The transportation problem. Informal accounts of the basic facts about infinite sets. Numerical methods for problems of linear algebra, including the solution of very large systems, eigenvalues, and eigenvectors. Fourier transforms, the two-sided Laplace transform, limitations of these methods, the Z transform. The real and complex number systems, basic set theory and topology, sequences and series, continuity, differentiation, Taylor's theorem.
Emphasis is placed on careful mathematical reasoning.
The Riemann-Stieltjes integral, uniform convergence of functions, Fourier series, implicit function theorem, Jacobians, and derivatives of higher order. Selected topics from projective geometry and convex geometry. May be repeated for credit. May be repeated for credit. May be repeated for credit.