Statistics and Mathematics

The course introduces the fundamental concepts of statistics and the essential tools for analysing and interpreting data in business and socio-economic contexts. The course is structured into four complementary thematic areas: descriptive statistics, probability, statistical inference and bivariate statistics. The first part is devoted to organising, representing and summarising data; the second introduces the fundamental concepts of probability and random variables; the third covers the main tools of statistical inference, from estimation to hypothesis testing; the final part focuses on group comparisons, the study of association between variables, correlation and simple linear regression. Particular attention is paid to the critical interpretation of results, the assessment of uncertainty and the correct communication of quantitative evidence.

The course introduces the main mathematical tools for the analysis of business and economic problems and is organised into four progressive blocks. Block 1 covers functions of one variable, domain, graphical representation, limits and continuity, with applications to cost, revenue, profit and demand. Block 2 addresses derivatives, marginal quantities, monotonicity, extrema, functions of two variables, partial derivatives and optimisation techniques, with particular attention to decisions concerning quantities, prices and profit. Block 3 introduces systems of linear equations, matrices, determinants, inverse matrices and simple linear programming problems applied to production and resource allocation. Block 4 is devoted to business financial mathematics: compounding, discounting, equivalent rates, annuities, amortisation and the evaluation of investments and financing. The course is completed by a cross-cutting project work that takes students from the construction of business functions to the search for the optimum, from the matrix representation of data to the formulation of a planning problem, and finally to the financial evaluation of an investment or financing.

The course, assuming that the contents of the Business Statistics module have been acquired, develops skills for managing, analysing and interpreting data to support business decisions and is organised into four progressive blocks. Block 1 introduces the data analysis process and the retrieval and use of data from business sources, open data and official statistical sources; the use of R is also introduced gradually. Block 2 covers importing, checking, cleaning, transforming and integrating datasets, as well as exploratory data analysis and data visualisation. Block 3 explores multiple linear regression and introduces logistic regression for analysing quantitative business phenomena and predicting binary events such as insolvency, customer churn or campaign response. Block 4 is devoted to the evaluation of classification models. The main limitations of predictive analysis, including overfitting and bias, and principles for the responsible use of models in business decisions are also addressed. The course is completed by a progressive project work.