Mathematics of Games and Puzzles
In the fall of 2017, I enrolled in and completed the honors seminar titled "Mathematics of Games and Puzzles." Lead by Dr. Robert Buckingham, the purpose of this course was to examine and understand the underlying mathematics of many of the games that we see and play in everyday life. To do this, the course was broken up into 5 units, or groupings, of games and puzzles: card games, game theory, logic puzzles, Markovian games, and combinatorial games. Throughout these various types of games, we explored topics such as combinatorics, permutations, combinations, probability, expected values, saddle points, deductive reasoning, groups, graphs, markov chains, binary expressions, trees, and logical proofs. Each unit was broken into two portions, theoretical and practical.
Depending on the unit, one side might be more prevalent than the other, such as with game theory focusing almost entirely on the theoretical portion. Throughout the course, we completed a few major projects that were the peaks of our analysis into games. Two of these projects involved an in depth examination of a single part of a chosen game, and the third was for each of us to actually design a logic puzzle. The third was by far my favorite, as I always enjoy creating things, and this was a unique area that I got to create in, combining both mathematics and creativity.
Overall, this class was a significant change from previous honors seminars that I've taken. Even if only tangentially, this course made use of many topics that I was already familiar with in the field of statistics. In addition to this, many of the previous seminars that I've taken have had some amount of social betterment incorporated into them, while this one did not. I believe I prefer the courses that include this bit. Much of my proscribed education in Computer Science includes very little in the way of social sciences, or examination of society, and while taking this course, I found that I missed that aspect of my previous seminars. My takeaway from this seminar has been completely personal, and only useful in the intellectual sense. I know more about games, and the math behind them, but there are very few ways in which that can be directly applied to the world, particularly as I only play games, not make them. That being said, the intellectual benefits of this course have been good. I've learned to examine the activities I do, and the work that I do in a more analytical sense, particularly in searching for patterns in things.
As an artifact for this class, I think it is appropriate to present one of the projects that I completed for the class. The goal of this project was to create our own game, I specifically chose a logic puzzle. The puzzle and a description of it can be found below.
Depending on the unit, one side might be more prevalent than the other, such as with game theory focusing almost entirely on the theoretical portion. Throughout the course, we completed a few major projects that were the peaks of our analysis into games. Two of these projects involved an in depth examination of a single part of a chosen game, and the third was for each of us to actually design a logic puzzle. The third was by far my favorite, as I always enjoy creating things, and this was a unique area that I got to create in, combining both mathematics and creativity.
Overall, this class was a significant change from previous honors seminars that I've taken. Even if only tangentially, this course made use of many topics that I was already familiar with in the field of statistics. In addition to this, many of the previous seminars that I've taken have had some amount of social betterment incorporated into them, while this one did not. I believe I prefer the courses that include this bit. Much of my proscribed education in Computer Science includes very little in the way of social sciences, or examination of society, and while taking this course, I found that I missed that aspect of my previous seminars. My takeaway from this seminar has been completely personal, and only useful in the intellectual sense. I know more about games, and the math behind them, but there are very few ways in which that can be directly applied to the world, particularly as I only play games, not make them. That being said, the intellectual benefits of this course have been good. I've learned to examine the activities I do, and the work that I do in a more analytical sense, particularly in searching for patterns in things.
As an artifact for this class, I think it is appropriate to present one of the projects that I completed for the class. The goal of this project was to create our own game, I specifically chose a logic puzzle. The puzzle and a description of it can be found below.
| design_a_logic_puzzle.pdf |
