Teaching |

Advanced Probability Theory

Wed, 01 Jan 2025 00:00:00 +0000

Based on the rigorous foundations of probability theory, hinging on measure and integration theory, this course covers a number of topics and methods from the theory of probability that are all of crucial importance for modern probability theory. The most significant subjects covered in the course include: Convergence in probability and in distribution, Fourier transforms and characteristic functions, The Central Limit Theorem, series of independent random variables, The Strong Law of Large Numbers, conditional expectations, martingales, submartingales and supermartingales.

Data Project

Thu, 01 Feb 2024 00:00:00 +0000

The fully-fledged data scientist has well-developed communicative, analytical and technical skills. The purpose of this course is to strengthen these competencies through a project where a professional issue can be elucidated and understood through a careful analysis of associated data. The issues, analyses and results are presented and discussed in writing and orally by the students in order to be able to communicate a data analysis, argue and relate to basic assumptions and preliminary conditions, derive and explain models and the associated analyses, discuss the results of the analysis, and address which questions have been answered and which remain open.

Linear Transformations

Fri, 01 Sep 2023 00:00:00 +0000

Linear algebra is the branch of mathematics which studies vector spaces, inner products on vector spaces, and linear mappings between vector spaces, the so-called linear transformations. Many problems in the natural and engineering sciences can be described and treated using methods from linear algebra; hence, the theory is at least as important as computational methods. The course’s concrete aim is to teach its participants the concepts named above and their mutual relationships, together with methods of calculation resulting from choices of basis and matrix algebra. It is often required to work with different vector spaces than R^{n or C}n. Another purpose of the course is to make the participants comfortable and familiar with using matrix representations of linear transformations on abstract vector spaces.

Ordinary Differential Equations

Sat, 01 Apr 2023 00:00:00 +0000

Differential equations is an important tool in all natural sciences. They are studied both for their strength as a modelling tool, and because of their central role in pure mathematics. This course will be concerned with the socalled ordinary differential equations, among which the linear differential equations with constant coefficients are known from the course ‘Linear Algebra’. The aim of the course is to give the participants knowledge of fundamental results and methods from the theory of ordinary differential equations. We will focus partly on solution methods for separable and linear equations, and partly on qualitative methods for analysing solutions, that is methods that do not depend on explicit knowledge of the form of the solutions.

Advanced Calculus for Engineers

Wed, 01 Feb 2023 00:00:00 +0000

The course aims to provide the students with advanced knowledge on calculus, including vector analysis. The knowledge is made operational by solving problems related to buildings and infrastructure along with building design, analytically as well as numerically. One of the primary purposes is to prepare the student for solving mathematical problems and formulate mathematical models related to solid mechanics and fluid mechanics, including continuum mechanics. Another purpose is to prepare the student for analysing problems related to optimisation as well as geometry and form-finding. Finally, the course serves as preparation for the analysis of dynamic processes.