Gentle introduction to the ideas of differential geometry, which are fundamental to our understanding of physical concepts like general relativity and black holes. Curves in Euclidean 2- and 3-space. Curvature and torsion. Surfaces. Gaussian and mean curvature. Topics will be tailored to student interest and background.

Learn about splay trees: the elegant and effective self-adjusting binary search tree! Topics covered include the construction of the data structure, runtime analysis, and discussion of performance in practice. Also will briefly discuss the dynamic optimality conjecture if time allows.