Mathematics 772-773: Algebraic Number Theory, Analytic Number Theory

General Information:

Course Description:

Algebraic Number Theory: A topics course in algebraic number theory. Selected topics include quadratic reciprocity, quadratic forms, rings of algebraic integers and Dedekind domains, factorization of elements and ideals, the different and discriminant, ramification, units, ideal classes and class number, norms, distribution of primes, orders, p-adic techniques, ideles and adeles, and elementary class field theory.

Analytic Number Theory: A topics course in analytic number theory. Selected topics include zeta-functions and L-functions, p-adic analysis, prime distribution, Dirichlet density, Chebotarev's density theorem, applications to quadratic fields.

Outline:

Goals:

Current Syllabus (Fall 1999-2000)

Note:

• Special Needs: "Any students with disabilities or other special needs, who need special accommodations in the course, are invited to share these concerns or requests with the instructoras soon as possible."
• Academic Honesty: All work in this course must be completed in a manner consistent with NDSU University Senate Policy, Section 335: Code of Academic Responsibility and Conduct.