MM568: Logic and Linear Algebra

The Study Board for Science

Teaching language: Danish or English depending on the teacher
EKA: N300055112, N300055122, N300055102
Assessment: Second examiner: None, Second examiner: Internal
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Bachelor

STADS ID (UVA): N300055101
ECTS value: 10

Date of Approval: 29-04-2025


Duration: 1 semester

Version: Archive

Comment


Entry requirements

The course can not be followed by students who: have passed: MM537, MM505, MM538, MM540, DM547 og DM549.

Academic preconditions

This course builds upon the students’ highschool competences in Mathematics.

Course introduction

The aim of the course is to enable the student to apply mathematical reasoning, mathematical methods and proof techniques and that the student achieves a basic understanding of philosophy of science. Moreover, it is the aim that the student acquires fundamental skills within the discipline of linear algebra in relation to applications in economy and linear models. The material covered is important in almost all aspects of mathematics and has wide-reaching applications in economics and throughout the natural sciences.
The course’s content is essential for later courses in the degree.

Expected learning outcome

Knowledge
  • How to prove assertions by applying proof techniques such as direct proof, indirect proof and proof by induction.
  • Understand principles of mathematical thinking and argumentation.
  • How to apply mathematical theory and results to solve concrete problems in linear algebra.
Skills
  • Ability to carry out and understand proofs.
  • Ability to present in written form precise mathematical arguments.
  • Argue in a mathematically correct and stringent way about the steps and techniques in the solution of given problems.
  • Assess whether achieved results are correct.
Competences
  • How to use concepts, results and techniques learned in this course on known as well as new concrete problems.
  • Ability to engage with abstract mathematical concepts.

Content

The following main topics are contained in the course:

  • Sets and cardinality 
  • Functions 
  • Logic 
  • Proof techniques: direct proof, proof by contrapositive, proof by contradiction and proof by induction 
  • Relations, including partial order and equivalence relations 
  • Systems of linear equations 
  • Matrices, determinants 
  • Vector spaces 
  • Linear independence and basis for vector spaces
  • Scalar product and orthogonality 
  • Linear transformations
  • Eigenvectors and eigenvalues 
  • Diagonalization 

Literature

Reading, Writing, and Proving: A Closer Look at Mathematics (2nd Edition) by Ulrich Daepp and Pamela Gorkin. 

Linear Algebra, Concepts and Methods by Martin Anthony and Michele Harvey.

Examination regulations

Exam element a)

Timing

Autumn

Tests

Obligatory assignments during the course

EKA

N300055112

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

Autumn

Tests

Obligatory assignment

EKA

N300055122

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Additional information

The re-exam will be changed to an oral exam, if 5 or fewer students are enrolled.

Exam element c)

Timing

January

Tests

Written exam

EKA

N300055102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Full name and SDU username

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 re-exam will be changed to an oral exam, if 5 or fewer students are enrolled.

Indicative number of lessons

94 hours per semester

Teaching Method

Planned lessons: 

Total number of planned lessons: 94

Hereof: 

Common lessons in classroom/auditorium: 54 

Team lessons in classroom: 40

In the lectures, the literature (curriculum) for the course will be explained, and opportunities will be provided for trying out concepts and asking questions. Lectures will be supplemented by exercise classes, where relevant exercises, relating to the lectures, will be solved and explained. 

Other planned teaching activities: 

  • Read the literature for the course
  • Solving tasks
  • Participating in discussions around tasks

Teacher responsible

Name E-mail Department
Kristin Courtney kcourtney@imada.sdu.dk Institut for Matematik og Datalogi

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

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.