The training complement is aimed at graduates in social and legal sciences (with the exception of economics and business), humanities, and other studies where mathematics have not been regularly used in teaching. Students who consider these training complements unnecessary should address the Master's Director, justifying their reasons and providing evidence of previous training in the specified fields of mathematics and statistics. This course has no formal prerequisites. It introduces basic mathematics and computer skills needed for quantitative and formal modeling courses offered at the Master's program. It prepares students, in particular, for MA courses in quantitative methods (Applied Quantitative Methods for the Social Sciences I & II), Political Economy, and Game Theory.

The course "Basic Statistics for Social Sciences" introduces students to fundamental concepts in calculus, matrix algebra, and set theory, as well as essential concepts in descriptive statistics, probability theory, the foundations of inferential statistics, and the use of statistical software. Acquired competencies: a) BASIC Students acquire the technical knowledge necessary to access advanced training in research methodology. b) GENERAL Students learn the logic of mathematical and statistical analysis. c) SPECIFIC Students become familiar with the foundations of calculus, matrix algebra, probability theory, descriptive statistics, and the use of statistical software.

1 Introduction to Maths 1.1 Arithmetic 1.2 Algebra 1.3 Graphs and functions 1.4 Linear Equations 1.5 Quadratic Equations 1.6 Financial Maths 1.7 Introduction to calculus 2 Matrix Algebra 2.1 Elementary Geometry and algebra 2.2 Vector Spaces 2.3 Matrix Basics 2.4 Norm, Rank, Trace, Determinant. 2.5 Matrix Inverse, Solution of Linear Systems 2.6 Eigenvalues and Eigenvectors 2.7 Matrices in Statistics and other applications 3 Optimization 3.1 One-dimensional optimization 3.2 Linear programming 3.3 Quadratic programming 4 Introduction to R (the statistical computing language used in the department¿s methods courses), RMarkdown, and LATEX(a typesetting language useful for producing documents with mathematical content).

Competences will be acquired by students from: [I] Theory classes: 3 sessions [II] Practical classes: 3 sessions Activities [I] and [II] will be devoted to exercises, problems, and practical cases. Teaching will make intensive use of resources available in Aula Global. Some short reading notes will be also distributed, for helping to understand specific parts of the course, and to facilitate the transmission of information during the lectures.