Number Theory

2018-2019
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

Doel vak

- 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.

Inhoud vak

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.

Onderwijsvorm

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

Toetsvorm

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%.

Literatuur

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

Doelgroep

Third year BSc Mathematics.

Aanbevolen voorkennis

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

Algemene informatie

Vakcode X_400632
Studiepunten 6 EC
Periode P1+2
Vakniveau 400
Onderwijstaal Engels
Faculteit Faculteit der Bètawetenschappen
Vakcoördinator dr. S.R. Dahmen
Examinator dr. S.R. Dahmen
Docenten dr. S.R. Dahmen

Praktische informatie

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Werkvormen Werkcollege, Hoorcollege
Doelgroepen

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