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.
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.
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