Courses:
Talks:
An introduction for applied mathematics majors at UC San Diego from the point of view of Math 20E Vector Calculus and Math 109 Proof. Starting with the Laplacian I show how vector calculus allows formulation of traditional PDEs of mathematical physics; define the graph Laplacian and its connection with PageRank; and discuss Malfatti's problem as an example of the need for proof even within applied mathematics.
Can you color the plane with three colors so that every equilateral triangle with sides of length 1 has one vertex of each color? In this talk I answer this question and describe several generalizations. Some of these have implications for the foundations of quantum mechanics (the Bell-Kochen-Specker theorem); I explain these using only linear algebra and some elementary number theory, without assuming any knowledge of quantum mechanics. Recent comments about these observations invoke Euclid's Postulates; I conclude with a brief discussion of this connection.
Quantum computers, if they existed, would be able to solve certain problems faster than is possible on a classical computer running the best algorithms known. In this talk I illustrate how such efficient quantum algorithms work by discussing the game of "20 questions". I explain the optimal classical strategies for such games, and then show how to do much better quantum mechanically. No knowledge of quantum mechanics is required; I describe the basic facts which are needed during the talk.