Print Course syllabus
Course syllabus - Discrete Mathematics, a Second Course
Scope
7.5 credits
Course code
MMA500
Valid from
Autumn semester 2022
Education level
Second cycle
Progressive Specialisation
A1N (Second cycle, has only first-cycle course/s as entry requirements).
Main area(s)
Mathematics/Applied Mathematics
School
School of Education, Culture and Communication
Ratified
2013-02-01
Revised
2021-12-14
Literature lists
Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.
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Books
Diskret matematik : fördjupning
Lund : Studentlitteratur, 2003 - [2], ix, [1], 393 s.
ISBN: 91-44-02878-4 LIBRIS-ID: 8860062
Compendiums
More Discrete Mathematics
Relations and Functions
Reference Literature
Combinatorics : topics, techniques, algorithms
Cambridge : Cambridge Univ. Press, cop. 1994 - 355 s.
ISBN: 0-521-45761-0 (hft.) LIBRIS-ID: 5021516
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
At least 30 credits in mathematics/applied mathematics including Discrete Mathematics, 7.5 credits, Basic Vector Algebra, 7.5 credits, and Basic Calculus, 7.5 credits, or equivalent, and 7.5 credits within the main field of computer science.
In addition Swedish course 3/Swedish course B and English course 6/English course A are required. For courses given entirely in English exemption is made from the requirement in Swedish course 3/Swedish course B.
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
Pass with distinction, Pass with credit, Pass, Fail