Teaching Plan Information

1. General information

The main objective is to acquire a solid foundation in Algebra and problem solving skills. To introduce the use of mathematical software and numerical problem solving. To work on mathematical rigor, logical and deductive capacity, to select efficient techniques and strategies, and to promote critical and abstract reasoning. To enable students to study other subjects of the curriculum.

Prerequisites: solid knowledge of high school mathematics (subjects Mathematics I and II) such as properties and operations of and with vectors, matrices and determinants, solution existence analysis of linear systems, Gaussian elimination.

The assessable contents do not provide direct capabilities for the achievement of the 2030 Agenda; however, they are essential to base subsequent knowledge that is related to the SDGs.

2. Learning results

To know the elementary algebraic structures.

To know and understand the basic concepts of linear algebra: systems of linear equations, vectors, linear dependence and independence and eigenvalues.

To know the approximate solution of linear equations, pivoting strategies, computational cost and various factorizations of matrices.

To know the iterative methods of approximate resolution of linear equations.

To know the approximate calculation of the eigenvalues of a matrix.

3. Syllabus

• Matrix algebra.
• Systems of linear equations.
• Algebraic structures.
• Vector spaces.
• Linear applications.
• Eigenvalues and eigenvectors.
• Orthogonality: approximate solution of systems of linear equations.

4. Academic activities

• Theory lessons: The explanations and examples will guide the students in understanding and application of mathematics.
• Problem sessions: The students will solve questions and problems, analyzing the different possible options.
• Practical classes with computer: Mathematical algorithms will be analyzed and programmed by means of symbolic and numerical programming software installed in the center's computer laboratories.
• Carrying out of proposed activities.
• Study and personal work.
• Assessment tests.

5. Assessment system

The following will be assessed: the correct use of efficient strategies and procedures; the absence of mathematical errors; the knowledge of the software used; the correct use of terminology and notation; clear and detailed explanations; the orderly, clear and organized exposition.

Students will be able to take a continued assessment, but they will also have the opportunity to pass the subject by means of a global test in the two official exams.

Continued assessment:
Practical block (20%): Assignments throughout the semester and final test with problems similar to those of the practical sessions.
Theory and problems block (80%, minimum mark 4):
1) Continued activity, PAC (30%):
- Activities will be proposed throughout the semester (10%).
- Partial written test (20%). Written test on theoretical-practical contents and problems towards the middle of the semester.
2) Reduced written test on theoretical-practical contents and problems of part of the subject (50%): Students will only take it in the 1st call and only if the PAC mark is equal to or higher than 5 (out of 10).
In the 2nd call, students will conduct the complete Theory and problems block.

Global assessment (official calls):
   Computer practices (20%).
   Theory and problems (80%, minimum mark 4).

6. Sustainable Development Goals

4 - Quality Education