MATH 410 - Ramsey Theory

Unbreakable, inevitable, assured, inescapable: choose whichever synonym you prefer. Ramsey theory is the study of properties that must occur for sufficiently large structures. We can try to break the structure through partitioning, but a Ramsey property will persist. We will survey the main results in Ramsey theory and, along the way, encounter several disparate proof techniques. We will visit van der Waerden’s Theorem on arithmetic progressions, Ramsey’s Theorem on graphs and hypergraphs, the Hales-Jewett Theorem on multi-dimensional tic-tac-toe, and Hindman’s Theorem on infinite sets of finite sums, among other fascinating results.

Credits: 1.00
When Offered: Spring semester only, in alternate years

Corequisite: None
Prerequisites: MATH 250 and (MATH 310 or MATH 360 or MATH 375 or MATH 320)
Major/Minor Restrictions: None
Class Restriction: None
Area of Inquiry: Natural Sciences & Mathematics
Liberal Arts CORE: None

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