Group theory including the Sylow theorem, the structure of abelian groups, and permutation groups.
Introduction to Linear Algebra. Topics include systems of linear equations matrices, de- terminants, abstract vector spaces, linear transformations, inner products, the geometry of Euclidean space, and eigenvalues.
A continuation of course 223A. Topics include theory of schemes and sheaf cohomology, formulation of the Riemann-Roch theorem, birational maps, theory of surfaces.
At Washington University in St. Louis I taught Multivariable Calculus, Differentiable Calculus, Combinatorics, Graph Theory, Foundations for Higher Mathematics, Optimization, Toric Varieties, and Polytopes. At UIUC I taught Multivariable Calculus, Linear Programming, Combinatorics, and Discrete Mathematics. At Cornell University I taught Differentiable Calculus.