Caput Number Theory 20/21

Uitgebreide vaknaam	Caput Number Theory 20/21
Leerdoelen	At the end of the course, the student is able to: 1. apply the bachelor's topics treated in abstract algebra and in basic mastermath courses in advanced examples relevant to the course in question. 2. apply the theory and algorithms presented in the course in concrete examples, such as computing the rational points on given algebraic curves defined over number fields. 3. understand, analyze and evaluate current techniques in an advanced topic in algebraic number theory or arithmetic geometry of current research interest, in this year the theory of rational points on curves. 4. create proofs and/or algorithms in an advanced topic in algebraic number theory or arithmetic geometry of current research interest, in this year the theory of rational points on curves. 5. use the computer algebra system magma for computations in arithmetic geometry.
Omschrijving	The subject of the course is an advanced topic in number theory of current research interest. The content varies every year. This course can lead to a master project in arithmetic geometry or algebraic number theory. This year's topic will be rational points on curves.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Werkcollege (T)
Toetsvorm	Mondeling tentamen (OR), Opdracht (AST) (To pass the course, a grade above 5.5 is required for both the oral exam and the average of the four homework sets. If this is satisfied, the final grade is computed as the average of the oral exam grade and the average of the four homework sets.)
Vaksoort	master
Coördinator	dr. J.S. Müller
Docent(en)	dr. J.S. Müller
Entreevoorwaarden	Group theory, algebraic structures and advanced algebraic structure are required. This year we also assume that students have taken or are taking at least one of the mastermath courses Algebraic Geometry 1 or Elliptic Curves. Students who would like to follow the course but are missing some of these requirements should contact the lecturer as soon as possible.
Opmerkingen
Opgenomen in	Opleiding Jaar Periode Type MSc Mathematics and Physics (double degree)  (Mathematics and Complex Dynamical Systems (40 ects)) - semester II b keuzegroep MSc Mathematics: Mathematics and Complex Dynamical Systems - semester II b keuzegroep MSc Mathematics: Science, Business and Policy  (Science, Business and Policy: Mathematics and Complex Dynamical Systems) - semester II b keuzegroep