ARITHMETIC GEOMETRY

MATH 764

Continuation ofMATH 763.

MATH 748

A rigorous introduction to the arithmetic of number fields; algebraic integers, geometry of numbers, Dirichlet's Unit Theorem, ideal class groups, first case of Fermat's Last Theorem; prime decompositions, Galois automorphisms. Basic graduate algebra courses (e.g.MATH 741and742) are strongly recommended.

MATH 461

An introduction to Euclidean or non-Euclidean geometry.

MATH 865

Selected from advanced projective geometry, non-Euclidean geometry, Riemannian geometry, distance geometry and the geometry of convex surfaces, geometry of numbers.

MATH 763

Algebraic preliminaries, including local rings; valuation theory, and power series rings; geometry of algebraic varieties with emphasis on curves and surfaces.