ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician, English
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Algebra
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Linear Algebra is an essential part of the mathematical toolkit required in the modern study of many areas of behavioral, natural, physical and social sciences, in engineering, in business, in computer science, and of course in pure and applied mathematics.
The purposes of this course is to develop the basic concepts of linear algebra and to illustrate their usability by means of a variety of selected applications. More precisely, one can say that the aims are:
i) To provide a first contact with algebraic structures: vector spaces and linear maps as a generalization of vectors in R^3 and matrices, respectively. To learn how to operate with vectors, basis, subspaces and linear maps.
ii)To get acquaintance with the use of matrices in different branches of knowledge.
iii) To understand the need for reducing matrices to predetermined forms and to practice the algorithms.
1.- Vector spaces. (5 theoretical hours)
Definition of vector space: Examples. Subspaces. Quotient spaces. Intersection and sum of subspaces. Systems of generators .
2.- Linear independence and dimension. (6 theoretical hours)
Linear dependence and independence. Bases and dimension. Equations for a subspace. Coordinates. Supplementary subspaces.
3.- Applications between vector spaces. (9 theoretical hours)
Definition of linear map: properties and examples. Subspaces associated to a linear map. The vector space of linear maps. Matrix of a linear map. Change of basis and linear maps.
4.- Matrices. (5 theoretical hours)
Operations with matrices and properties. Non singular matrices. Elementary matrices. Equivalent matrices. Rank of a matrix.
5.- Systems of linear equations. (3 theoretical hours)
Systems of linear equations. Gaussian elimination. The Rouché-Frobenius Theorem.
If scenario 3 occurs, units 4 and 5 will be replaced by the new Unit 4.- Matrices and Systems of linear equations.
Basic.
1.-Cohn, P. M. Algebra, Vol. 1(2ª Ed.). Wiley and Sons, Chichester, 1982.(the pdf containing the pages related to the subject will be posted in the virtual course, when operational).
2.-Jeronimo, G., Sabia, J., Tesauri, S. Álgebra lineal. http://mate.dm.uba.ar/~jeronimo/algebra_lineal/AlgebraLineal.pdf
3.-López Camino, Rafael. Apuntes Geometría I. Curso 2003-2004. Universidad de Granada.
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema1.pdf
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema2.pdf
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema3.pdf
4.-Algunas lecciones de ÁlgebraLineal. https://www.usc.es/regaca/apuntes/notas_alg_lin.pdf
Complementaria.
Complementary
1.-Bolos, J.; Cayetano, J.; Requejo, B. Álgebra lineal y Geometría. UNEX, 2007.
2.-Merino, L.; Santos, E. Álgebra lineal con métodos elementales. Thomson, 2006.
Contribute to achieving the basic, general and transversal competences included in the report of the Degree in Mathematics of the USC: CB1, CB2, CB3, CB4, CB5, CG1, CG2, CG3, CG4, CG5, CT1, CT2, CT3, CT5.
Know the basic concepts of Linear Algebra.
Know the algorithms to reduce matrices to row-echelon forms and know how to apply them to the calculation of the range, calculation of base, resolution of systems, etc.
Understand the close relationship between matrices, linear applications and systems of linear equations and be able to use them in different contexts.
Scenario 1
The Expository classes will be used for the presentation of the basic contents that compose this subject (CE1, CE2, CE6, CG1, CG4).
The interactive seminar classes in small groups, which will serve to illustrate the theoretical contents, will be dedicated to the resolution of questions and problems by the teacher with the participation of students (CB4, CT3, CE5, CE6).
In the interactive laboratory classes in very small groups, the questions and problems proposed will be worked on individually and / or in groups (CB2, CB3, CE3, CE4) and presentations will be made (CB4, CG4).
In the tutorials in the classroom in very small groups there will be a personalized follow-up of the learning of the students and of their work outside the class (CG5, CG4, CT5).
A course will be opened on the Virtual Campus in which there will be various support materials and activities scheduled (CT1, CT2, CT5, CG5).
Scenario 2.
Given that face-to-face and online teaching will coexist, and that it is up to the institution to define the coexistence formulas of both teaching modalities, once these are known, the telematic means or other resources provided by the academic authorities will be used. Both the explanations of the contents and the practices of the subject will always be carried out synchronously.
Scenario 3.
The teaching, which will be entirely virtual, will be carried out synchronously using the means provided by the USC.
The tutorial sessions will be online and the e-mail can also be used for its development.
In any of the scenarios, problem bulletins will be posted in the virtual course, programming them in a staggered way and always in relation to the theory. In the case of scenarios 2 and 3 the solutions would also be hung.
Continuous assessment combined with a final test ared planned as evaluation criterion. The final test will be held on the date set by the Faculty of Mathematics for that purpose.
Continuous assessment will consist of the individual resolution of tasks, such as exercises, and tests that in the cases of scenarios 2 and 3 will be proposed through the virtual course. In scenario 1 the participation in the class will also be part of the continuous assessment.
Calculation of the final qualification:
- In the first scenario the final test will be face-to-face. The qualification of both the first and the second chance will be the max {F; 0.3xC + 0.7xF} where C is the grade of the continuous assessment and F the grade of the final test.
- In the second scenario, the final test will be telematic and the final grade will be the sum of 40% of the grade for the continuous assessment and 60% of the grade for the final test.
- In the third scenario, the final test will be telematic and the final grade will be the sum of 50% of the grade for the continuous assessment and 50% of the grade for the final test.
For the second opportunity in scenarios 2 and 3, the final grade will be the sum of 40% of the mark of the continuous evaluation and 60% of the mark of the test of the second chance.
For cases of fraudulent performance of exercises or tests, the provisions of the Regulations for the evaluation of students' academic performance and the review of qualifications will apply.
It will be considered as Not Presented that student that does not show to the final test, both in the first and in the second chance.
Expository classes:: 28
Seminar clases: 14
Laboratory clases: 14.
Tutorials in very small groups: 2
Personal work (non presential) of the student: 92
Total: 150
Study daily with the help of bibliographic material.
Carefully read the theoretical part until it is assimilated and try to answer the questions, exercises or problems presented in the bulletins.
Contingency plan:
Teaching methodology:
Scenario 2.
Given that face-to-face and online teaching will coexist, and that it is up to the institution to define the coexistence formulas of both teaching modalities, once these are known, the telematic means or other resources provided by the academic authorities will be used. Both the explanations of the contents and the practices of the subject will always be carried out synchronously.
Scenario 3.
The teaching, which will be entirely virtual, will be carried out synchronously using the means provided by the USC.
The tutorial sessions will be online and the e-mail can also be used for its development.
In any of the scenarios, problem bulletins will be posted in the virtual course, programming them in a staggered way and always in relation to the theory. In the case of scenarios 2 and 3 the solutions would also be hung.
Assessment system
Continuous assessment combined with a final test ared planned as evaluation criterion. The final test will be held on the date set by the Faculty of Mathematics for that purpose.
Continuous assessment will consist of the individual resolution of tasks, such as exercises, and tests that in the cases of scenarios 2 and 3 will be proposed through the virtual course.
Calculation of the final qualification:
- In the second scenario, the final test will be telematic and the final grade will be the sum of 40% of the grade for the continuous assessment and 60% of the grade for the final test.
- In the third scenario, the final test will be telematic and the final grade will be the sum of 50% of the grade for the continuous assessment and 50% of the grade for the final test.
For the second opportunity in scenarios 2 and 3, the final grade will be the sum of 40% of the mark of the continuous evaluation and 60% of the mark of the test of the second chance.
For cases of fraudulent performance of exercises or tests, the provisions of the Regulations for the evaluation of students' academic performance and the review of qualifications will apply.
It will be considered as Not Presented that student that does not show to the final test, both in the first and in the second chance.
Jose Manuel Fernandez Vilaboa
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813167
- josemanuel.fernandez [at] usc.es
- Category
- Professor: University Professor
Maria Purificacion Lopez Lopez
Coordinador/a- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813157
- mpurificacion.lopez [at] usc.es
- Category
- Professor: University Lecturer
Rosa Mª Fernandez Rodriguez
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813158
- rosam.fernandez [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_02 | Galician, Spanish | Classroom 08 |
| 12:00-13:00 | Grupo /CLIS_04 | Spanish, Galician | Classroom 03 |
| 12:00-13:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 08 |
| Tuesday | |||
| 12:00-13:00 | Grupo /CLIS_03 | Galician, Spanish | Classroom 03 |
| 13:00-14:00 | Grupo /CLE_01 | Spanish, Galician | Classroom 08 |
| Wednesday | |||
| 12:00-13:00 | Grupo /CLIS_02 | Galician, Spanish | Classroom 02 |
| 13:00-14:00 | Grupo /CLIS_01 | Galician, Spanish | Ramón María Aller Ulloa Main Hall |
| Thursday | |||
| 09:00-10:00 | Grupo /CLIL_03 | Spanish, Galician | Classroom 06 |
| 11:00-12:00 | Grupo /CLE_02 | Spanish, Galician | Classroom 08 |
| 12:00-13:00 | Grupo /CLIL_04 | Galician, Spanish | Classroom 02 |
| Friday | |||
| 10:00-11:00 | Grupo /CLIL_02 | Galician, Spanish | Boardroom |
| 10:00-11:00 | Grupo /CLIL_05 | Galician, Spanish | Classroom 03 |
| 11:00-12:00 | Grupo /CLIL_06 | Galician, Spanish | Classroom 02 |
| 11:00-12:00 | Grupo /CLIL_01 | Galician, Spanish | Classroom 03 |
| 06.08.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 02 |
| 06.08.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 03 |
| 06.08.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 06.08.2021 10:00-14:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 07.14.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |