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.

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.

Representation theory studies the way groups, rings and other algebraic structures can act by linear symmetries. We will consider representations of finite groups, the general linear group, the symmetric group, and quiver algebras. If time permits, we cover the theory of Soergel bimodules and applications to knot homology. We will provide suggestions for further reading to explore the beyond the listed examples. Students will prepare a presentation on a topic related to class discussion. A list of topics will offered in class.

Elliptic curves, as the only smooth projective algebraic curves equipped with a group law, play a central role in modern arithmetic geometry. The goal of this course is to learn the tools and techniques required to study these groups over the rational numbers by first studying them over finite fields, p-adic fields and archimedean fields.

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.