Mathematics

This course provides a mathematical background essential for understanding the theory behind various machine learning techniques. After this course, students are able to design and execute machine learning algorithms such as regression analysis, classification with support vector machine, feedforward neural network, principal component analysis, k-means clustering, etc. without relying on pre-programmed packages. Topics of this course include (1) linear algebra (basic and advanced), (2) probability and information theory, (3) analytical geometry, (4) calculus (basic and advanced), (5) optimization, (6) machine learning applications: distance-based classifiers, Naive Bayes classifier, linear & logistic regression, neural network, SVM, PCA, k-means clustering, etc.

Probability theory, the mathematical description of chance, is a subject in its own right but also the bedrock on which statistics and data science are built. We are surrounded by important questions involving chance but our intuition on the subject is often wrong. This course gives an understanding of the subject that help students understand issues where chance plays a central role as well as preparing them for further study.
 

Through lectures and problem solving, students learn combinatorics, generating functions, recurrence relations, difference equations, and rings and fields with application to coding theory.

The aim of the course is to give the necessary knowledge of digital image analysis for further research within the area and to be able to use digital image analysis within other research areas such as computer graphics, image coding, video coding, and industrial image processing problems. The course also prepares students for further studies in computer vision, multispectral image analysis, and statistical image analysis.

This course introduces students to basic concepts from abstract algebra, especially the notion of a group. The course helps prepare students for further study in abstract algebra as well as familiarize them with tools essential in many other areas of mathematics. The course is also intended to help students in the transitions from concrete to abstract mathematical thinking and from a purely descriptive view of mathematics to one of definition and deduction.