SEMINAR IN NUMBER THEORY

MATH 467

An introduction to proof writing techniques through a study of classical topics in elementary number theory. Topics include the divisibility, basic properties of primes, congruences, Fermat's theorem.

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.

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 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.