K4: To know the definitions and fundamental results of ordinary and partial differential equations and stochastic differential equations, including both the statements and their proofs. S2: Apply combined knowledge of mathematics and physics to model phenomena in areas such as biology, economics, or data science. 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. " C5: Abstract complex problems from real life or other sciences and formulate them in terms of mathematical equations, using variables, constants and parameters to make them understandable and solvable.

Statistical mechanics. Emergent properties: critical phenomena. Complex physical systems: percolation, Ising model. Stochastic dynamic models: random walks and others. Complex networks. Network processes. Complex adaptive systems: biology, social systems

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.