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
- 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
Course ContentThe 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 MethodsLectures and exercise sessions (‘werkcolleges’), both 2 hours per week.
Method of AssessmentHomework 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%.
LiteratureLecture notes, the relevant literature will be made available online.
Target AudienceThird year BSc Mathematics.
Recommended background knowledgeBasic knowledge of groups, rings, and fields is essential.
|Language of Tuition||English|
|Faculty||Faculty of Science|
|Course Coordinator||dr. S.R. Dahmen|
|Examiner||dr. S.R. Dahmen|
dr. S.R. Dahmen
You need to register for this course yourself
Last-minute registration is available for this course.
|Teaching Methods||Seminar, Lecture|
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