Basic knowledge of group theory (groups, (normal) subgroups, cosets, quotients, first isomorphism theorem, group actions) and complex analysis (holomorphic/meromorphic functions, Taylor/Laurent series, path integrals, the residue theorem). These concepts are covered by most introductory courses in group theory and complex analysis, respectively, and can be found in almost any standard text on (abstract) algebra and complex analysis, respectively (see e.g. texts by Ahlfors or Lang).
Aim of the course
The aim of this course is to familiarize students with basic concepts, techniques, and applications of modular form theory as well as with some modern (deep) results about modular forms and their applications. The students will also learn how to perform explicit calculations with modular forms using the (free open-source) mathematics software system SageMath.