18.786 | Spring 2006 | Graduate
Topics in Algebraic Number Theory
Course Description
This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running …
This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet’s units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.
Course Info
Learning Resource Types
assignment Problem Sets
grading Exams
Illustration of Minkowski's theorem.
Some important properties of algebraic numbers follow from Minkowski’s theorem: given a lattice in a Euclidean space, any bounded, convex, centrally symmetric region of large enough volume contains a nonzero lattice point. (Image courtesy of Jesus De Loera, Department of Mathematics, University of California, Davis. Used with permission.)