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: Statistics, Mathematical Analysis and Optimisation
Areas: Mathematical Analysis
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
To know the most important concepts, results and techniques of measure theory. To know the geometric properties of conformal mappings.
MEASURE THEORY
Positive Borel measures: The Riesz representation theorem. Regularity of Borel measures.
Lp-spaces: types of convergence. Approximation by regular functions. Complex measures. The Lebesgue-Radon-Nikodym theorem.
COMPLEX VARIABLE
Conformal mappings: geometric meaning of the derivative. Preservation of angles. Möbius transformations: properties (symmetry and orientation principles). Schwarz lemma: applications. Riemann mapping theorem.
S. G. Krantz, Complex variables: a physical approach with applications and Matlab, Boca Raton, FL, Chapman & Hall, 2008.
J. B. Conway, Functions of one complex variable, New York, Springer-Verlag, 1973.
W. Rudin, Análisis real y complejo, Madrid, McGraw-Hill, 1988.
M. E. Taylor, Measure Theory and Integration, Chapel Hill - AMS, 2006.
BASIC AND GENERAL COMPETENCES
GENERAL
• CG01 - Introduce students into the research, as an integral part of a deep formation, preparing them for the eventual completion of a doctoral thesis.
• CG02 - Acquisition of high level mathematical tools for diverse applications covering the expectations of graduates in mathematics and other basic sciences.
• CG03 - Know the broad panorama of current mathematics, both in its lines of research, as well as in methodologies, resources and problems it addresses in various fields
• CG04 - Train for the analysis, formulation and resolution of problems in new or unfamiliar environments, within broader contexts.
• CG05 - Prepare for decision making based on abstract considerations, to organize and plan and to solve complex issues.
BASICS
• CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context
• CB7 - That students know how to apply the knowledge acquired and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study.
• CB8 - That students are able to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments
• CB9 - That students know how to communicate their conclusions and the knowledge and ultimate reasons that sustain them to specialized and non-specialized audiences in a clear and unambiguous way
• CB10 - That students have the learning skills that allow them to continue studying in a way that will be largely self-directed or autonomous.
3.2 TRANSVERSAL COMPETENCES
• CT01 - Use bibliography and search tools for general and specific bibliographic resources of Mathematics, including Internet access
• CT02 - Optimally manage work time and organize available resources, establishing priorities, alternative paths and identifying logical errors in decision making
• CT03 - Enhance capacity for work in cooperative and multidisciplinary environments.
3.3 SPECIFIC COMPETENCES
• CE01 - Train for the study and research in mathematical theories in development.
• CE02 - Apply the tools of mathematics in various fields of science, technology and social sciences
• CE03 - Develop the necessary skills for the transmission of mathematics, oral and written, both in regard to formal correction, as well as in terms of communicative effectiveness, emphasizing the use of appropriate ICT.
According to the general directions of the master. It will combine lectures with reading and studying assigments, making special emphasis in the resolution of problems.
The general criteria of the master will be followed. Continuous assessment with periodical written and oral exercises of theoretical-practical character. The students may reach maximum score without attending the final exam.
WORK AT CLASSROOM
Blackboard classes 22 hours
Tutorials in group or individualized 2 hours
TOTAL work at classroom: 24 hours
PERSONAL WORK OF THE STUDENT
Autonomous individual study or in group 41 hours
Writing of exercises, conclusions or other works 5 hours
Recommended reading, activities at library or similar 3 hours
Preparation of oral presentations, discussions or similar 2 hours
TOTAL Personal work of the student: 51 hours
To work regularly, to study daily and to complete the proposed activities.
Rosa Mª Trinchet Soria
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813205
- rosam.trinchet [at] usc.es
- Category
- Professor: University Lecturer
Daniel Cao Labora
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813174
- daniel.cao [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
| Wednesday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom 10 |
| Thursday | |||
| 11:00-12:00 | Grupo /CLIL_01 | Galician | Classroom 10 |
| 01.10.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 10 |
| 06.09.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 10 |