K5: Know the fundamental definitions and results of probability and statistics and know how to use them to model uncertain systems. S5: Break large or complex problems into smaller, more manageable parts, and apply mathematical or computational analysis techniques to each component. "C2: Propose solutions to practical problems, using the most appropriate results and techniques, and critically analyze the results obtained, explaining the hypotheses and limitations of the models used. " C3: Use numerical or symbolic calculation, statistical analysis, or optimization software to approximate the solution of mathematical problems arising in a professional context and know how to analyze and predict behaviors in different contexts, implementing efficient solutions to complex problems.

Introduction to Stochastic Processes Discrete Markov chains Markov Chains of Continuous Time Renewal processes Queuing theory Random graphics Case studies: Monte Carlo algorithm, PageRank algorithm, Call centers, Social networks.

A1: CLASSROOM LECTURES. Each subject has two weekly sessions: a lecture session, with more theoretical content, and a reduced session, with more practical content. In this session, the main theoretical content takes place. 100% de presencialidad / A2: FACE-TO-FACE CLASSES: REDUCED (WORKSHOPS, SEMINARS, CASE STUDIES). As indicated above, this session has a more practical content where teachers can carry out some of the examples given. 100% de presencialidad / A3: STUDENT INDIVIDUAL WORK. 0% de presencialidad / A4: LABORATORY SESSION. This is a series of additional hours where teachers reinforce more practical content with students. 100% de presencialidad / A5: FINAL EXAM. 100% de presencialidad M1: SEMINARS AND LECTURES SUPPORTED BY COMPUTER AND AUDIOVISUAL AIDS. / M2: PRACTICAL LEARNING BASED ON CASES AND PROBLEMS, AND EXERCISE RESOLUTION. / M3: INDIVIDUAL AND GROUP OR COOPERATIVE WORK WITH THE OPTION OF ORAL OR WRITTEN PRESENTATION. / M4: INDIVIDUAL AND GROUP TUTORIALS TO RESOLVE DOUBTS AND QUERIES ABOUT THE SUBJECT.