MATH 586
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Introduction to Algebraic Number Theory
Mathematics
College of Computational, Mathematical, & Physical Sciences
Course Description
Algebraic integers; different and discriminant; decomposition of primes; class group; Dirichlet unit theorem; Dedekind zeta function; cyclotomic fields; valuations; completions.
When Taught
Fall Even Years
Min
3
Fixed/Max
3
Fixed
3
Fixed
0
Other Prerequisites
Math 372 or equivalent.
Title
Overview
Learning Outcome
Number Fields
Prime decomposition in rings of integers
Ideal Class Group
Dirichlet's unit theorem
Cebotarev Density Theorem (Statement)
Dedekind zeta function
Title
Learning Outcomes
Learning Outcome
Students should achieve an advanced mastery of the topics listed on the 586 Math Wiki page. This means that they should know all relevant definitions, correct statements and proofs of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving difficult problems related to these concepts, and by proving theorems about the below concepts, even if the theorems go beyond the material in the text.
