DS820: Discrete Methods for Data Science

Study Board for Natural Scientific IT Programmes

Teaching language: Danish
EKA: N340093112, N340093102
Assessment: Second examiner: None, Second examiner: External
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master

STADS ID (UVA): N340093101
ECTS value: 10

Date of Approval: 27-03-2025


Duration: 1 semester

Version: Approved - active

Internal Course Code

DS820

Comment

The course is co-read with DM547, DM549 og MM537.

Entry requirements

The course cannot be chosen by students who: have either followed, or have passed DM549, MM537 or DM547.
The course cannot be taken by students enrolled in the master programme in Computer Science.

Academic preconditions

Knowledge and skills corresponding to A-level in mathematics from the Danish ‘gymnasium’.

Course introduction

The course will train the students to deal with mathematical concepts important to Data Science. This is necessary for the students to be able to describe, analyze, and solve problems met in Data Science.

The course gives an academic basis for studying the topics of all Computer Science courses on later semesters.

Expected learning outcome

The learning objectives of the course are that the student demonstrates the ability to:
  • formalize logic expressions correctly
  • use various proof methods such as direct proofs, proofs by contraposition, proofs by contradiction, and induction
  • use concepts, results, and techniques acquired in the course for solving concrete (known or new) problems
  • argue sufficiently for the chosen solutions
  • express problems, solutions, and arguments succinctly

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 a)

Timing

Autumn

Tests

Mandatory assignments

EKA

N340093112

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

N340093102

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

Additional information

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

Indicative number of lessons

84 hours per semester

Teaching Method

Planned lessons: 
Total number of planned lessons: 84 
Hereof: 
Common lessons in classroom/auditorium: 84 
 
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 that encourage more student interaction. 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

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.