NMAK14027U Transcendental numbers

Volume 2015/2016
Education

MSc Programme in Mathematics

Content

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
Credit
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
Aid
All aids allowed

NB: If the exam is held at the ITX, the ITX will provide computers. Private computer, tablet or mobile phone CANNOT be brought along to the exam. Books and notes should be brought on paper or saved on a USB key.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Re-exam

Resubmission of failed assignments (no later than two weeks before the beginning of the re-exam week) and a 30-minutes oral exam with several internal examiners. The oral exam will be with preparation time during which all aids are allowed. During the examination no aids are allowed.

Criteria for exam assesment

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