The course covers the fundamental concepts required for the description, modeling and forecasting of time series data, both in the time- and frequency-domains. Attention to the theoretical underpinnings of the subject is complemented by the analysis of real-world data sets, and a practical laboratory component introduces students to the software package R.

Poetically, “Group theory is the branch of mathematics that answers the question “What is symmetry?” (N. C. Carter).  Various physical systems, such as crystals and the hydrogen atom, can be modeled by symmetry groups. Group theory and the closely related representation theory have many applications in physics and chemistry. We first start by consider some main classes of groups such as permutation groups, matrix groups, transformation groups, topological and algebraic groups.