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
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Mathematical Analysis
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
To introduce the student, with the support of examples and practice, in the comprehension of the first structure of the Mathematical Analysis: the ordered and complete field of the real numbers.
To introduce and consolidate, with examples and exercises, the convergence notions of sequences and numerical series.
To present, practising with the different notations, the operations with the complex numbers.
To come into contact with the MAPLE programme like support for the calculus and the comprehension and the visualization of the principal concepts of the course.
1. REAL NUMBERS (approx. 8 lectures)
1.1 Natural numbers. Principle of induction.
1.2 Rational numbers. Countability.
1.3 Axiomatic of the real numbers (R). Supreme axiom and consequences.
1.4 Archimedian property of R. Density of Q in R.
2. SEQUENCES OF REAL NUMBERS (approx. 9 lectures)
2.1 Intuitive introduction to the concepts of sequence and limit. Generalities.
2.2 Convergent sequences and their limits. Properties.
2.3 Infinite limits.
2.4 Convergence and divergence of monotone sequences.
2.5 Subsequences. Bolzano-Weierstrass Theorem. Limits of oscillation.
2.6 Cauchy sequences. Completeness of R.
2.7 Calculus of limits. Stirling and Stolz criteria.
3. SERIES OF REAL NUMBERS (approx. 7 lectures)
3.1 Intuitive introduction to the concepts of series and their sum.
3.2 Numerical series. Convergence of series.
3.3 Series of non-negative terms. Convergence criteria.
3.4 Absolute and conditional convergence. Criteria of non-absolute convergence.
4. COMPLEX NUMBERS (approx. 2 lectures)
4.1 Complex numbers. Expressions, operations and roots of complex numbers.
BASIC:
T.M. APOSTOL. Análisis Matemático. Reverté, 1996.
R. G. BARTLE - D. R. SHERBERT. Introducción al Análisis Matemático de una Variable (2ª Ed.). Limusa, 2000.
A. GARCÍA LÓPEZ y otros. Cálculo I. Teoría y problemas de Análisis Matemático en una variable (2ª Ed.). Clagsa, 1994.
M. SPIVAK. Calculus (2ª Ed.). Reverté, 1994.
COMPLEMENTARY:
J. CASASAYAS e M.C. CASCANTE. Problemas de Análisis Matemático de una variable real. Edunsa, 1990.
In addition to contribute to achieve the general and transverse competences taken up in the memory of the degree, this subject will allow the student to get the following specific competences:
CE1 - To understand and use mathematical language;
CE2 - To know rigorous proofs of some classical theorems in different areas of mathematics;
CE3 - To devise demonstrations of mathematical results, formulate conjectures and imagine strategies to confirm or refute them;
CE4 - To identify errors in faulty reasoning, proposing demonstrations or counterexamples;
CE5 - To assimilate the definition of a new mathematical object, and to be able to use it in different contexts;
CE6 - To identify the abstrac properties and material facts of a problem, distinguishing them from those purely occasional or incidental;
CE9 - To use statistical analysis applications, numerical and symbolic computation, graphical visualization, optimization and scientific software, to experience and solve problems in mathematics.
It will follow the general methodological instructions established in the Memory of the Title of Degree in Mathematics of the USC.
Teaching is programmed in lectures, small group practices , practices with computer in reduced groups and tutorials. In the theoretical classes the essential contents of the subject will be presented, and they will allow the work of basic, general and transversal skills, in addition to the specific competences CE1 , CE2 , CE5 and CE6 . Meanwhile, in interactive sessions some exercises and / or problems for more autonomous realization will be proposed. This will emphasize the acquisition of specific skills CE3 and CE4, as well as the transversal skills CT1, CT2, CT3 and CT5 . Finally, in the tutorials we will discuss with the students, and we solve some exercises for the students to practice and secure the knowledge and the transversal skills previously commented. In computer classes the MAPLE program will be used as a study tool, being worked in this way the specific competence EC9 .
Moreover, teaching material will be available to students in the virtual USC.
SCENARIO 1 (adapted normality):
Lectures and small group practices will be face-to-face and will be complemented by the virtual course of the subject, in which the students will find notes, problem bulletins, Maple worksheets, etc.
The tutorials will be in person or through email.
SCENARIO 2 (distancing):
Partially virtual teaching, according to the distribution organized by the Faculty of Mathematics. For this, the virtual classroom of the course will be used, with explanatory videos of the contents, to more than all the material mentioned in scenario 1.
The tutorials will be attended by email or through MS Teams.
SCENARIO 3 (closure of the facilities):
Totally remote teaching through the virtual course of the subject. Explanatory videos of the theoretical content for the lectures, and videos that will deal with the resolution of exercises, will be uploaded during the usual course hours for the interactive sessions (apart from the material cited in scenario 1).
The tutorials will be by email or MS Teams.
SCENARIO 1 (adapted normality):
The evaluation will be carried out by combining a continuous formative evaluation with a final exam.
The continuous evaluation will consist of two exams of a theoretical-practical nature. In the first of them, the content worked on in topics 1 and 2 will enter, and said exam will have a weight of 60% within the mark of the continuous evaluation. In the second of the exams, with a weight of the remaining 40%, the contents of topic 3 will be asked.
In the final written exam, the knowledge obtained by the students in relation to the concepts and results of the subject will be measured, both from a theoretical and practical point of view, also assessing the clarity and logical rigor shown in the exposition of the themselves.
Both in the continuous assessment and in the final exam the specific competences from CE1 to CE6 will be evaluated.
For the calculation of the final mark (CF), the continuous assessment grade (EC) and the final exam score (EF) will be taken into account, and the formula CF = EC / 3 + (1-EC / 30) will be applied. ) * EF. For details of this formulation the work can be consulted:
Xavier Bardina, Eduardo Liz, "Mathematics and evaluation", MATerials MATemàtics, 2011, 6, 19 pp.
http://www.mat.uab.cat/matmat/PDFv2011/v2011n06.pdf
Any student who has not taken any test in the continuous assessment or the final exam will be understood as not presented.
In the second opportunity, the same evaluation system will be used, but with the exam corresponding to the second opportunity, which will be an exam of the same type as that of the first.
SCENARIO 2 (distancing):
Same procedure as that described for SCENARIO 1, with the only difference that the continuous assessment exams and the final exam, in both opportunities, could be online, depending on the circumstances. In this case, the virtual campus will be used to carry them out.
SCENARIO 3 (closure of the facilities):
Same procedure as that described for SCENARIO 1, with the difference that the continuous assessment exams and the final exam, for both opportunities, will be online. The virtual course will be used for this.
Warning. In cases of fraudulent performance of exercises or exams (plagiarism or improper use of technologies), the provisions of the Regulations for the evaluation of student academic performance and review of grades will apply.
PRESENCE WORK IN THE CLASS
Plenary lectures (26 hours)
Reduced group lectures(13 hours)
Lab lectures (13 hours)
Tutorials in much reduced group (2 hours)
Total hours of presence work in the class 54
PERSONAL WORK OF THE STUDENT
Autonomous Individual Study or in group (61 hours)
Writing of exercises, conclusions or other works (20 hours)
Programming/experimentation or other works in computer/laboratory (10 hours)
Recommended readings, activities in library or similar (5 hours)
Total hours of personal work of the student 96
To study every day by using the bibliographical material. To read carefully the theoretical part until it has been assimilated, then, to answer the corresponding questions, exercises or problems. To follow the suggestions that may give the teacher throughout the academic year.
Contingency plan:
Adaptation of the methodology to Scenarios 2 and 3:
SCENARIO 2 (distancing):
Partially virtual teaching, according to the distribution organized by the Faculty of Mathematics. For this, the virtual classroom of the course will be used, with explanatory videos of the contents, to more than all the material mentioned in scenario 1.
The tutorials will be attended by email or through MS Teams.
SCENARIO 3 (closure of the facilities):
Totally remote teaching through the virtual course of the subject. Explanatory videos of the theoretical content for the lectures, and videos that will deal with the resolution of exercises, will be uploaded during the usual course hours for the interactive sessions (apart from the material cited in scenario 1).
The tutorials will be by email or MS Teams.
Adaptation of the evaluation system to Scenarios 2 and 3:
SCENARIO 2 (distancing):
Same procedure as that described for SCENARIO 1, with the only difference that the continuous assessment exams and the final exam, in both opportunities, could be online, according to the calendar of the Faculty. In this case, the virtual campus will be used to carry them out.
SCENARIO 3 (closure of the facilities):
Same procedure as that described for SCENARIO 1, with the difference that the continuous assessment exams and the final exam, for both opportunities, will be online. The virtual course will be used for this.
Maria Victoria Otero Espinar
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813170
- mvictoria.otero [at] usc.es
- Category
- Professor: University Professor
Óscar Alejandro Otero Zarraquiños
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813173
- oscaralejandro.otero [at] rai.usc.es
- Category
- Professor: Temporary supply professor to reduce teaching hours
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLIS_03 | Spanish | Classroom 06 |
| 12:00-13:00 | Grupo /CLIS_04 | Spanish | Ramón María Aller Ulloa Main Hall |
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| Tuesday | |||
| 12:00-13:00 | Grupo /CLE_02 | Galician, Spanish | Classroom 08 |
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| Wednesday | |||
| 10:00-11:00 | Grupo /CLE_02 | Spanish, Galician | Classroom 08 |
| 10:00-11:00 | Grupo /CLIL_02 | Spanish | Computer room 2 |
| 12:00-13:00 | Grupo /CLIL_01 | Spanish | Classroom 06 |
| 13:00-14:00 | Grupo /CLIL_03 | Spanish | Computer room 4 |
| Thursday | |||
| 10:00-11:00 | Grupo /CLIL_05 | Galician, Spanish | Computer room 2 |
| 11:00-12:00 | Grupo /CLIL_06 | Galician, Spanish | Classroom 03 |
| 12:00-13:00 | Grupo /CLIS_01 | Galician, Spanish | Ramón María Aller Ulloa Main Hall |
| 13:00-14:00 | Grupo /CLIS_02 | Spanish | Ramón María Aller Ulloa Main Hall |
| Friday | |||
| 09:00-10:00 | Grupo /CLIL_04 | Spanish | Computer room 4 |
| 01.26.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 02 |
| 01.26.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 03 |
| 01.26.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 01.26.2021 10:00-14:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 06.25.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 02 |
| 06.25.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 03 |