221a and b. The theory of higher dimensional space. Differential calculus of vector functions, implicit function theorem, extreme values, multiple integrals, vector field theory. Open only to seniors whose major is mathematics. Measure theory, the Lebesgue integral, Banach spaces of measurable functions.
Topics vary from year to year.
Additional topics drawn from sufficient statistics, estimation theory, statistical testing, and inferences about normal models. Topics are drawn from computability theory, model theory, and set theory. Mathematical and philosophical implications also are discussed. Rings and fields, with a particular emphasis on Galois theory.