Mathematics

General objectives: to acquire knowledge in Probability theory and improve problem solving ability. Specific objectives: Knowledge and understanding: at the end of the course the student will have acquired the basic notions ergodic and information theory, stochastic domination and percolation theory. Apply knowledge and understanding: at the end of the course the student will be able to solve problems on discrete random fields, concerning ergodic and information theory, stochastic domination and percolation theory. Critical and judgmental skills: the student will have the basis to analyze the similarities and relationships between the topics covered in the course and the discrete probability developed in the first probability course. It will acquire familiarity with key concepts in Probability theory, useful also in other fields. Communication skills: the student must show the ability to present the contents of the course in the oral part of the assessment and in the solution of problems in the written test. Learning skills: the acquired knowledge will allow the student to study in depth some aspects of the theories presented in the course and will facilitate the study into very active research fields.