EAUMP-ICTP School: Topics in Concrete Mathematics – Kigali, Rwanda

This School will be held at the ICTP-East African Institute for Fundamental Research [EAIFR] in Kigali, Rwanda; it will offer students concrete and effective mathematical tools from algebra, group theory and geometry that can be applied to any scientific field.

Description of Courses:

• Advanced linear algebra

This goes beyond a first course on the subject. Topics like Jordan normal form will be studied as well as bilinear forms, multilinear forms and tensor products;

• Groups, Counting and FFT

We start with group theory via rotations in 3d space; this will be used in Pólya counting problems. We then moves on to character theory culminating in fast Fourier transform;

• Introduction to Lie Algebras

The course introduces Lie algebras and aims towards of the classification of semisimple Lie algebras  which is widely considered one of the most elegant results in mathematics;

• Modular forms

The course introduces modular forms. We will study many concrete
examples, like the Eisenstein series, from which we will construct
the finite dimensional spaces of modular forms of any weight.