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.

Instruction Details

Types of instruction: Lectures, seminars

Examination Details

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

Contact and Other Information

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