The course presents a revision of basic concepts and tools of Calculus and Linear Algebra that may be of application in the empirical research in Social Sciences. The course is of intermediate level. It is then advisable to have a solid background of Linear Algebra and Mathematical Analysis

Knowledge of basic concepts of Calculus and Linear Algebra

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 using R 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 Simulation 3.1 Random numbers 3.2 Monte Carlo simulations 3.3 Monte Carlo integration 3.4 Simulating physical systems 4 Optimization 4.1 One-dimensional optimization 4.2 Linear programming 4.3 Quadratic programming

Competences will be acquired by students from: [I] Theory classes: 5 sessions [II] Practical classes: 5 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.