Algebra Code:  22.600    :  6
View general information   Description   Prior knowledge   Learning objectives and results   Content   View the UOC learning resources used in the subject   Additional information on support tools and learning resources   Guidelines on assessment at the UOC   View the assessment model  
This is the course plan for the first semester of the academic year 2024/2025. To check whether the course is being run this semester, go to the Virtual Campus section More UOC / The University / Programmes of study section on Campus. Once teaching starts, you'll be able to find it in the classroom. The course plan may be subject to change.
This course aims to provide the student with basic training on linear algebra, which is instrumental for other subjects more directly related to computer science.

On the other hand, as a mathematics subject, it has to help the student in their scientific-technical training, providing language and methodologies typical of the mathematical and scientific disciplines. 


It is convenient to have recently taken the mathematics courses corresponding to Baccalaureate or equivalent level.


This course introduces the student to the topic of linear algebra and it is aimed at future computer scientists.

The general objectives are the following:

- Provide the student with basic knowledge and skills of algebra, necessary in the learning and application of other disciplines linked to different subjects of the degree.
- Develop the skills of the student with regard to formal modeling and subsequent resolution of problems that may arise in various fields of computing.
- Learn to use mathematical software (in this course the CALCME software will be used) that allows the student to experiment with concepts interactively and automate manual resolution of algorithms.

Specific objectives

- Introduce the set of complex numbers and understand their usefulness. Know how they are represented and learn to manipulate them.
- Learn the key concepts of the theory associated with vector spaces, matrices and determinants, and understand some of their applications.
- Learn the basic techniques of solving systems of equations using matrix theory and determinants.
- Learn how to interpret systems of linear equations geometrically.
- Know the concepts of linear dependence and independence, bases, base changes, linear transformations, diagonalization, etc.
 - Learn how to use mathematical software as a calculation, experimentation and visualization tool.

- Operate with complex numbers and know when to use this set of numbers.
- Learn how to model phenomena through systems of equations, know how to solve them and interpret the result.
- Learn how to use the concepts of linear algebra to solve geometric problems.
- Use mathematical software as a calculation and learning tool.

- Master basic mathematical language to express scientific knowledge, both written and orally
- Know the mathematical foundations of computer science 
- Know and formally represent rigorous scientific reasoning
- Know and use mathematical software
- Analyze a problem and isolate variables
- Master the most common mathematical methods in computer science and apply them in solving problems
- Have the ability to synthesize
- Have the capacity for abstraction. Ability to face new problems consciously resorting to strategies that have been useful in previously solved problems.
- Have the ability to learn and act autonomously: Know how to work independently, receiving only the essential information and guidance.


Module 1. Complex Numbers

Module 2. Linear Systems of Equations

Module 3. Vector Spaces

Module 4. Linear Transformations

Module 5. Geometric Transformations


Numbers. Natural numbers, principle of induction and complex numbers PDF
Linear systems of equations. Discussion, solution and geometric interpretation PDF
Elements of linear algebra and geometry PDF
Linear transformations. Associated matrix, eigenvalues, eigenvectors and diagonalization PDF
Geometric transformations.Translation, rotation and scaling PDF
Vector spaces Audiovisual
Matrices and systems of linear equations Audiovisual
Linear transformations Audiovisual
Complex numbers Audiovisual
Linear systems of equations. Discussion, solution and geometric interpretation PDF
Linear transformations. Associated matrix, eigenvalues, eigenvectors and diagonalization PDF


The didactic material for this subject consists of:

- A reference book.

- The CalcME calculator.

- The CalcME calculator manuals. 


The assessment process is based on the student's personal work and presupposes authenticity of authorship and originality of the exercises completed.

Lack of authenticity of authorship or originality of assessment tests, copying or plagiarism, the fraudulent attempt to obtain a better academic result, collusion to copy or concealing or abetting copying, use of unauthorized material or devices during assessment, inter alia, are offences that may lead to serious academic or other sanctions.

Firstly, you will fail the course (D/0) if you commit any of these offences when completing activities defined as assessable in the course plan, including the final tests. Offences considered to be misconduct include, among others, the use of unauthorized material or devices during the tests, such as social media or internet search engines, or the copying of text from external sources (internet, class notes, books, articles, other students' essays or tests, etc.) without including the corresponding reference.

And secondly, the UOC's academic regulations state that any misconduct during assessment, in addition to leading to the student failing the course, may also lead to disciplinary procedures and sanctions.

The UOC reserves the right to request that students identify themselves and/or provide evidence of the authorship of their work, throughout the assessment process, and by the means the UOC specifies (synchronous or asynchronous). For this purpose, the UOC may require students to use a microphone, webcam or other devices during the assessment process, and to make sure that they are working correctly.

The checking of students' knowledge to verify authorship of their work will under no circumstances constitute a second assessment.


In order to pass the course, you must sit an exam. Your mark from this will be supplemented by your mark from the continuous assessment.

  • If you get an Absent mark in the continuous assessment, your final mark for the course will be your numerical mark from the exam.
  • If your continuous assessment mark is something other than Absent, your final mark will be the more favourable of: the numerical mark from the exam; or the calculation of your continuous assessment mark weighted with your exam mark, as specified in the course plan. In order to apply this calculation, you must get a minimum mark of 4 in the exam (if your mark is lower, your final mark for the course will be your mark from the exam).
  • If you don't sit the exam, you'll receive a final mark of Absent.