The Stanford University Mathematical Organization recently began a speaker series. The goal of the series is to let students listen to professors discuss their backgrounds and research, as well as to let students hear some interesting problems or ideas.
Click png or pdf for full details. Update: the provided reference isAbstract: The proof of the change of variables formula is reduced to the one-dimensional case. The fixed point theorem is a corollary.
Lax, Peter D., Change of variables in multiple integrals, American Mathematical Monthly, 106 (1999), no. 6, 497--501.
Click png or pdf for full details.Abstract: Gamblers and magicians can shuffle cards perfectly (demonstrations provided). Understanding the mathematics behind shuffling leads to the edge of number theory. The findings are used in analyzing computer-generated random numbers and dynamical systems.