Discrete Probability Distributions. Continuous Probability. Combinatorics and Permutations. Discrete Conditional Probability. Distributions and Densities. Expected Value and Variance. Random Variables, Sums of Discrete Random Variables. Law of Large Numbers. Central Limit Theorem. Generating Functions. Markov Chains and Random Walks.
LEARNING OUTCOMES: The teaching consists of lectures and exercises and aims to provide students with a solid basic preparation and the fundamentals of probabilistic methods for physics and main applications of its methods of investigation in various fields.
KNOWLEDGE AND UNDERSTANDING: Students must acquire the knowledge of the theory of probability and its applications. The verification of the students' learning outcomes is aimed at assessing the students' ability to apply the acquired knowledge, and is carried out with written exams, both during the course and at the end of the course, and with a final oral exam.
APPLYING KNWOLEDGE AND UNDERSTANDING: Students must be familiar with the scientific method of investigation and must be able to apply it in the representation and/or modeling of physical reality. They must be able to apply the methods and procedures described during the classes by demonstrating a professional approach, and must have adequate skills both to support theoretical arguments and to solve problems in the field of theory of probability. They must be able to identify the essential ingredients in a problem, knowing how to handle them with the necessary approximations.
MAKING JUDGMENTS: Students must be able to critically analyze the results. They must also be able to use books with technical content and must be able to use the electronic archives available on the WEB for a possible support, making the necessary selection of the information available. Finally, they must know how to motivate the techniques used and the descriptions performed, assessing the correctness, consistency, completeness and effectiveness of their treatments.
COMMUNICATION SKILLS: Students must be able to present their results in a synthetic and analytical way, highlighting the relevant and essential points, providing examples, and using a competent technical language. To this end it is important to have a sufficient knowledge of English to understand the scientific texts, by participating in specific English courses for the Macro Area of Sciences.
LEARNING SKILLS: Students must acquire an understanding of the theory of probability and how this is applicable to various fields of study. This will be done by reading and understanding technical descriptions, selecting and correlating various topics and asking the right questions. In this way they will be able to tackle new fields through an independent study.