MATH 427
Tiling Theory Spring 2020
Division III Quantative/Formal Reasoning

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Since humans first used stones and bricks to tile the floors of their domiciles, tiling has been an area of interest. Practitioners include artists, engineers, designers, architects, crystallographers, scientists and mathematicians. This course will be an investigation into the mathematical theory of tiling. The course will focus on tilings of the plane, including topics such as the symmetry groups of tilings, the topology of tilings, the ergodic theory of tilings, the classification of tilings and the aperiodic Penrose tilings. We will also look at tilings in higher dimensions, including “knotted tilings”.
The Class: Type: lecture
Limit: 30
Expected: 20
Class#: 3978
Grading: no pass/fail option, yes fifth course option
Requirements/Evaluation: problem assignments, exams and a presentation/paper
Prerequisites: MATH 250 Linear Algebra and MATH 355 Abstract Algebra
Enrollment Preferences: senior majors, seniors, juniors, sophomores, first-year students (this is a senior seminar, one of which is required for all senior majors, so they have first preference)
Materials/Lab Fee: cost of book which will be under $50
Distributions: Division III Quantative/Formal Reasoning

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