INTRODUCTION TO NUMBER THEORY

MATH 967

Selected topics in Number Theory.

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 749

An introduction to the Riemann zeta function and Dirichlet L-functions, and their application to topics such as the distribution of prime numbers and the arithmetic of quadratic fields. Familiarity with elementary number theory [such asMATH 567] and complex analysis [such asMATH 623] is strongly recommended.

MATH 848

This is an advanced graduate topic course in number theory. Topics will vary. Target audience: Advanced graduate students in number theory, representation theory, and algebraic geometry.

MATH 567

A course in number theory covering fundamentals and modern applications in topics of recent interest: Modular arithmetic, quadratic reciprocity, arithmetic functions, zeta function, Diophantine equations, transcendental numbers, Roth's theorem, continued fractions, and the circle method. Optional material from probability including random matrix theory.