ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Algebra
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Management suitable software for research in mathematics (SageMath).
To give solutions of mathematical problems with the help of computer algebra systems.
PROGRAMME:
• Graphical representations in dimensions 2 and 3.
Teaching:
Expository hours: 3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 3 / 2 / 2
Tutorial: 0.2
• Graph theory.
Teaching:
Expository hours: 3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 2 / 1 / 2
Tutorial: 0.2
• Matrices.
Teaching:
Expository hours:3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 2 / 1 / 2
Tutorial: 0.2
• Differentiation and integration.
Teaching:
Expository hours: 3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 2 / 2 / 2
Tutorial: 0.2
• Differential equations. Laplace transforms.
Teaching:
Expository hours: 3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 3 / 2 / 3
Tutorial: 0.3
• Vector calculus.
Teaching:
Expository hours: 3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 3 / 2 / 2
Tutorial: 0.3
• Differential geometry.
Teaching:
Expository hours: 3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 2 / 1 / 2
Tutorial: 0.3
• Polynomial ideals. Gröbner bases.
Teaching:
Expository hours: 3
Independent / supervised learning activities:
Hours study / work / programming and experimentation: 3 / 2 / 3
Tutorial: 0.3
Basic bibliography
• F. Aguado, F. Gago, M. Ladra, G. Pérez, C. Vidal, A. M. Vieites, Problemas resueltos de Combinatoria. Laboratorio de Sagemath, Ediciones Paraninfo, S.A., 2018.
• G. V. Bard, Sage for Undergraduates, 2nd ed., American Mathematical Society, 2022.
http://gregorybard.com/Sage.html
• M. O'Sullivan, D. Monarres, M. Polimeno, SDSU Sage Tutorial Documentation, 2019.
https://mosullivan.sdsu.edu/Teaching/sdsu-sage-tutorial/SDSUSageTutoria…
• A. M. Vieites, F. Aguado, et al., Teoría de Grafos: Ejercicios resueltos y propuestos. Laboratorio con Sage, Paraninfo, 2014.
• P. Zimmermann, A. Casamayou, et al., Computational Mathematics with SageMath, 2018.
https://www.sagemath.org/sagebook/
Complementary bibliography
• V. Dobrushkin, SAGE Tutorial for the First Course in Applied Differential Equations.
http://www.cfm.brown.edu/people/dobrush/am33/sage/
• T. W. Judson, The Ordinary Differential Equations Project, 2022.
http://faculty.sfasu.edu/judsontw/ode/html-snapshot/odeproject.html
GENERAL COMPETENCE:
• Acquisition of high-level math tools for several applications covering the expectations of graduates in mathematics and other basic sciences (CG02).
• Training for the analysis, formulation and problem-solving in new or unfamiliar environments within much broader contexts (CG04).
TRANSVERSAL COMPETENCE:
• Enhance the ability to work in cooperative and multi-disciplinary environments (CT03).
SPECIFIC COMPETENCE:
• To apply the tools of mathematics in several fields of science, technology and social sciences (CE02).
• To develop the skills necessary for the transmission of mathematics, oral and written, both in terms of formal correctness and in terms of communication effectiveness, emphasizing the use of appropriate information and communication technologies (CE03).
• The program will be developed, combining computer practices with work and presentations of the students, encouraging student participation. Weekly expositions will be held, so that the student can deepen in the development of the topics. Therefore, in addition to the presentations by the teacher of the different topics of the program, the student will have to develop some of the topics throughout the course (competence CG02, CG04, CE02, CE03).
• Exercise worksheets will be periodically given to students, some of which will be proposed to be presented at the end of the course while the rest will be solved in class under the supervision of the teacher. Students will be encouraged to attend the different seminars that may be held throughout the course on research topics related to the contents of the program (competence CG02, CG04, CT03, CE02, CE03).
• Graphical representations in dimensions 2 and 3.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 3 / 2 / 2
Tutorial: 0.2
• Graph theory.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 2 / 1 / 2
Tutorial: 0.2
• Matrices.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 2 / 1 / 2
Tutorial: 0.2
• Differentiation and integration.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 2 / 2 / 2
Tutorial: 0.2
• Differential equations.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 3 / 2 / 3
Tutorial: 0.3
• Vector calculus.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 3 / 2 / 2
Tutorial: 0.3
• Differential geometry.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 2 / 1 / 2
Tutorial: 0.3
• Polynomial ideals. Gröbner bases.
Teaching:
Expository hours: 3
Hours study / work / programming and experimentation: 3 / 2 / 3
Tutorial: 0.3
In cases of fraudulent performance of exercises or tests, the provisions of the Regulations on the Evaluation of Students' Academic Performance and the Review of Grades will apply.
The students will have to make presentations of some parts of the syllabus and will deliver several proposed exercises. The evaluation may be completed through a written examination or the completion of works, in addition to considering active participation in the classes and the completion of the proposed exercises. The management of programmes as well as the performance of tasks on the computer will be considered.
The qualification will be based on these expositions, as well as on the completion of the exercises. The levels of clarity of exposure and concision will be evaluated, as well as the answers of the student to questions that will be asked during the presentations.
In another case, the evaluation system contemplates, on the one hand, a mark of the final exam (E) and, on the other hand, a continuous evaluation (C), made throughout the course, based mainly on the participation of each student in the classroom, the realization of written controls, delivered works, tutorials and other means.
First Call (February):
With the exception of those not presented, 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, 0.4*C+0.6*E)
The evaluation of the final exam is done through of a written examination.
Second Call (July):
The mark (C) obtained in the continuous evaluation of the first call in February is preserved, and a new final writing exam (E) will be carried out.
With the exception of those not presented, 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, 0.25*C+0.75*E)
The evaluation of the final exam is done through a written examination.
According to article 5.2 of the Regulations on permanence in bachelor's and master's degrees of the University of Santiago de Compostela, students who do not carry out any assessable academic activity according to that established in the teaching programme will be included in the minutes as "not presented".
The competence {CG02, CG04, CT03, CE02, CE03} will be evaluated both in the processes of continuous evaluation and in the written examination.
Class meeting:
Interactive lessons in small groups in a specialised classroom (computer science, laboratory, practices of field, ...): 22
Tutorships in a very small group: 2
Work hours total in person: 24
Independent work:
Individual self-study or in a group: 20
Writing exercises, conclusions or other derivative works of the subject: 13
Programming / experimentation or other tasks by technical means (computer, laboratory): 18
Total hours working personal: 51
Mathematics knowledge at bachelor level.
There will be an e-learning platform to support the teaching of this subject at USC.
Manuel Eulogio Ladra Gonzalez
Coordinador/a- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813138
- manuel.ladra [at] usc.es
- Category
- Professor: University Professor
| Friday | |||
|---|---|---|---|
| 12:00-13:00 | Grupo /CLE_01 | Spanish | Classroom 10 |
| 13:00-14:00 | Grupo /CLIL_01 | Spanish | Classroom 10 |
| 01.22.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 10 |
| 06.20.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 10 |