Topics in Algebraic Number Theory

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.)


MIT Course Number


As Taught In

Spring 2006



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Course Description

Course Features

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 throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.

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This is a graduate-level course in Algebraic Number Theory. The content varies year to year, according to the interests of the instructor and the students.

Related Content

Kiran Kedlaya. 18.786 Topics in Algebraic Number Theory. Spring 2006. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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