MATH 435
Chip-firing Games on Graphs Fall 2021
Division III Quantitative/Formal Reasoning
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Class Details

Starting with a graph (a collection of nodes connected by edges), place an integer number of poker chips on each vertex. Move these chips around according to “chip-firing moves”, where a vertex donates a chip along each edge. These simple and intuitive games quickly lead to challenging mathematics with applications ranging from dynamical systems to algebraic geometry. In this course we’ll build up a mathematical framework for studying chip-firing games, drawing on linear algebra and group theory. We’ll discover algorithms for winning these games, and study their complexity; and we’ll prove graph-theoretic versions of famous results like the Riemann-Roch theorem. A key component of this course will be research projects that draw on open questions about chip-firing.
The Class: Format: seminar
Limit: 25
Expected: 15
Class#: 1326
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation: Weekly homework for the first eight weeks, four quizzes spaced evenly throughout the semester, and a cumulative project worked on throughout the semester (10-20 pages)
Prerequisites: Math 250 and Math 355
Enrollment Preferences: Math majors who need the course to graduate
Distributions: Division III Quantitative/Formal Reasoning
QFR Notes: All topics are quantitative

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