The Games People Play
Institution: Carleton University (Herzberg 3422)
Category: Faculty of Science
Course DescriptionA week of games and tournaments in math! Come test your problem solving and pattern recognition with fun puzzles. Students will work in teams and individually to solve classic brain teasers and open real-world problems.
Discrete mathematics has important applications across a wide variety of fields. For example, solving puzzles, designing experiments, and software testing. It will allow students to better understand how to solve and create puzzles, like Sudoku, Kenken, and Kakoru. It will also encourage abstract thinking. We will compare several types of discrete structures and emphasize that adding and removing restrictions can really change a question.
Topics for this course will include:
-Latin Squares, MOLs, Orthogonal Arrays, and Sudokus
-Set Notation: Sets, subsets, union, intersection, Venn Diagrams
-Counting: addition principle, pigeonhole principle, 3 friends and 3 strangers, multiplication principle, binomial numbers, four types of counting, binomial theorem, and Sieve Principle
-Permutations and games we can play with them. (The 15-Puzzle, Mastermind, Grams)
-Designs: BIBD, the Fano Plane, incidence matrix, compliments, necessary conditions of existence, symmetric designs, derived and residual designs
-Graphs: constructions, modeling equivalencies
-Secrets of the Rubik's Cube
-If time permits: Combinatorial Game Theory VS Economic Game Theory.
-Relating the above topics.
We will go over definitions and examples. We will have some more difficult questions that will be proposed during the sessions. The following session we will take up solutions to these problems. There will be lots of group activities to emphasis the different ways to enumerate(count) problems. When we reach orthogonal arrays, we will ask the class to try and set up tournament brackets and then use them to solve other problems. If time permits, we may talk about type general type setting strategies for puzzles.
Your workshop leader Amanda Chafee is a PhD students at Carleton specializing in discrete mathematics and enjoys sharing her love and expertise of math with everyone.