Course syllabus - Discrete Mathematics, a Second Course

Objectives

The aim of the course is to give deeper and broader knowledge in discrete mathematics and its applications within various scientific disciplines. Special emphasis is put on development of high proficiency in mathematical problem solving and proof techniques.

Learning outcomes

At the end of the course the student is expected to be able to

- explain, in a way adapted to the mathematical level of the reader/listener, the concepts presented in this course,
- describe a handful of areas of applications
- give a detailed account of one area of application
- construct algebraic proofs that rely on relations, functions and group axioms
- construct combinatorial proofs that rely on bijections and properties of discrete structures like permutations and partitions
- construct graph theoretic proofs within the areas of planarity and colorability
- construct analytic proofs using generating functions
- analyze combinatorial games to formulate optimal strategies
- formulate a plan to attack a research problem in discrete mathematics, and decide the correctness of a solution to a problem.

Course content

Relations and functions. Group algebra. Permutations. Partitions and generating functions. Graph theory: planarity and colorability. Combinatorial game theory. Research in discrete mathematics. Application of student's own choice, e.g. in cryptography, computer science, games, social networks or matching.

Tuition

Lectures and group work sessions.

Specific requirements

Discrete Mathematics, 7,5 credits, Vector Algebra, 7,5 credtis, or equivalent, and 7,5 credits within the main field of computer science. In addition Swedish course B/Swedish course 3 and English course A/English course 6 are required. For courses given entirely in English exemption is made from the requirement in Swedish course B/Swedish course 3.

Examination

Exercise (INL1), 4.5 credits, marks Pass (G)
Examination (TEN1), 3 credits, marks 3, 4 or 5

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Grading scale: 5, 4, 3