Temple University 3 credits MATH
This course introduces students to the basic objects, tools, and questions of algebraic number theory. The focus is on number fields and their rings of integers, though some topics related to local fields or global function fields may be introduced. After covering the basics of Dedekind domains and the behavior of prime ideals in extension fields, the two major finiteness theorems -- Dirichlet's unit theorem and the finiteness of class groups -- are proved. Additional possible topics include the analytic class number formula, Dirichlet's Theorem for primes in arithmetic progressions, Chebotarev's Density Theorem, the Kronecker-Weber Theorem, and an introduction to class field theory.
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