## autumn 2020 MAT-3802 Discrete Mathematics with Game- and Graph Theory - 5 ECTS

Last changed 31.12.2020

Applicants from Nordic countries: 1 June. Exchange students and Fulbright students: 15. April.

## Type of course

Theoretical. The course can be taken as a single course.

Recommended passed mathematics courses in the bachelor engineering education or corresponding mathematics courses.

Application code: 9371

## Course overlap

SMN6192 Discrete Mathematics 5 stp
SMN6192 Game- and Graph Theory / Discrete Mathematics 5 stp

## Course content

• Combinatorics including combinations
• Properties of integers and number theory
• Types of proofs
• Relations and functions, equivalence relations
• Finite state machines and minimization of these
• Recurrence relations with unarranged problems
• Graph theory
• Examples of applications in gaming

## Recommended prerequisites

IGR1518 Mathematics 1 (3-semester), IGR1600 Mathematics 1, IGR1601 Mathematics 2, IGR1613 Mathematics 3 / Physics 2, TEK-1507 Mathematics 1, TEK-1510 Mathematics 1 (3-semester), TEK-1516 Mathematics 2, TEK-2800 Mathematics 3, TEK-2801 Physics 2

## Objectives of the course

Knowledge (K):

After completing the linear algebra course the candidate:

• Has advanced knowledge of concepts within discrete mathematics.
• Has thorough knowledge of central arguments, combinatorial counting methods and methodologies within the listed concepts in discrete mathematics and know how to apply these in mathematical problems.
• Can analyse formulated discrete problems and identify methods to solve these.

Skills (S):

After completing the linear algebra course the candidate:

• Can recognize and identify discrete problems, make use of a variety of counting methods, elementary number theory, finite state machines, recurrence relations and graphs and trees in order to solve problems.
• Can analyse and deal critically with theories and arguments within the field and use these to structure and formulate scholarly arguments.
• Can identify arguments that can be utilized to solve practical problems like unarranged recurrence relations and game related tasks.

General competence (GC):

After completing the linear algebra course the candidate:

• Can analyse relevant discrete mathematics problems.
• Can apply the knowledge and skills within discrete mathematics to complete assignments.
• Can communicate about different aspects in discrete mathematics, particularly explaining in mathematical terms how to deal with counting problems.
• Can use the knowledge for concepts, theories and methods in discrete mathematics in relevant engineering areas.

English

## Teaching methods

The course is taught intensively during two non-consecutive weeks, in which a combination of lectures followed by task solving sessions and project work.

All lectures are streamed and recorded. Videos provided in addition to this are made available to all students attending the course.

## Assessment

Course work requirements:

One individual project work in Graph Theory must be submitted and approved in a 3-steps process.

Examination and assessment:

A written school exam, 3 hours.

Scale of grades: A-F in which F means ‘fail’

A re-sit exam will be arranged for this course