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Prospectus

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Diophantine approximation (BM)

Course
2015-2016

Description
Geometry of numbers (study of lattice points in convex bodies, Minkowski’s theorems), transcendence results (transcendence of e and pi), approximation of algebraic numbers by rational numbers, and maybe, time depending, some other topics.
(See the course webpage, link below, for more information.)

Number of hours/week
2

Examination
homework assignments+oral exam. In case of many students, the oral exam will be replaced by a written exam.

Prerequisites
Analysis and algebra up to the second year.
We assume familiarity with Algebra 1 and Algebra 2 (groups and rings).
During the course we need also part of the theory treated in Algebra 3 (field extensions and Galois theory). However, it is not really necessary to be familiar with the contents of Algebra 3 since what is needed will be recalled during the course.

Literature
Lecture notes will be posted on the course website

Remark 1
The basic course is for 6 ECTS points, but interested students may extend this to 8 points by studying additional literature and/or doing some extra homework.

Remark 2
This course will not be given in 2016/17.

Course webpage