COURSE SYLLABUS

On completion of the course the student shall:

• show familiarity with the mathematical language used in set, vector and matrix calculations, as well as in probability and statistics theory

• demonstrate the ability to compute partial derivatives, find directional derivatives and identify the directions of fastest increase and decrease of a differentiable function
• demonstrate the ability to identify and classify local critical points of a function
• demonstrate the ability to perform basic probability calculations involving random variables
• demonstrate the ability to compute point and interval estimates of relevant statistical parameters from a random sample
• demonstrate the ability to perform hypothesis tests of various kinds
• demonstrate the ability to design an experiment using a single facor design

• demonstrate an understanding of the concept of random variability and judge the benefits and risks of using different statistical models

The course contains elements from various fields of mathematics and mathematical statistics used when intelligent systems and machine learning are developed, used and analyzed.

The course includes the following elements:

• Vector and matrix calculations, linear maps Rn to Rm, eigenvectors and eigenvalues.
• Partial and total order relations, complexity, Big-O notation
• Partial derivatives, gradients, local convexity and extrema for smooth functions Rn to R
• Basic probability theory, Bayes’ theorem
• Discrete and continuous random variables
• Probability distributions, in particular binomial and normal distribution
• Point and interval estimation
• Hypothesis tests
• Single factor design experiments

Lectures and tutorials.

Language of instruction is in English.

Please note that changes may be made to the reading list up until eight weeks before the start of the course.

Course material will be distributed during the course.