ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 97 Hours of tutorials: 3 Expository Class: 25 Interactive Classroom: 25 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics, Mathematics
Areas: Applied Mathematics, Algebra
Center Higher Technical Engineering School
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
This subject must serve the students to become familiar with mathematical language and logical reasoning, along with the basic concepts to be applied in the remaining subjects of the grade. In the practical part, scientific software will be used so that students learn how to solve numerically and / or symbolically the proposed problems.
ITEM 1. Introduction to logic.
Propositions: propositional equivalences. Truth tables: tautology and contradiction. Logical Reasoning: paralogisms. Predicates and quantifiers. Methods of proof.
Teaching
Hours lecture / interactive: 5 / 6
Independent / supervised learning activities
Hours study / problem solving / practice / computer tutorial: 4 / 2 / 2 / 0.5
ITEM 2. Introduction to set theory
Elements of a set: Membership. Subsets: The powerset. Representation of Sets: Venn diagrams. Set operations: Properties. Cartesian product of sets. Maps between sets: Composition. Types of maps: injective, surjective and bijective.
Teaching
Hours lecture / interactive: 4 / 4
Independent / supervised learning activities
Hours study / problem solving / practice / computer tutorial: 3 / 3 / 1 / 1
ITEM 3. Mathematical reasoning, induction and recursion.
Proof strategies. Mathematical induction. Recursive definitions. Structural induction.
Teaching
Hours lecture / interactive: 4 / 4
Independent / supervised learning activities
Hours study / problem solving / practice / computer tutorial: 3 / 3 / 0 / 0.5
ITEM 4. Introduction to mathematical analysis and numerical computation.
Real numbers. Functions and their graphs. Elementary functions. Review of basic concepts of numerical analysis.
Teaching
Hours lecture / interactive: 3 / 3
Independent / supervised learning activities
Hours study / problem solving / practice / computer tutorial: 2.4 / 1 / 2 / 0.5
ITEM 5. Polynomial interpolation
Lagrange polynomials. Runge phenomenon. Interpolation by cubic splines.
Teaching
Hours lecture / interactive: 1 / 1
Independent / supervised learning activities
Hours study / problem solving / practice / computer tutorial: 1.2 / 0.5 / 1.5
ITEM 6. Limits and continuity.
Basic limits. Laws of the boundaries. Limits of rational functions. Continuity at a point. Continuous functions.
Teaching
Hours lecture / interactive: 1 / 1
Independent / supervised learning activities
Hours study / problem solving / practice / computer tutorial: 0.8 / 1 / 0.5 / 0.25
ITEM 7. Differential calculus of one variable. Numerical derivation.
Derivation. Rules of derivation. Rule in the chain. Implicit derivation. Mean value theorem. Taylor polynomial. Numerical derivation. Extremes of functions.
Teaching
Hours lecture / interactive: 7 / 6
Independent / supervised learning activities
Hours study / problem solving / practice / computer tutorial: 5.6 / 2.5 / 3.5 / 1
Basic:
ROSEN, K. H. Matemática Discreta y sus Aplicaciones. 5ª ed. McGraw-Hill, 2004. ISBN: 9788448140731
THOMAS, G. B. Cálculo. 13ª ed. Pearson, 2015. ISBN: 9789702627340
Complementary:
ANASTASSIOU, G. A. & MEZEI, R. Numerical Analysis Using Sage. Springer, 2015. ISBN: 9783319167398
BLYTH, T. S. & ROBERTSON, E. F. Sets, Relations and Mappings. Cambridge University Press, 1984. ISBN: 9780412278808
DOERR, A. & LEVASSEUR, K. Applied Discrete Structures, 2013. ISBN: 9781105559297
(available from https://discretemath.org)
- Expose and argue with clarity the assumptions and development made in problem solving, using appropriate terminology.
- Develop analytical skills in solving problems.
- Attitude of criticism when faced with different types of solutions.
- Master the notation, method and vocabulary for mathematical modeling and case studies.
- knowledgeable use of the mathematical language.
- Capacity for abstraction and to use the language of formal logic to express themselves with precision and rigor.
- Knowledge of mathematical techniques to solve problems related to engineering.
In general, to reach the competences contained in the memory of the the degree GrEI FB1, CG8-10, TR1-3.
Class time will be used for an expository presentation of the basic elements that make up this area; here FB1 and CG8 competences will be considered.
Interactive classes will be conducted in small groups and practical exercises on computer; here competences CG9, CG10, TR1, TR2 and TR3 will be considered.
Moreover, study topics and problems will be proposed to be solved by students and to present their results in very small groups in tutorials, which also provide support for them; here competences CG9, CG10, TR1, TR2 and TR3 will be considered.
There will be a course in the Virtual Campus in which, in addition to having various support materials, we will keep a daily record of what is treated in each class meeting, as well as the programming of activities, some of which will be carried out in groups.
Tutorials and communication with students can be face-to-face or virtual. In the virtual case they can be asynchronous, through the virtual course forums or e-mail, or synchronous, through the MS Teams platform.
Two cases will be distinguished:
First opportunity (January / February)
A method of continuous assessment will be followed, through directed academic activities, taking into account the work done both individually and in groups, including that done with the computer, in which students must demonstrate their knowledge of the subject; and a final exam.
• (60% of the mark) Final exam of the theoretical-practical contents, that will include some question relative to the practices with computer. In this part the competences FB1, CG8, CG9 and TR1 will be evaluated.
• (40% of the mark) Continuous evaluation of the work, throughout the course, which may include the following items:
- preparation of group work to be presented in front of the class, and any member of the group can be questioned. Competences FB1, CG8, CG9, TR2 and TR3 will be assessed.
- Individual resolution of problems and / or practices with the computer with author control of authorship over some part of it. Competences FB1, CG9 and TR1 will be assessed.
- answer to questionnaires in class and / or in the virtual course. Competences FB1, CG8 and TR1 will be assessed.
- Group preparation of a blog with the essential contents of the treatise in class. Competences FB1, CG8, CG9, CG10, TR1, TR2 and TR3 will be assessed.
Repeating students will be required to take these tests in the current course to obtain the mark of the continuous assessment.
Second chance (June / July)
The evaluation of the students will be based on a final exam with the following percentages:
• Final theoretical-practical exam that may include questions about computer practices: 70%
• Continuous evaluation 30%
It will be considered presented to all students who take the exam or a percentage of 75% of the continuous assessment.
In the case of fraudulent behavior in assignments, tests, or exams, the provisions of the "Regulations for the evaluation of the academic performance of students and grades review" will apply, in particular those in Article 16:
Committing fraud in any assignment or test required in the evaluation of the subject will imply the qualification of fail in the corresponding call, regardless of the disciplinary process that may be followed against the offender.
Face:
25 hours of theory classes
25 hours work in small groups
3 hours tutoring in very small groups
3 hours final written exam
2 hours final exam computer
Non-attendance:
45 hours self-study-related classes (20 hours for theory, for problems 10, 15 practices with computer)
25 hours to work on the proposed bulletins problems
15 hours to program a computer solutions to problem sets
7 hours evaluation activities in the virtual campus
Total workload: 150 hours
Attendance with active participation in them. Using the textbook and the recommended material. Carrying out the practices and neede exercises related to the various chapters to achieve the planned objectives.
Francisco Jose Pena Brage
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813194
- fran.pena [at] usc.es
- Category
- Professor: Temporary PhD professor
Felipe Gago Couso
Coordinador/a- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813140
- felipe.gago [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 17:30-19:30 | Grupo /CLIL_01 | Galician | Computer Room I5 |
| Tuesday | |||
| 12:00-13:00 | Grupo /CLE_01 | Galician | Classroom A1 |
| 17:30-19:30 | Grupo /CLIL_02 | Galician | Computer Room I5 |
| Wednesday | |||
| 12:00-13:00 | Grupo /CLE_01 | Galician | Classroom A1 |
| 17:30-19:30 | Grupo /CLIL_03 | Galician | Computer Room I5 |
| Thursday | |||
| 17:30-19:30 | Grupo /CLIL_04 | Galician | Computer Room I5 |
| Friday | |||
| 16:00-18:00 | Grupo /CLIL_05 | Galician | Computer Room I5 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_01 | Classroom A3 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_02 | Classroom A3 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_03 | Classroom A3 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_04 | Classroom A3 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_05 | Classroom A3 |
| 01.09.2025 10:00-14:00 | Grupo /CLE_01 | Classroom A3 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_01 | Classroom A4 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_02 | Classroom A4 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_03 | Classroom A4 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_04 | Classroom A4 |
| 01.09.2025 10:00-14:00 | Grupo /CLIL_05 | Classroom A4 |
| 01.09.2025 10:00-14:00 | Grupo /CLE_01 | Classroom A4 |
| 06.18.2025 16:00-20:00 | Grupo /CLE_01 | Classroom A1 |
| 06.18.2025 16:00-20:00 | Grupo /CLIL_01 | Classroom A1 |
| 06.18.2025 16:00-20:00 | Grupo /CLIL_02 | Classroom A1 |
| 06.18.2025 16:00-20:00 | Grupo /CLIL_03 | Classroom A1 |
| 06.18.2025 16:00-20:00 | Grupo /CLIL_04 | Classroom A1 |
| 06.18.2025 16:00-20:00 | Grupo /CLIL_05 | Classroom A1 |