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MM541: Combinatorial Mathematics (5 ECTS)

STADS: 13012101

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: yeo@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 10-12 U140 6-8,12
Common I Monday 09-11 U140 10
Common I Tuesday 08-10 U140 9,11
Common I Wednesday 08-10 U168 8
Common I Thursday 10-12 U182 5
Common I Thursday 14-16 U182 6
Common I Thursday 08-10 U181 9
Common I Thursday 14-16 U140 11
Common I Friday 10-12 U181 5
H16 TE Tuesday 12-14 U156 6-7,10,12
H16 TE Friday 11-12 U155 8-9,11
H17 TE Monday 14-16 U156 7
H17 TE Tuesday 11-12 U57 9
H17 TE Tuesday 12-13 U141 11
H17 TE Tuesday 10-12 U153 12
H17 TE Wednesday 10-12 U143 6
H17 TE Wednesday 11-12 U24 8
H17 TE Thursday 14-16 U148 10
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Comment:
Ubegrænset deltagerantal

Prerequisites:
None

Academic preconditions:
Students taking the course are expected to have knowledge of the topics from MM537 (Introduction to Mathematical Methods).

Course introduction
The course will teach the student to use methods from combinatorial mathematics, (algorithmic) graph theory and (primary combinatorial use of) linear programming.

  These skills are important when new algorithms are being developed and when practical problems need to be optimised. It is furthermore important for the understanding of why the given algorithms and methods work.

The course builds on the knowledge of logic and formulating proofs acquired in the course MM537. It is thus presupposed that the student can formulate simple proofs. 
 
If the course is supplemented with other courses in similar areas it is possible to write a BA-project in discrete mathematics.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give knowledge and understanding of selected mathematical subjects such as linear programming and counting techniques.
  • Give knowledge and understanding of using discrete models  and be able to criticize such models.
  • Give skills and competence in the use of the above.
 


Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
  • Count the number of elements in a set.
  • Formulate counting problem based on a written description.
  • Solve linear recursion equations.
  • Solve graph theoretical problems similar to the ones given in the course.
  • Formulate linear programming problems and use the duality theorem.
 


Subject overview
The following main topics are contained in the course:
  • Combinatorics
  • Techniques for counting permutations and combinations.
  • Binomial coefficients.
  • Inclusion/exclusion.
  • Linear recursion equations.
  • Graph Theory (definitions, transportation problems, spanning trees and matchings).
  • Greedy algorithms.
  • Linear programming and duality.
  • Algorithmic proofs.
  • Good characterizations.
 


Literature
    Meddeles ved kursets start


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
    1. Mandatory assignments. Evaluated by internal censorship by the danish 7 mark scale. (5 ECTS). (13012102).

During the course there will be three obligatory homework assignments. The first one needs to be passed and the two others each count 50% towards the final grade.



Expected working hours
The teaching method is based on three phase model.
Intro phase: 26 hours
Skills training phase: 22 hours, hereof:
 - Tutorials: 22 hours

Educational activities Study phase: 30 hours

  • Self study of the teaching material.
  • Solving weekly assignments in order to discuss these at the tutorials.
  • Written assignments as part of the exam. 
  • Self guided  follow up on the intro and tutorial classes
  • Repetition for the exam
 
Educational form
The course consists of lectures and problem sessions. During the course there is also three problem sets, where the last two has to be solved individually and the first one in a group of up to 3 people.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.