ton of prerequirements. I may prove a few things in class, but I will almost certainly stay away from proofs.

    This will certainly not be a graduate-level course, so I doubt it's the sort of thing you'd be looking to take. Sorry if that was confusing. I do recommend Winning Ways and Lessons in Play as texts for learning the material if you can't find an adequate course to take.

  3. I plan on picking up Winning Ways pretty soon. Right now, I'm reading up on CGT as an area of possible future research, and as a tool for teaching.

    Like I said, I think CGT can be a powerful tool in teaching math. I've always been attracted to the competitive nature of games, and I think that the concept of "winning" can create a level of enjoyment in math that isn't present in the simple memorization of formulas that many lower level math classes present.

    If the students can also be learning something like Gaussian elimination, geometry, or even calculus concepts then it becomes an added bonus. But, as of yet, I don't know of any games that have this bonus. I've been playing around with a few, but I don't have a proof that they are well formed in the sense that they always result in a winner.

  4. Blake,

    in many different ways, you are speaking my language. :)

    I really like the use of games as teaching aides. For example, I might have a hard time understanding (or believing) Sperner's Lemma, except that I've played a lot of Atropos.