Not available at this time.

Not available at this time.

Not for credit toward major. How cancer and AIDS begin and progress. The roles of individual cells, the immune system, mutations and viruses. How various physical and subtle factors influence one's chances of getting cancer. How to not get AIDS. The principles of vaccine development and why AIDS presents special difficulties. Established and new medical treatments for cancer and AIDS. What cancer and AIDS can teach us about health, healing, disease, living, and dying. (Gen.Ed. BS)

Maximum credit, 6.

Maximum credit, 6.

This class is a second course in algebraic topology, taking the next steps after (co)homology and homotopy. The central objects of study are vector bundles, which are families of vector spaces parametrized by a topological space. Associated to a vector bundle are cohomology classes called characteristic classes, which provide a measure of how ``twisted" the bundle is.

Introduction to the modern methods in partial differential equations. Calculus of distributions: weak derivatives, mollifiers, convolutions and Fourier transform. Prototype linear equations of hyperbolic, parabolic and elliptic type, and their fundamental solutions. Initial value problems: Cauchy problem for wave and diffusion equations; well-posedness in the Hilbert-Sobolev setting.

This course introduces Riemann surfaces from the points of view of 1-dimensional complex manifolds and also 2-dimensional real oriented conformal manifolds. Topics covered included the structure of holomorphic maps between Riemann Surfaces (Riemann-Hurwitz Theorem), holomorphic line;vector bundles, Chern classes, the Picard group of holomorphic line bundles, the Abel-Jacobi map, and the basic theorems of Riemann Surface theory: Mittag-Leffler, Riemann-Roch, Serre duality, Kodaira embedding and Serre's GAGA principle.

Valuations, rings of integral elements, ideal theory in algebraic number fields of algebraic functions of one variable, Dirichlet unit theorem and Riemann-Roch theorem for curves. Prerequisites: Math 611, 612 or equivalent.

Inverse and implicit functions theorems, rank of a map. Regular and critical values. Sard's theorem. Differentiable manifolds, submanifolds, embeddings, immersions and diffeomorphisms. Tangent space and bundle, differential of a map. Partitions of unity, orientation, transversality embed-dings in Rn. Vector fields, local flows. Lie bracket, Frobenius theorem. Lie groups, matrix Lie groups, left invariant vector fields, tensor fields, differential form, integration, closed and exact forms. DeRham's cohomology, vector bundles, connections, curvature.