DM549: Discrete Mathematics

Study Board of Science

Teaching language: Danish or English depending on the teacher
EKA: N330079102, N330079142
Assessment: Second examiner: External, Second examiner: None
Grading: 7-point grading scale, Pass/Fail
Offered in: Odense
Offered in: Autumn
Level: Bachelor

STADS ID (UVA): N330079101
ECTS value: 10

Date of Approval: 03-04-2024


Duration: 1 semester

Version: Approved - active

Comment

The course is co-read with DM547, DS820, MM537.

Entry requirements

The course cannot be taken by students who have passed DM547, MM537, MM540, MM568 or DS820.

Academic preconditions

See danish version

Course introduction

Participants should learn basic techniques for working with mathematical concepts important to computer science. This is an essential prerequisite for describing, analyzing, and solving problems in computer science.

The course lays a foundation for all courses on the second semester of the computer science education.

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

  • communicate knowledge of several proof methods
  • give the competence of analyzing and generalizing problems and algorithms in computer science
  • give the skill of formulating ones knowledge in a clear and precise manner
  • develop the skills of describing, analyzing, and solving problems in computer science using modeling formalisms from the core areas of computer science and their mathematical underpinning.

Expected learning outcome

The learning objectives of the course are that the student demonstrates the ability to:

  • express statements as formal logical propositions
  • write statements concisely
  • use various proof methods such as direct proofs, proofs by contraposition, proofs by contradiction, and proofs by induction
  • use concepts, results, and techniques learned in the course for solving concrete problems that may or may not be know from the course

Content

The following main topics are contained in the course:

  • Logic
  • Proof techniques: Direct proof, proof by contraposition, proof by contradiction, and proof by induction
  • Sets and cardinality
  • Functions
  • Recursive definitions and strong induction
  • Relations, including various representations of relations, closures, partial orders and equivalence relations
  • Number theory, including divisibility, primes, and congruences
  • Structural induction
  • Matrices: addition, multiplication, and transposition
  • Sequences and series
  • Counting techniques, including permutations, combinations, and binomial coefficients

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element b)

Timing

January

Tests

Written examination

EKA

N330079102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card - Exam number

Language

Normally, the same as teaching language

Duration

4 hours

Examination aids

All common aids are allowed e.g. books, notes, computer programmes which do not use internet etc. 

Internet is not allowed during the exam. However, you may visit system DE-Digital Exam when answering the multiple-choice questions. If you wish to use course materials from itslearning, you must download the materials to your computer the day before the exam. During the exam itslearning is not allowed.  

ECTS value

9

Exam element a)

Timing

Autumn

Tests

Mandatory assignments

EKA

N330079142

Assessment

Second examiner: None

Grading

Pass/Fail

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course.

ECTS value

1

Indicative number of lessons

84 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase. These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

  • Intro phase (lectures, class lessons) - 42 hours
  • Training phase: 42 hours
  • Study phase: 20 hours
In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the training phase hours.

Activities during the study phase:
  • Solve assignments
  • Read the assigned literature
  • Practice to apply the acquired knowledge.

Teacher responsible

Name E-mail Department
Kevin Schewior kevs@sdu.dk Algoritmer

Timetable

Administrative Unit

Institut for Matematik og Datalogi (datalogi)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.