Lectures will be posted here regularly in the form of videos and scanned lecture notes.
In this lecture we will focus on proving identities involving modular functions and modular forms. The course has an algorithmic flavour and is adapted for people who are interested in algorithms and programming. Also if time allows we will model sums using difference fields. This can be seen as a modest introduction to Symbolic Summmation methods used and developed by Carsten Schneider.
Topics covered in the course are
Sturm's theorem for modular forms
Dedekind Eta function
Weierstrass gap theorem
Symbolic summation using difference fields
Newman's theorem on Eta quotients
A major emphasis of the lecture is to present the basic notions, to
develop the basic ideas of the underlying algorithms and to put computer
algebra into action for concrete examples.