## Graduate Program (& Advanced Certificate) Status

The course introduces the basic principles of statistics that you need in everyday life and research in the first half, and the fundamental tools about matrices and functions that you need in order to handle data.

You would experiment with many examples with the help of the tutor. Topics include

*Statistics and probability*

Basic statistics and probability theory, independence, conditional probability, expected value, standard deviation, correlation indicators (Pearson, Spearman), distributions. Multivariate distributions. Statistical tests, p-value, regression, modelling data distributions.

*Linear algebra*

Vector space, operations (scalar product, vector product), distance in multidimensional space, matrices as linear transformations, inverse of matrix, transpose, determinants, eigenvalues, eigenvectors, power of a matrix, solution of linear set of equations.

*Calculus*

Series, limit, continuity of functions. Derivative, rules, chain rule, inverse function. Higher order derivatives, analysis of functions (convexity, concavity, minimum, maximum, inflection). Multivariate functions, partial derivatives. Integration as limit, definite integrals, primitive function, relation to derivation, rules, integration by parts. Simple differential equations

The learning outcomes of the course:

By the end of the course, students are experts on the topic of the course, and how to use these methods to solve specific problems. In addition, they develop some special expertise in the topics covered, which they can use efficiently in other mathematical fields, and in applications, as well. They also learn how the topic of the course is interconnected to various other fields in mathematics, and in science, in general.

Weekly homework, midterm and final

no