ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Hours of tutorials: 1 Expository Class: 30 Interactive Classroom: 20 Total: 51
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Algebra
Center Higher Technical Engineering School
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
A general goal, shared with other mathematics subjects, is to get the student acquainted with the mathematical language and the mathematical methods, improving their ability to reason, analyze, synthesize and formulate arguments.
Other specific objectives of the subject are the following:
- To know and manage concepts and techniques of Linear Algebra and Euclidean Geometry that are detailed in the program.
- To apply matrix algebra techniques.
- To solve systems of linear equations.
- To develop geometric interpretation of some results.
1.- Matrix Algebra:
Matrices. Operations defined for matrices. Elementary Matrices. Echelon matrices. The rank of a matrix. Determinant of a square matrix. Properties and calculation of the determinant. Inverse of a matrix.
Classes:
Lecture/practical hours: 6/4.
2.- Systems of Linear Equations:
Interpretation of a system of linear equations. Equivalent systems. Resolution of systems of linear equations: Gauss Method and Cramer's Rule.
Classes:
Lecture/practical hours: 3/2.
3.- Vector Spaces:
Vector spaces and subspaces. Intersection and sum of subspaces. Generators and linear independence. Bases and dimension. Grassman identity. Implicit equations of a subspace.
Classes:
Lecture/practical hours: 6/4.
4.- Linear Maps:
Linear maps. Subspaces associated to linear maps. Matrix associated to a linear map. Base change matrix. Rank of a linear map. Equivalent Matrices.
Classes:
Lecture/practical hours: 6/5.
5.- Diagonalization:
Eigenvalues and Eigenvectors. Characteristic polynomial. Diagonalization of matrices by base change.
Classes:
Lecture/practical hours: 5/3.
6.- Scalar Product and Orthogonality:
Scalar Product and Euclidean spaces. Norm of a vector. Orthogonality. Orthogonal projection. Distances. Similar matrices and congruent matrices.
Classes:
Lecture/practical hours: 4/2.
Basic bibliography:
-LARSON, R.; EDWARDS, B.; FOLVO, D.C.: Álgebra Lineal; Pirámide, 2004.
-MERINO, L.; SANTOS, E.: Álgebra Lineal con Métodos Elementales; Thomson, 2006.
Further reading:
-ARVESÚ, J.; MARCELLÁN, F.; SÁNCHEZ, J.: Problemas Resueltos de Álgebra Lineal; Thomson, 2005.
-BURGOS, J.: Álgebra Finita y Lineal; García-Maroto Editores, 2010.
-HERNÁNDEZ, E. : Álgebra Lineal y Geometría; Addison-Wesley/Universidad Autónoma de Madrid, 1994.
To contribute to achieving the generic, specific and transversal competencies listed in the Report on the Degree in Artificial Intelligence from USC (CB2, CB3, CB5, CG2, CG4, TR3, CE1).
In addition, this subject will allow the student to achieve the following specific skills:
- To know the basic concepts of linear algebra: linear dependence and independence, bases, coordinates, change of bases, operations of subspaces, linear equations of subspaces, linear transformations, etc.
- To know the algorithms to reduce matrices to echelon forms and know how to apply them to compute the range of a matrix, to decide if a set of vectors is a base, resolution of systems of linear equations, etc.
- To understand the close relationship between matrices, linear transformations and systems of linear equations.
- To be able to check quickly whether a matrix is diagonalizable or not, and if a matrix is diagonalizable to compute a diagonalizing bases.
- To be familiar with some examples of Euclidean vectorial spaces, and to use the scalar product, the Gram-Schmidt method and the orthogonal projection in real finite-dimensional vectorial spaces to solve some geometric problems.
The general methodological indications established in the Memory of the Undergraduate Degree in Artificial Intelligence of the USC will be followed.
In the expository classes, the teacher will present the theoretical concepts, examples and will provide the proofs of the results most useful for understanding the subject (working on the CG8, CG10 and TR3 skills).
The interactive laboratory classes will serve to illustrate the theoretical contents and will be dedicated to the resolution of questions and problems by the teacher with the participation of the students (working on the CG9 and TR3 competences) also serving for the acquisition of practical skills (working on the TR1, TR2, FB1, CG9 and CG10 competencies).
In the tutorials in very small groups, there will be a personalized follow-up of the students learning and their work outside the class. Problems will also be proposed, to be done in class (competences TR1, TR2 and CG8).
A virtual course will be available on the Virtual Campus to support the teaching of this subject, with materials specific to the content of the expository classes and exercise bulletins to work in the laboratories.
During the semester, the students may be asked to do written exercises in class. The combined marking of these activities will be part of the qualification.
For the calculation of the final mark (F) the continuous evaluation (C) and the final exam mark (E) will be taken into account, and the following formula will be applied: F= max (E, 0.30*C+0.70*E).
The same applies to the extra opportunity in July.
The written exam will consist of theory and theoretical-practical questions and exercises.
Students who do not attend either of the two final examinations will be considered "unqualified".
Attendance at classes: 60 hours.
Lecture classes: 30 hours.
Interactive problem classes in small groups: 20 hours.
Hours of tutorials in very small groups: 1 hours.
Evaluation Activities: 9 hours.
Personal work hours: 90 hours
Autonomous study, individually or in group: 45 hours.
Solving/writing exercises, conclusions or other works: 45 hours.
Total workload: 150 hours (6 ECTS).
Continuous attendance to classes.
For the classes to be useful, it is necessary to study the subject explained each day.
It is essential that the student attends the laboratory classes having worked on the exercises proposed for each session. For this, it is necessary that he acquires sufficient knowledge of the theory that allows him to address the problems.
Rosa Mª Fernandez Rodriguez
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813158
- rosam.fernandez [at] usc.es
- Category
- Professor: University Lecturer
Ana Jeremías López
Coordinador/a- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813366
- ana.jeremias [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 09:00-10:00 | Grupo /CLE_01 | Galician, Spanish | IA.01 |
| 12:00-14:00 | Grupo /CLIL_01 | Galician, Spanish | IA.01 |
| Wednesday | |||
| 09:00-10:00 | Grupo /CLE_01 | Galician, Spanish | IA.01 |
| 12:00-14:00 | Grupo /CLIL_02 | Spanish, Galician | IA.01 |
| 01.09.2023 09:15-14:00 | Grupo /CLIL_02 | Classroom A1 |
| 01.09.2023 09:15-14:00 | Grupo /CLIL_01 | Classroom A1 |
| 01.09.2023 09:15-14:00 | Grupo /CLE_01 | Classroom A1 |
| 07.07.2023 09:15-14:00 | Grupo /CLE_01 | Classroom A2 |
| 07.07.2023 09:15-14:00 | Grupo /CLIL_02 | Classroom A2 |
| 07.07.2023 09:15-14:00 | Grupo /CLIL_01 | Classroom A2 |