Applied Mathematics

General Goals: rigorous knowledge of probabilistic models from applications to the relationship with other part of mathematic. Specific goals: Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to probability spaces, random variables, independence, laws of large numbers, characteristic functions, weak convergence, limit theorems. Apply knowledge and understanding: at the end of the course the student will be able to solve simple problems that require the use of probabilistic techniques both in applications and in problems of pure mathematics. Critical and judgmental skills: the student will have the basis to analyze the analogies and the relationships between the topics covered and topics of analysis or mathematical physics; will also acquire the tools that have historically led to the solution of classical problems. Communication skills: ability to expose the contents in the oral part of the assessment and in any theoretical questions present in the written test. Learning skills: the acquired knowledge will allow a study, individual or given in an LM course, related to more specialized aspects of probability.