# Topics in Algebraic Number Theory

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.)

### Instructor(s)

Prof. Abhinav Kumar

### MIT Course Number

18.786

### As Taught In

Spring 2010

### Level

Graduate

###

Some Description
Instructor(s) | Prof.
As Taught In | Spring 2002
Course Number | 2.24
Level | Undergraduate/Graduate
Features | Lecture Notes, Student Work

## Course Description

## Course Features

- Assignments: problem sets (no solutions)

## 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.

## Other Versions

## Other OCW Versions

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.

- 18.786 Number Theory II: Class Field Theory (Spring 2016)
- 18.786 Topics in Algebraic Number Theory (Spring 2006)

## Related Content

## Course Collections

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### Find Courses by Topic

- Algebra and Number Theory

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

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