Math 208: Mathematical Explorations is a half credit class for intended Math/Statistics/Applied Math/Mathematical Economics majors. In this class, students:
- Investigate a wide-range of math ideas beyond intro calculus and statistics
- Build community and work closely with the other first-year majors
- Get involved with the math & stat department
This semester, Prof. Kelly Bickel is teaching the class. Most class days involve hands-on activities where students explore math-related ideas in groups. On Wednesday August 26th, the topic of class was Mathematical Games- games whose rules are governed by mathematical principles. If you have such a game, some natural questions are:
- If it’s a one-player game, when is it winnable?
- If it’s a two-player game, what’s the best strategy for each player?
- Does either player have a winning strategy?
During class, students played some mathematical games and tried to answer those questions. First they looked at grids of different sizes with two dots marking two grid cells. Is there a path between the two dots that goes through each grid cell exactly once? Once students played a few boards, they were then asked to come up with more general questions about these grid games. One question in particular was popular: is there a pattern to when boards are unsolvable?
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Next up, was a two-player game. Groups split into pairs to play a game and try to determine a way to win.
The group in the top middle photo is made up of Finley Wardrip (Mathematical Economics major, ’30), Joe Cavalcanti (Mathematical Economics major, ’30), Abigail Angler (Applied Mathematics Major, ’30) and Rose Wayland (Mathematics Major, ’30)
The group in the top right photo is made up of Zach Timms (Mathematics major, ’30), Cora Milner (Applied Mathematics Major, ’30), Emily Koplin (Mathematical Economics major, ’30), and Nathan Small (Statistics Major and Data Science Co-Major, ’30).
The group in the bottom left photo is made up of Izzy Van Dyke (Mathematics major, ’30), Cece Sonthonnax (Applied Mathematics Major, ’30), Nguyen Nguyen (Mathematical Economics major, ’30) and Ariah Vona (Mathematics Major + seeking teacher certification, ’30)
The group in the bottom right is made up of Ava Abrahamson (Mathematical Economics Major, ’30), Yosmairi Arias (Mathematics Major + seeking teacher certification, ’30), and Peter Caputa (Mathematical Economics major, ’30).
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Want to experience this game yourself? Grab a friend and put 10 beads/pennies/pick your object on a table. During each turn, a player can take between 1 and 4 beads. How do you win? Take the last bead. Can you come up with a winning strategy? What if you start with 11 beads? 24 beads? N beads?
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