Quo-Shin Chi

An introduction to the rigorous techniques used in advanced work in mathematics. At least 3 papers (of length 4-5 pages) will be required, each with at least one revision.

Introduction to the linear algebra of finite-dimensional vector spaces. Includes systems of equations, matrices, determinants, inner product spaces, spectral theory.

An introductory graduate-level course including differential calculus in n-space; differentiable manifolds; vector fields and flows; differential forms and calculus on manifolds; elements of Lie groups and Lie algebras; Frobenius theorem; elements of Riemannian geometry.