DM547: Discrete Mathematics

Study Board for Natural Scientific IT Programmes

Teaching language: Danish or English depending on the teacher
EKA: N330014112, N330014102
Assessment: Second examiner: None, Second examiner: External
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Bachelor

STADS ID (UVA): N330014101
ECTS value: 5

Date of Approval: 12-03-2025


Duration: 1 semester

Version: Archive

Internal Course Code

DM547

Comment

Unlimited number of participants.
Joint teaching with DM549: discrete methods for computer science and MM537: Introduction to mathematical methods.

Entry requirements

The course cannot be chosen by students, who has have either followed or passed DM549, DS820, MM537, MM540 or MM568.

Academic preconditions

Students who follow the course are expected to have A level in mathematics from an upper secondary school education.

Course introduction

See Danish version

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
  • argue sufficiently for the chosen solutions

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

    Literature

    See itslearning for syllabus lists and additional literature references.

    Examination regulations

    Exam element a)

    Timing

    Autumn

    Tests

    Mandatory assignments

    EKA

    N330014112

    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

    Exam element b)

    Timing

    January

    Tests

    Written exam

    EKA

    N330014102

    Assessment

    Second examiner: External

    Grading

    7-point grading scale

    Identification

    Student Identification Card - Exam number

    Language

    Normally, the same as teaching language

    Duration

    3 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

    4

    Additional information

    The exam paper is MCQ format. The MCQ is handed out in the system DE-Digital Exam 

    Indicative number of lessons

    48 hours per semester

    Teaching Method

    Planned lessons:

    Total number of planned lessons: 48
    Hereof: 
    Common lessons in classroom/auditorium: 48 


    In the lectures 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. In these lessons there is room for questions and discussions. In the team lessons the students work with problems related to the content of the previous lectures. In these lessons there is a possibility of working specifically with selected difficult concepts. 
     

    Other planned teaching activities: 
    • Solve assignments
    • Read the assigned literature
    • Practice applying the acquired knowledge

    The students work independently with problems, developing their understanding of the terms and concepts of the topic. Questions arising during this phase can afterwards be presented in either the lectures or during team lessons.

    Teacher responsible

    Name E-mail Department
    Kevin Aguyar Brix kabrix@imada.sdu.dk Institut for Matematik og Datalogi
    Lene Monrad Favrholdt lenem@imada.sdu.dk Institut for Matematik og Datalogi

    Additional teachers

    Name E-mail Department City
    Teresa Anna Steiner Steiner@imada.sdu.dk Institut for Matematik og Datalogi

    Timetable

    Administrative Unit

    Institut for Matematik og Datalogi (datalogi)

    Team at 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.