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. 


Assessment at the UOC is, in general, online, structured around the continuous assessment activities, the final assessment tests and exams, and the programme's final project.

Assessment activities and tests can be written texts and/or video recordings, use random questions, and synchronous or asynchronous oral tests, etc., as decided by each teaching team. The final project marks the end of the learning process and consists of an original and tutored piece of work to demonstrate that students have acquired the competencies worked on during the programme.

To verify students' identity and authorship in the assessment tests, the UOC reserves the right to use identity recognition and plagiarism detection systems. For these purposes, the UOC may make video recordings or use supervision methods or techniques while students carry out any of their academic activities.

The UOC may also require students to use electronic devices (microphones, webcams or other tools) or specific software during assessments. It is the student's responsibility to ensure that these devices work properly.

The assessment process is based on students' individual efforts, and the assumption that the student is the author of the work submitted for academic activities and that this work is original. The UOC's website on academic integrity and plagiarism has more information on this.

Submitting work that is not one's own or not original for assessment tests; copying or plagiarism; impersonation; accepting or obtaining any assignments, whether for compensation or otherwise; collaboration, cover-up or encouragement to copy; and using materials, software or devices not authorized in the course plan or instructions for the activity, including artificial intelligence and machine translation, among others, are examples of misconduct in assessments that may have serious academic and disciplinary consequences.

If students are found to be engaging in any such misconduct, they may receive a Fail (D/0) for the graded activities in the course plan (including final tests) or for the final grade for the course. This could be because they have used unauthorized materials, software or devices (such as artificial intelligence when it is not permitted, social media or internet search engines) during the tests; copied fragments of text from an external source (the internet, notes, books, articles, other students' work or tests, etc.) without the corresponding citation; purchased or sold assignments, or undertaken any other form of misconduct.

Likewise and in accordance with the UOC's academic regulations, misconduct during assessment may also be grounds for disciplinary proceedings and, where appropriate, the corresponding disciplinary measures, as established in the regulations governing the UOC community (Normativa de convivència).

In its assessment process, the UOC reserves the right to:

  • Ask students to provide proof of their identity as established in the UOC's academic regulations.
  • Ask students to prove the authorship of their work throughout the assessment process, in both continuous and final assessments, through a synchronous oral interview, of which a video recording or any other type of recording established by the UOC may be made. These methods seek to ensure verification of the student's identity, and their knowledge and competencies. If it is not possible to ensure the student's authorship, they may receive a D grade in the case of continuous assessment or a Fail grade in the case of the final assessment.

Artificial intelligence in assessments

The UOC understands the value and potential of artificial intelligence (AI) in education, but it also understands the risks involved if it is not used ethically, critically and responsibly. So, in each assessment activity, students will be told which AI tools and resources can be used and under what conditions. In turn, students must agree to follow the guidelines set by the UOC when it comes to completing the assessment activities and citing the tools used. Specifically, they must identify any texts or images generated by AI systems and they must not present them as their own work.

In terms of using AI, or not, to complete an activity, the instructions for assessment activities indicate the restrictions on the use of these tools. Bear in mind that using them inappropriately, such as using them in activities where they are not allowed or not citing them in activities where they are, may be considered misconduct. If in doubt, we recommend getting in touch with the course instructor and asking them before you submit your work.


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.