DS820: Discrete Methods for Data Science

The course is co-read with DM547, DM549 og MM537.

The course will train the students to deal with mathematical concepts important to Data Science. This is necessary for the students to be able to describe, analyze, and solve problems met in Data Science.

The course gives an academic basis for studying the topics of all Computer Science courses on later semesters.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• Give knowledge of several proof methods
• Give the competence of analyzing and generalizing problems and algorithms met in Data Science
• Give the skill of expressing one's knowledge in a clear and precise manner
• Give skills to describe, analyze and solve Data Science problems applying methods and modeling formalisms from the core area of Data Science and its mathematical support disciplines

• formalize logic expressions correctly
• use various proof methods such as direct proofs, proofs by contraposition, proofs by contradiction, and induction
• use concepts, results, and techniques acquired in the course for solving concrete (known or new) problems
• argue sufficiently for the chosen solutions
• express problems, solutions, and arguments succinctly

The following main topics are contained in the course:

• Logic
• Sets and cardinality
• Functions
• Proof techniques: Direct proof, proof by contraposition, proof by contradiction, and proof by induction
• Number theory, including divisibility, primes, and congruences
• Matrices: addition, multiplication, and transposition
• Relations, including various representations of relations, closures, partial orders and equivalence relations
• Introduction to graphs, including trees
• Sequences and series, including convergence analysis

• Intro phase: 42 hours
• Training phase: 42 hours, all of which are tutorials