Algebra
Code: 103795 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| Electronic Engineering for Telecommunications | FB | 1 |
| Telecommunication Systems Engineering | FB | 1 |
Contact
- Name:
- Gil Solanes Farres
- Email:
- gil.solanes@uab.cat
Teachers
- Pol Orobitg Bernades
- Noelia Sanchez Ruiz
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
There are no prerequisites. However, it would be beneficial for the student to have a solid understanding of the concepts of rational numbers, real numbers, and complex numbers. It is also advisable that they be familiar with some method for solving systems of linear equations.
Objectives and Contextualisation
This is an introduction to the most basic aspects of Linear Algebra, with an emphasis on the functional and instrumental aspects of linear techniques.
A fundamental objective is to achieve a smooth and efficient transition between the following three levels of knowledge:
-
the abstract understanding of a mathematical concept related to linear phenomena
-
a deeper understanding of the same concept through practical "manual" manipulation
-
a deeper understanding of the same concept through practical manipulation using a computer.
The most important underlying goal is to learn how to design efficient strategies for applying specific techniques to solve complex problems.
Learning Outcomes
- KM01 (Knowledge) Identify elementary mathematical models and tools of calculus, linear algebra and differential equations in telecommunications engineering.
- KM01 (Knowledge) Identify elementary mathematical models and tools for calculus, linear algebra, and differential equations in telecommunications engineering.
- KM03 (Knowledge) Associate the main methods of matrix decomposition with their practical applications in telecommunications engineering.
- KM03 (Knowledge) Associate the main methods of matrix decomposition with their practical applications in telecommunications engineering.
- SM01 (Skill) Solve simple matrix calculation problems, linear equations and first-order differential equations in telecommunications engineering.
- SM01 (Skill) Solve simple matrix calculus problems, linear equations and first-order differential equations in telecommunications engineering.
- SM04 (Skill) Express oneself appropriately using the basic mathematical language in telecommunications engineering.
- SM04 (Skill) Express themselves appropriately using basic mathematical language in telecommunications engineering.
Content
1. Matrices
Matrices. Operations with matrices. Special matrices: symmetric, Toeplitz, circulant, invertible, Hermitian, orthogonal.
Elementary row transformations. Gauss–Jordan normal form of a matrix. Rank of a matrix.
Invertibility criterion and computation of inverse matrices.
Systems of linear equations and linear varieties. Gaussian elimination method. Direction vectors and dimension of linear varieties. Rouché’s theorem.
2. Vector Spaces
Definition of a vector space and examples. Linear combinations of vectors. Subspaces. Generating sets.
Linear mappings. Matrix associated with a linear map. Composition of linear maps. Kernel and image subspaces of a linear map. Isomorphisms.
Linear dependence of vectors. Criterion for linear dependence.
Bases, dimension, and coordinates. Working with coordinates. Change of basis.
3. Diagonalization of matrices and scalar products.
Determinant of a square matrix. Properties of the determinant.
Eigenvalues and eigenvectors of a square matrix. Diagonalization criterion.
Applications of diagonalization: computing powers of matrices and solving systems of linear differential equations with constant coefficients.
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Lectures | 36 | 1.44 | KM01, KM01, KM03, SM01, SM04 |
| Problem sessions | 12 | 0.48 | KM01, KM01, KM03, SM01, SM04 |
| Type: Autonomous | |||
| Individual problem solving | 61.5 | 2.46 | KM01, KM01, KM03, SM01, SM04 |
| Personal study of the theory | 36 | 1.44 | KM01, KM01, KM03, SM01, SM04 |
The central part of the learning process is the student’s own work. The role of the instructor is to support the student in this task by providing information or pointing out sources where it can be found, and guiding their progress so that the learning process can be carried out effectively. In line with these ideas, and according to the course objectives, the development of the course will be based on the following activities:
- Lecture classes. The scientific and technical knowledge related to the subject will be presented in the form of lectures. These classes will introduce the basic concepts outlined in the syllabus and provide clear guidance on how to complete and deepen this content.
- Problem-solving classes. These sessions will build on the scientific and technical knowledge introduced in the lectures, with the aim of reinforcing and deepening understanding. Basic techniques will be practiced through the resolution of practical exercises.
Note: 15 minutes of one class, scheduled in accordance with the center’s or degree program’s calendar, will be set aside for students to complete surveys evaluating the instructor’s performance and the course/module.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Final test | 0.5 | 2 | 0.08 | KM01, KM03, SM01, SM04 |
| Mid-term test | 0.35 | 2 | 0.08 | KM01, KM03, SM01, SM04 |
| Problem test | 0.15 | 0.5 | 0.02 | SM01 |
Assessment will be continuous and individual. It will consist of the following:
-
A first mid-term exam during the first part of the semester, worth 35% of the final grade.
- A second mid-term exam at the end of the semester, worth 50% of the final grade.
- In-class follow-up tests, globally worth 15% of the final grade.
The final course grade is the weighted average of the midterm exams and the in-class tests, provided that the average of the midterm exams is at least 3.5 out of 10. If this condition is not met, the final grade will not exceed 3.5 out of 10.
If the final grade is 5 or higher, the course is considered passed and cannot be reassessed.
If the final grade is below 5, the student may opt for a reassessment, as described below, provided that they have completed activities representing at least 60% of the total course grade.
Reassessment consists of a comprehensive exam covering the entire course. If the grade obtained in this exam is 3.5 or higher, a weighted average will be calculated using 85% from the exam and 15% from the follow-up tests.
If this average is 5 or higher, the final grade will be a pass with a 5. Otherwise, the course will be failed with the obtained grade.
Students who opt for the single assessment system will take two exams equivalent to the midterms and one test equivalent to the follow-up tests in a single day. The weights, reassessment and other aspects of the assessment will be the same as for continuous assessment.
The awarding of an Honors Distinction (Matrícula d'Honor) is at the discretion of the course instructors. UAB regulations state that Honors Distinctions may only be granted to students with a final grade of 9 or higher, and may be awarded to up to 5% of enrolled students.
A student will be considered Not Assessable (NA) if they do not complete at least 50% of thecourse’s assessment activities.
For the midterm exams, the instructor will set a date for students to submit claims or questions about the grade received.
Without prejudice to other disciplinary measures that may be deemed appropriate, and in accordance with current academic regulations, any irregularity committed by a student that could affect the outcome of an assessment will be penalized with a grade of zero. This means that cheating or allowing others to cheat on any activity will result in a zero for that activity, and if that activity is required to pass, the entire course will be failed.
Assessment activities graded in this manner cannot be retaken, and the course will therefore be failed with no option for recovery during the academic year.
There will be no differentiated treatment for students who repeat the subject.
The dates for continuous assessments will be published on the virtual campus and may be subject to changes due to unforeseen circumstances. All such changes will be communicated via the virtual campus, which is considered the official communication platform between instructors and students.
Bibliography
1. M. Masdeu, A. Ruiz, Apunts d'Àlgebra Lineal,
https://mat.uab.cat/~albert/wp/wp-content/uploads/2020/02/MR_Apunts_d__lgebra_Lineal2020.pdf
2. E. Nart X. Xarles, Apunts d'àlgebra lineal, Materials de la UAB, núm. 237, 1a edició.
3. S. I. Grossman, Álgebra lineal con aplicaciones, McGraw-Hill, 1991.
5. P. Lancaster, Theory of Matrices, Academic Press, NY, 1969.
6. J. Arvesu, F.J. Marcellán, J. Sánchex Ruiz, Problemas resueltos de álgebra lineal , S.A. EDICIONES PARANINFO
Software
No specific software will be used.
Groups and Languages
Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 311 | Catalan | second semester | morning-mixed |
| (PAUL) Classroom practices | 312 | Catalan | second semester | morning-mixed |
| (PAUL) Classroom practices | 331 | Catalan | second semester | morning-mixed |
| (PAUL) Classroom practices | 332 | Catalan | second semester | morning-mixed |
| (TE) Theory | 31 | Catalan | second semester | morning-mixed |
| (TE) Theory | 33 | Catalan | second semester | morning-mixed |