DAFE1000 Mathematics 1000 Course description

Through the work in this course, the students will gain insight into areas of mathematics that are important to the modelling of technical and natural science systems and processes. The topics covered are included in engineering programmes the world over. The topics are necessary in order to enable engineers to communicate professionally in an efficient and precise manner and to participate in professional discussions. Students will practise using, and to some extent also develop, mathematical software in the work on the course, which will enable to perform calculations in a work situation. Such implementations are exclusively motivated by numerical problems solving and understanding mathematical concepts.

No requirements over and above the admission requirements.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence.

Knowledge

The student can:

• explain fundamental concepts in regression analysis such as explanatory variables, response variable, explained variance, prediction intervals and the least squares method
• know of maximum likelihood estimation, likelihood ratio test, bootstrapping and generalized linear models
• explain how machine learning methods are trained, validated, and evaluated
• explain the difference between local and global explanations, and how the explainability methods partial dependence plot, accumulated local effects plot, Friedman's H-statistic, and surrogate models work.

Skills

The student can:

• use linear and logistic regression to study the relationship between one or more explanatory variables and a response variable
• fit an appropriate regression model by studying the model's residuals and, if necessary, attempt various variable transformations and variable selection
• formulate and perform hypotheses tests and calculate confidence intervals for parameters in a regression model
• identify the most important predictors in a model using explainable artificial intelligence (XAI)
• write source code to perform calculations for regression analyses and XAI in Python

General competence

The student can:

• apply statistical thinking to real-world problems and communicate these both in writing and orally
• solve real-world problems using regression analysis, machine learning and XAI
• identify the limitations of the methods and assess similarities and differences with methods from mathematical modeling, numerical analysis, and machine learning

Lectures and individual exercises. The exercise sessions will consist of both problem-solving and programming.

The following coursework is mandatory and must be approved to be eligible for the exam:

Three mandatory assignments, of which at least two must be approved. The work is done in groups of 1-4 members.

Individual written exam of 3 hours under supervision.

The exam result can be appealed.

In the event of resit or rescheduled exams, another exam form may also be used. If oral exams are used, the result cannot be appealed.

All written and printed aids are allowed. Handheld calculator that cannot be used for wireless communication or to perform symbolic calculations. If the calculator has the capability for internal memory storage, the memory must be cleared before the exam. Random checks may be carried out.

Grade scale A-F

One internal examiner. External examiners are used regularly.

Kristoffer H. Hellton