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
Center Faculty of Mathematics
Call: Second Semester
Teaching: Sin Docencia (En Extinción)
Enrolment: No Matriculable (Sólo Alumnado Repetidor)
Introduce students to the major stochastic mathematical models, strengthening the mathematical foundations of Probability acquired in graduate study, and initiating the study of stochastic processes.
1. Introduction to the theory of probability. (6h)
2. Sequences of random variables. Laws of large numbers. (3h)
3. Central limit theorem. (3h)
4. Introduction to stochastic processes. (3h)
5. Markov models. (3h)
6. Poisson models. (2h)
7. Gaussian models. (2h)
8. Convergence of stochastic processes. (2h)
Basic bibliography
ATHREYA, K.B.; LAHIRI, S.N. “Measure Theory and Probability Theory”, Springer, 2006.
BATH, U. N.; MILLER, G.K. “Elements of Applied Stochastic Processes”, 3 ed., Wiley, 2002.
BILLINGSLEY, P. “Probability and Measure”, 3ª ed., Wiley, 1995.
ROSS, S.M. “Stochastic Processes”, 2ª ed., Wiley, 1996.
Complementary bibliography
BILLINGSLEY, P. “Convergence of Probability Measures”, 2ª ed., Wiley, 1999.
KARLIN, S.; TAYLOR, H.M. “A Second Course in Stochastic Processes”, Academic Press, 1981.
LAHA, R.G.; ROHATGI, V.K. “Probability Theory”, Wiley, 1979.
POLLARD, D. “Convergence of Stochastic Processes”, Springer, 1984
1. BASIC AND GENERAL COMPETENCES
1.1 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.
1.2 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.
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. 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.
• Blackboard sessions will basically consist of lessons taught by the teacher, dedicated to the exhibition of the theoretical contents and resolution of problems or exercises, encouraging student participation (competences CG02, CG03, CB6, CE01 and CE02).
• Exercises and assignments for independent resolution by students with teacher supervision (competences CG01, CG04, CG05, CB7, CB8, CB9, CB10, CT01, CT02, CT03 and CE03) will be proposed.
• In addition to classroom teaching there will be a course in the Virtual Campus of the University, where students can find additional materials and asynchronous communication tools.
• Continuous assessment based on the resolution of proposed problems, submitted or exposed works and participation in class, in order to check the different skills.
• Students who do not pass the continuous assessment must take a final exam, which will weigh 70% on the grade of the subject.
• In the case of fraudulent exercises or tests, the provisions of the "Regulations on the Evaluation of Students' Academic Performance and on the Review of Qualifications" shall apply.
The working time required to pass the subject relies heavily on prior knowledge and skill of the student. Typically, average working hours and personal (the study of theoretical results and problem solving) for each hour of class should be sufficient.
• To successfully overcome the matter is required class attendance and review and resolution of problems is proposed.
• With the use of general literature or recommending specific matters can complement and extend any topic.
Pedro Faraldo Roca
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813216
- pedro.faraldo [at] usc.es
- Category
- Professor: University Lecturer