**EDUCATIONAL PROGRAMMES**

#### Mathematics for Engineering and Systems Biology

This course prepares graduate-level students for the demands and challenges in mathematics and statistics of our PhD program. It provides an overview of a wide range of essential topics ranging from basics of sets to multidimensional calculus, differential equations, linear algebra, numerical solutions of nonlinear systems, and stochastic calculus. Related topics in systems biology will also be outlined.

#### Signal Processing for Engineering and Systems Biology

This graduate-level course covers advanced topics in signal processing (e.g., spectral estimation, Wiener filtering, adaptive signal processing, etc) and introduces related scientific challenges in systems biology.

#### Differential and Information Geometry

This course introduces the concepts of differential and information geometry to students with undergraduate knowledge of calculus, analytical geometry and statistics. The course is divided into two parts, one mainly concerned with differential geometry while the following part focuses on information geometry. However, throughout the course many connections are made between the two fields. The aim is to provide a thoughtful and rigorous introduction that will allow students to grasp the intuition behind general concepts of differential geometry and to become familiar with the techniques and possible applications of information geometry.

#### Real Mathematics for Engineers (and Mathematicians)

This graduate level programme will endeavour to convey the importance and usefulness of advanced mathematics by demonstrating how concepts and results from analysis, geometry and topology provide a high-up vantage point from which can be spied the route to solutions of otherwise seemingly complicated or intractable problems of relevance to engineers.The course is founded on the belief that it is faster to gain a working command of advanced mathematics not by studying in depth one area of mathematics at a time, but rather, by tackling problems carefully chosen to showcase the strength of combining different areas of mathematics to offer

up a solution. Techniques which are learnt in response to solving a meaningful problem are more likely to be remembered and better understood than techniques learnt for their own sake.

#### Introduction to Stochastic Filtering

NSP Lab periodically holds an advanced introductory course on stochastic filtering. The course is divided into four self contained topics. 1-Conditional expectation and statistics, 2-Discrete time martingales, 3-Ito Calculus, 4-Equations of optimal filtering. Stochastic filtering is the process of using partial observations corrupted by noise to make inference about an evolving system. It has important applications in most branches of engineering and is a fundamental part of signal processing theory. The goal of this course is to quickly build prerequisite knowledge which will allow students to access the stochastic filtering literature and have a global view of the subject which will allow them to understand ongoing research.