2011 Section Meeting

Invited talks

Judy Holdener, Kenyon College

When Thue-Morse meets Koch

Abstract: The Thue-Morse sequence and the Koch snowflake have much in common. Both are defined iteratively. Both exhibit properties of self-similarity. Both first appeared in the early 1900's (the von Koch curve in 1906 and the Thue-Morse sequence in 1912). And both continue to appear frequently - yet independently - in popular mathematical writing today. In this talk, we will show that the commonality between these two famous objects is deeper yet. By realizing the Thue-Morse sequence geometrically as the limit of polygonal curves in the plane, we will show that the connection between the Thue-Morse sequence and the von Koch curve is much stronger than one might expect. This connection was discovered and formalized with the extensive help of undergraduate students through Kenyon's Summer Science Scholar research program.

Danny Otero, Xavier University

Determining the Determinant (1693-1812), the Early History of a Sophisticated Idea

Abstract: The history of the development of the matrix determinant, a standard topic in college mathematics, is a complicated one. And while it has been well studied before, it is not well known in the mathematics community. This talk will review the early period of this development, spanning the 18th century (plus a few years on either end), illustrating the contributions of a variety of mathematicians -- Leibniz, Maclaurin, Cramer, Bezout, Vandermonde, Laplace, Lagrange, Gauss, Binet, Cauchy and Jacobi. It will document how the powerful notion of a determinant coalesced out of their work on many different kinds of mathematical problems, and how a multiplicity of notations were devised to represent this complex idea until it settled into a form that is recognizable to every linear algebra student today.

Ivars Peterson, MAA

The Jungles of Randomness

Abstract: From slot machines and amusement park rides to dice games and shuffled cards, chance and chaos pervade everyday life. Sorting through the various meanings of randomness and distinguishing between what we can and cannot know with certainty proves to be no simple matter. Inside information on how slot machines work, the perils of believing random number generators, and the questionable fairness of dice, tossed coins, and shuffled cards illustrate how tricky randomness can be.