Syllabus Information

1. General information

The objective of Algebra is for the student to consolidate and learn the basic knowledge related to vector spaces , linear and bilinear applications, quadratic forms, Euclidean space and the ring of integers and its applications. In addition, they must learn to relate this knowledge in order to acquire the ability to adapt it to the resolution of the problems of Telecommunication Engineering.

These goals are aligned with the Sustainable Development Goals (SDGs) of the United Nations 2030 Agenda, insofar as mathematics is a tool used by engineers and scientists to model, analyze and optimize a multitude of systems.

It is recommended to have a precise knowledge of the contents of the Mathematics I and II subjects included in High school curriculum.

2. Learning results

The contents of this subject should provide the student with sufficient techniques and skills to enable him/her to address the following issues and problems related to the following aspects:

1.- To know the basic algebraic structures and modular arithmetic.

2.- Solve systems of linear equations exactly and with numerical methods.

3.- Operate with matrices.

4.- Know the properties of vector spaces.

5.- Know the linear applications between vector spaces and know how to represent them.

6.- Determine whether a matrix or an endomorphism is diagonalizable by calculating its eigenvalues and eigenvectors.

7.- Know and apply the properties of vector spaces endowed with a scalar product.

8.- Use scientific software to solve problems related to linear algebra.

As a consequence of the previous learning results, the student should recognize and know how to apply the properties of elementary algebraic structures, know how to work with polynomials and remainder classes, know how to apply the concepts and techniques of linear algebra, Euclidean geometry and its matrix representation.

3. Syllabus

The program of the course is divided into the following topics:

Topic 1: MATRIXES AND LINEAR SYSTEMS

Topic 2: VECTOR SPACES

Topic 3: LINEAR APPLICATIONS

Topic 4: SPECTRAL THEORY: EIGENVALUES AND EIGENVECTORS

Topic 5: BILINEAR AND QUADRATIC FORMS

Topic 6: EUCLIDEAN VECTOR SPACE

Topic 7: GROUPS AND RINGS

Topic 8: THE RING OF INTEGERS

Appendix: SETS AND RELATIONs

4. Academic activities

The subject is developed through an appropriate combination of the following activities:

Participatory lectures 40 hours

Theoretical contents and results are presented, complemented with some problems and practical exercises.

Problem solving classes: 8 hours

In small groups, models are presented in which some of the mathematical aspects of the subject are presented, solved in class or as autonomous work material for the student.

Practical classes: 12 hours

In small groups a scientific software is used to solve the proposed exercises related to some numerical methods and applications in Telecommunications of the mathematical contents.

5. Assessment system

In the first call the student may choose between a continuous assessment or a global assessment.

The global assessment consists of an exam containing theoretical-practical questions, problems and exercises corresponding to the topics developed in the lectures, problems and practical classes carried out with the help of the computer.

The continuous assessment consists of the following tests:

An academic paper related to the practices.

Control activities carried out in the classroom during class hours and announced well in advance in Moodle.

A final exam with theoretical and practical questions, exercises and problems.

The final grade for the subject will be calculated according to the following formula:

                                  NFC *0.3+NF*0.45+NTA*0.25

where

NFC=final score of the controls out of 10.

NF= final exam score out of 10.

NTA= grade of the academic work out of 10.

The final exam allows the student to recover the grade of the failed controls in the control activities outlined above, provided that the student has taken all of them.

In the second call the student will perform the global assessment previously described.

In all the tests, the correctness of the answers will be evaluated, as well as the justification of the solutions obtained.