UE Advanced algebra and analysus - MAT239 -

The first part of this course is on analysis. It covers the topics of calculation of limits of functions, continuity (e.g., formal definition, Rolle’s theorem, intermediate value theorem) and derivatives (e.g., formal definition, mean value theorem, reciprocal functions), series expansions (e.g., Taylor polynomials, Landau notation, Taylor-Young formula and operations with Landau notations)
The second part of this course is on algebra. It covers finite dimensional vector spaces (e.g., formal definition, generators, bases, dimension theorem) and linear maps (e.g., definition, image, kernel, matrix representation, change of basis formula, practical determination of image and kernel).