Ateneo - UPO

PROBABILITY AND STATISTICS: Introduction to the theory of probability and to statistical inference. NUMERICAL METHODS: finite arithmetic and error analysis, numerical resolution of linear systems by direct methods, approximations of functions, numerical integration. Introduction to Octave.

PROBABILITY AND STATISTICS: + Lecture notes uploaded on the IT platform DIR. + Paolo Baldi: Calcolo delle Probabilità e Statistica, McGraw-hill, 1998. + Sheldon M. Ross: Probabilità e Statistica per l'Ingegneria e le Scienze, Apogeo Education - Seconda Edizione 2008. NUMERICAL METHODS: + Notes of the teacher uploaded on the IT platform DIR.

Introducing the student to the theory and applications of probability with emphasis on discrete random variables. Introducing the student to the basic elements of statistics with emphasis on parameter estimation. Provide knowledge about basic numerical methods and the analysis of their main properties; develop the student's ability to correctly and consciously use and implement on the computer the mathematical tools introduced.

PROBABILITY AND STATISTICS: Differential and integral calculus in one dimension and more. NUMERICAL METHODS: The knowledge of the main notions provided during a basic course of Mathematics is required. In more details: Functions and sequences, Limits, Differential calculus, Taylor expansion, Integral calculus in one variable. Vector spaces, Linear systems, Matrix algebra.

Teaching will take place through lectures on the blackboard. In addition to the theoretical lessons, classroom exercises will be carried out by the teacher with the active involvement of the students to deepen the topics covered during the theoretical lessons. The concepts covered by the course will come stimulate collegially in the classroom and applied directly during classroom exercises for students' critical sense and autonomy of judgment.

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the __Staff
Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities.

Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the
tutor in charge of the course to define the examination modalities, concerning academic aspects.

The exam consists of two examinations, one for each module. The examinations will focus on the entire program covered in class and might also include some exercises. The student is guaranteed the possibility of taking the two modules of the exam separately (i.e. "Probability and Statistics" and "Numerical Methods"). However, a single mark is recorded for the two courses of "Probability and Statistics" and "Numerical Methods", which will be assigned starting from the average rounded up of the two marks obtained by a collegial evaluation. The exam results highlight the degree of understanding of theoretical concepts and the ability to use them to solve new problems.

PROBABILITY AND STATISTICS: - Basic probability theory: fundamental axioms, space with equally likely outcomes and combinatorics, conditional probability, Bayes' formula - Random variables and expectation: random variables on finite spaces, independent variables, expected value, variance and covariance, binomial random variables - Limit theorems: Markov and Chebyshev inequalities, law of large numbers, central limit theorem - Basic inferential statistics: sample statistics, maximum likelihood estimators - Shannon entropy: entropy as a measure of uncertainty, exponential families and estimation of their parameters - Gaussian random variables: introduction to infinite probability spaces, Gaussian sample, confidence intervals for the mean and the variance. NUMERICAL METHODS: The course provides notions on error analysis, finite precision number system and arithmetic, efficient methods for the solution of systems of linear. The course also approaches the main issues related to function approximation and numerical integration. Finally, the use of the OCTAVE software from the command window and by using M-files is presented.

- Knowledge and understanding: a study of the theoretical foundations (theorems, definitions) of statistical and numerical techniques and study of their applications.
- Applying knowledge and understanding: full ability to apply the calculation and analysis techniques provided by the course. Development of necessary software, use of already available automatic calculation methods, and implementation of new algorithms.
- Communication skills: be able to provide both orally the details of the calculation and the results of applying the methods to the problem. Ability to communicate calculation procedures through the detailed analysis of the stages of both manual and automatic calculation through the implementation of software.
- Learning skills: acquisition of a good mastery of statistical-probabilistic and numerical methods, in order to be able to expand one's knowledge in the continuation of the studies.