Number Theory

2019-2020

Course Objective

- The student is able to perform basic number theoretic calculations
(including congruence arithmetic, primes, continued fractions algorithm,
arithmetic functions, Jacobi symbols, constructions of rational points
on conic sections and cubic curves from other rational points) to solve
concrete problems.
- The student knows some central applications, open problems, and
related directions in number theory (including factorization,
cryptography, abc-conjecture, Mason-Stothers theorem) and can analyze
their consequences for specific situations.
- The student knows fundamental number theoretic concepts and theorems
(including primitive roots, quadratic reciprocity, Diophantine
equations, some algebraic number theory, continued fractions) and can
solve problems/create proofs about and with those in explicit
situations.

Course Content

The following subjects will be treated:
- integers, primes, prime distribution
- congruences, primitive roots
- primality tests, factorization
- public key cryptography
- quadratic reciprocity
- Diophantine equations, abc-conjecture
- algebraic numbers, algebraic integers
- continued fractions

Next to a theoretical approach, practical/algorithmic aspects will also
be covered. The mathematics software system "SageMath" will be used to
illustrate some explicit number theoretic calculations.

Teaching Methods

Lectures and exercise sessions (‘werkcolleges’), both 2 hours per week.

Method of Assessment

Homework assignments (25%) and a final written exam (75%).
Extra rule: the grade for the final exam must be at least 5.0 in order
to pass the course.

The re-examination possibility consists of a written exam whose mark
determines the final grade in principle for 100%.

Literature

Lecture notes, the relevant literature will be made available online.

Target Audience

Third year BSc Mathematics.

Recommended background knowledge

Basic knowledge of groups, rings, and fields is essential.

General Information

Course Code X_400632
Credits 6 EC
Period P1+2
Course Level 400
Language of Tuition English
Faculty Faculty of Science
Course Coordinator dr. S.R. Dahmen
Examiner dr. S.R. Dahmen
Teaching Staff dr. S.R. Dahmen

Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: