Vector spaces, linear transformations, eigenvalues and eigenvectors, the Jordan canonical form, bilinear forms, quadratic forms, real symmetric forms and real symmetric matrices, orthogonal transformations and orthogonal matrices, Euclidean space, Hermitian forms and Hermitian matrices, Hermitian spaces, unitary transformations and unitary matrices, skewsymmetric forms, tensor products of vector spaces, tensor algebras, symmetric algebras, exterior algebras, Clifford algebras and spin 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.
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.