*Course Syllabus for*
# Number Theory

Talteori

## MATM15F, 7.5 credits

**Valid from:** Autumn 2018

**Decided by:** Professor Thomas Johansson

**Date of establishment:** 2019-02-27

## General Information

**Division:** Mathematics

**Course type:** Course given jointly for second and third cycle

**The course is also given at second-cycle level with course code:** MATM15

**Teaching language:** English

## Aim

That the postgraduate student should learn the basic concepts of Number Theory. This is an important research field within Mathematics, but also has applications in Cryptography, Coding Theory and Computer Science.

## Goals

*Knowledge and Understanding*

For a passing grade the doctoral student must

- be able to state and prove the Quadratic Reciprocity Law
- be able to state and prove some results about when it is possible to express an integer as a sum of squares
- be able to account for the basic theory of Diophantine approximation of real numbers.

*Competences and Skills*

For a passing grade the doctoral student must
be able to solve systems of linear congruences.

## Course Contents

Classical theory of modulo arithmetic, quadratic reciprocity, quadratic forms and Diophantine approximation.

## Course Literature

Burton, David M.: Elementary Number Theory. 2010. ISBN 9780071289191.

**Types of instruction:** Lectures, seminars

**Examination formats:** Written exam, oral exam

**Grading scale:** Failed, pass

**Examiner:**

## Admission Details

**Assumed prior knowledge:** Calculus in one and several variables. Linear Algebra.

## Course Occasion Information

**Course coordinators:**

**Web page:** http://www.ctr.maths.lu.se/course/numtheo/