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Applied Linear Algebra

Code

IT-ALI1

Version

2.0

Offered by

ICT Engineering

ECTS

5

Prerequisites

Upper level mathematics equivalent to A-levels.

There is a limit of 40 participants in the course. In the event that more than 40 students select the course, we will select the 40 students based on their grades in DMA1 or other equivalent math courses.

Main purpose

The purpose of the course is to equip the student with basic knowledge about linear algebra and its applications. This will enable the student to not only understand but also apply linear algebra in solving practical engineering problems. Skills in linear algebra are of high importance when dealing with scientific computing, image processing graphics, robot technology, algorithmics, coding theory, and more. As an example, the fo​unders of Google have cited their course in linear algebra as the backbone of Google’s PageRank feature (i.e. ordering web pages after importance). The course familiarizes students with scalars, vectors, matrices, determinants, operations on vectors and matrices, and systems of linear equations in matrix form. The course also presents applications of matrix theory to linear models, including examples from engineering.

Knowledge

After successfully co​mpleting the course, the student will have gained knowledge about:

  • What a vector space is, and
  • How a linear representation of such spaces can be analyzed using matrix operations
  • Application of linear algebra in engineering

 

Skills

After successfully completing the cours​e, the student will be able to:
  • Apply techniques and results from linear algebra to solve problems in linear systems, matrices, vector space, orthogonality, eigen vectors, and eigenvalue
  • Apply theory to analyze basic theoretic tasks within the below mentioned topics
  • Express mathematically correct arguments
  • Use mathematical terminology and symbol language

 

Competences

After successfully ​completing the course, the student will have acquired competences in:

  • Applying linear algebra to the study of various phenomena in engineering science
  • Using matrices to solve concrete problems
  • Using vector operations to solve concrete problems
  • Applying methods and results from linear algebra in the solution of engineering problems
 

Topics

 

Teaching methods and study activities

The course is taught as an intensive 3-week course starting Monday week 32. The total workload is expected to be around 120 hours.

Topics: 

  • Systems of linear equations and their solutions
  • Matrix algebra
  • Determinants
  • Vector spaces
  • The eigenvalue problems
  • Orthogonality
  • Singular value decomposition

Resources

David C. Lay, 4. edition: Linear Algebra and its applications
Python

Evaluation

Examination

Exam prerequisites:
None

Type of exam
The final exam has two parts.

  • The first part is a Flowlock exam in Wiseflow. 
  • The second part is a Wiseflow exam without Flowlock.

The second part must be completed in the Jupyter Notebook environment and the answers must be submitted in Wiseflow.
The exam has a total duration of 4 hours. The student will not be able to access the second part before the first part is concluded.
Each part has a duration of 2 hours and weighs equally in the final grade. 
​Internal assessment

Tools allowed

In the first part the students are allowed to use any notes, books, and/or other written/printed material and will have access to pdf files on their laptop.
In the second part all supplementary materials and aids are allowed, e.g., using a computer as a reference work.
It is not allowed, however, to use AI-tools such as CoPilot, ChatGPT, Bing, etc. as per the general VIA rules.
Communication of any sort is not allowed during the exam and will lead to expulsion of all involved parties from the exam.

​Re-exam
Re-exams may be oral.

Grading criteria

Grading according to the 7-point grading scale..

 

Additional information

For more information, please contact Richard Brooks (rib@via.dk).

Responsible

Richard Brooks (rib)

Valid from

8/1/2023 12:00:00 AM

Course type

6. semester
7. semester
Electives
Web 6 og 7

Keywords

Linear algebra, matrices, vectors