Algebraic Number Theory OpenCourseWare: A Free Graduate Study Course by MIT on the Study of Computer Algebra

Published Jan 03, 2009

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'Topics in Algebraic Number Theory' is a free OpenCourseWare offered by MIT. The first in a series of courses on algebraic number theory, this course covers a wide variety of topics preparing students for more in-depth study. While the course is available to undergraduate Mathematics students, it is taught at a graduate level, and prior knowledge of number theory, abstract and commutative algebra and real and complex analysis is recommended.

Topics in Algebraic Number Theory: Course Specifics

Degree Level Free Audio Video Downloads
Graduate Yes No No Yes

Lectures/Notes Study Materials Tests/Quizzes
No Yes Yes

Topics in Algebraic Number Theory: Course Description

Professor Kiran Kedlaya's course, 'Topics in Algebraic Number Theory,' provides a solid foundation for further study of number theory. Presented as a series of 25 lectures, the course guides students through a variety of topics, including Dirichlet's units theorem, decomposition and inertia groups. Other topics covered will include algebraic valuations, basic analytic methods, ramification and basic class field theory. While covering these foundational topics, students will also employ computer algebra to complete numerical experiments using SAGE (Software for Algebra and Geometry Exploration). Numerical experimentation is the key to discovering results in number theory, explains Professor Kedlaya. Several texts are recommended, including Gerald J. Janusz's Algebraic Number Fields, which is used for several of the assignments.

This course includes a list of required readings, assignments and a mid-term and final exam. If you are interested in this OpenCourseWare, visit the topics in algebraic number theory course web page.

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