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Algebraic Number Theory: Course Outline (MAT-609)

Algebraic number theory is a major branch of number theory that studies algebraic structures related to algebraic integers.

Course Outline

Algebraic Numbers: Algebraic numbers and number fields, Discriminants, Norms and traces, Algebraic integers and integral bases, Factorization and divisibility, Applications of unique factorization, Quadratic fields, Cyclotomic fields, Units in number rings. Valuation rings,  Properties of Ideals, PID’s and UFD’s, Dedikind rings, norms of ideals, class group and class numbers of quadratic fields. 

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