• Description

• Prior knowledge

• Learning objectives and results

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

Knowledge
- 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.

Skills
- 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.

Competencies
- 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.

• Content

Module 1. Complex Numbers

Module 2. Linear Systems of Equations

Module 3. Vector Spaces

Module 4. Linear Transformations

Module 5. Geometric Transformations

• View the UOC learning resources used in the subject

• Additional information on support tools and learning resources

• Guidelines on assessment at the UOC

The assessment process is based on students' own work and the assumption that this work is original and has been carried out by them.

In assessment activities, the following irregular behaviours, among others, may have serious academic and disciplinary consequences: someone else being involved in carrying out the student's assessment test or activity, or the work being not entirely original; copying another's work or committing plagiarism; attempting to cheat to obtain better academic results; collaborating in, covering up or encouraging copying; or using unauthorized material, software or devices during assessment.

If students are caught engaging in any of these irregular behaviours, they may receive a fail mark (D/0) for the assessable activities set out in the course plan (including the final tests) or in the final mark for the course. This could be because they have used unauthorized materials, software or devices (e.g. social networking sites or internet search engines) during the tests, because they have copied text fragments from an external source (internet, notes, books, articles, other student's projects or activities, etc.) without correctly citing the source, or because they have engaged in any other irregular conduct.

In accordance with the UOC's academic regulations , irregular conduct during assessment, besides leading to a failing mark for the course, may be grounds for disciplinary proceedings and, where appropriate, the corresponding punishment, as established in the UOC's coexistence regulations.

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

• Ask the student to provide proof of their identity, as established in the university's academic regulations.
• Request that students provide evidence of the authorship of their work, throughout the assessment process, both in continuous and final assessment, by means of an oral test or by whatever other synchronous or asynchronous means the UOC specifies. These means will check students' knowledge and competencies to verify authorship of their work, and under no circumstances will they constitute a second assessment. If it is not possible to guarantee the student's authorship, they will receive a D grade in the case of continuous assessment or a Fail in the case of final assessment.
  For this purpose, the UOC may require that students use a microphone, webcam or other devices during the assessment process, in which case it will be the student's responsibility to check that such devices are working correctly.

• View the assessment model