107124 - ALGEBRA

Subject type: Basic

Coordinator: Adso Fernández Baena

Trimester: Second term

Credits: 6

The subject enables the student to understand and / or solve mathematical problems, which may arise in engineering, related to linear algebra.

This subject has methodological and digital resources to make possible its continuity in non-contact mode in the case of being necessary for reasons related to the Covid-19. In this way, the achievement of the same knowledge and skills that are specified in this teaching plan will be ensured.

The learning outcomes specify the specific measure of the competencies worked on.

This subject contributes to the following learning outcomes specified for the subject to which it belongs:

• LO1: Become familiar with mathematical language and logic and know their applications in the field of computer science. Know how to accurately express mathematical concepts. Be able to understand a demonstration and perform demonstrations using various methods (particularly the last two points).
• LO2: Understand the operations and properties of sets and applications.
• LO3: Know and understand the basic properties of real numbers and functions (mainly operational properties and elementary functions).
• LO4: Understand and be able to apply the methods of solving linear algebra problems involving vectors and matrices. Understand the concept of linear independence and the importance of bases in a vector space. Familiarize yourself with linear applications and their study using matrices.
• LO5: Understand the importance and applications of the use of reference systems in plan and space. Know the main related transformations of the plan and space.
• LO6: Plan oral communication, answer appropriately to the questions asked and write basic level texts with spelling and grammar correction. Properly structure the content of a technical report. Select relevant materials to prepare a topic and synthesize its content. Answer appropriately when asked questions.

The classes will be master classes (development of the theory and practical examples) and participatory (conceptual questions, guided resolution of exercises and presentation of exercises by the students).

1. The teacher will explain in class the theoretical and practical concepts (examples), focusing on the most important aspects and leaving some content for individual study. The teacher will also ask conceptual questions regarding the concepts explained.
2. The proposed exercises should be tried by the students to solve them individually or in pairs. Some will be solved by the teacher and / or the students themselves in class in a participatory way.
3. Students can complete class content and notes with bibliography books.

1. Sets and applications

   1. Sets and their operations

   2. Cartesian product of sets, correspondences and applications

2. Vectors and matrices

   1. Vectors and systems of linear equations

   2. Operations with matrices

   3. Vector spaces and bases

3. Linear applications

   1. Linear applications and associated matrices

   2. Basic changes in a linear application

4. Geometry of the plane and space

   1. Equations of lines and planes

   2. Relative positions of straight lines and planes

   3. Related transformations

Master class: development of theory and practical examples.

Participatory class: collaborative instruction with conceptual questions and resolution of exercises guided by the teacher (collect evidence of learning of almost all expected results, as a guide for self-assessment of the student and their active participation in class) .

Resolution and presentation of exercises: resolution and presentation of exercises by students (collect evidence of all expected results, especially RA6).

Evaluation exercises: four exercises, one per topic, which collect evidence of general learning (LO3), and more specific as indicated below:

• Topic 1: RA1 and RA2
• Topic 2: RA1 and RA4
• Topic 3: LO4
• Topic 4: LO5

90% Tests

There will be two exams during the course (45% each test), a first partial (2 first subjects) and a final exam with 4 questions each. Those who have failed the first exam will have to be examined in this part in the final exam. Those who have passed the first part will not have to take, in this part, the final exam (the first part is a liberating subject). Students who fail the final exam will go for recovery. The maximum mark on recovery is 6 points.

10% Active participation in class

It will be evaluated based on the participation in class and the answers to the questions that the teacher will propose during the development of the classes.

Castellet, M .; Llerena, I. (1988): Linear algebra and geometry. Bellaterra: Publications of the Autonomous University of Barcelona

Lay, David C; Murrieta Murrieta, Jesús Elmer (2007). Linear algebra and its applications. 3ª ed. Pearson Education

Holt, Jeffrey (2013). Linear Algebra with Applications. Freeman

Queysanne, Michel (1990). Basic Algebra. Vicens-Vives