NSCPHD1024 Transcendental numbers

Volume 2015/2016

MSc Programme in Mathematics



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The aim of this course is to discover some techniques for
proving that a number is transcendental. The course will start from
simple and very classical examples (Pi, e, Zeta(2), etc) and will move
on to more recent results, including theorems of Gelfond, Schneider,
Lang, Mahler, Beukers, Rivoal.

Learning Outcome

Knowledge: The student should be familiar with the main results of the 
topics of the course.
Skills: At the end of the course the student is expected to be able to follow
and reproduce arguments at a high, abstract level corresponding to the
contents of the course.
Competences: The student should be able to apply the theory to solve 
problems of moderate difficulty within the topics of the course. In 
particular decide whether a number is transcendental or not using a 
combination of different results from the course.

Algebra 3 or a similar course is an advantage
6 hours of lectures and 2 hours of tutorials each week for 7 weeks
  • Category
  • Hours
  • Exam
  • 2
  • Exercises
  • 14
  • Lectures
  • 42
  • Preparation
  • 148
  • Total
  • 206
7,5 ECTS
Type of assessment
Written examination, 2 hours under invigilation
Continuous assessment
Two assignments counts each 10% and a final written exam counts the remaining 80% of the grade
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.

Resubmission of failed assignments and an oral exam with several internal examiners. The failed assignments must be re-submitted at the latest two weeks before the beginning of the re-exam week.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.