Topics in Algebraic Number Theory

Computer generated image of relatively prime integers and zeta(2)

Relatively prime integers and zeta(2): The red dots are the coprime pairs of integers (x,y) with distance at most N (N = 20 in this picture) from the origin. They are connected to the origin by non-overlapping rays. The blue dots are all pairs of integers in the same disk. Their ratio tends to 1/zeta(2) = 6/pi^2 as N tends to infinity, where zeta(s) is the Riemann zeta funtion Sum_n (1/n^s). (Image by Prof. Abhinav Kumar.)


MIT Course Number


As Taught In

Spring 2010



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Course Description

Course Features

Course Description

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

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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

Abhinav Kumar. 18.786 Topics in Algebraic Number Theory. Spring 2010. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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