MATHSSets, numbers and proofs - Functions on - Concept of real function - Polynomials -Linear functions - Exponential function - Inverse function - Logarithms - The slope of afunction - Computing derivatives - Differentiability and continuity - Limits - Higherorderderivatives - Approximation by differentials - Using first and second derivativesfor graphing - Asymptotes - Maxima and minima - Composite functions and the chainrule - Inverse functions and their derivative - Integral calculus - The fundamentaltheorem of calculus - Indefinite integrals - Introduction to linear algebra - Systems oflinear equations - Matrix algebra- Determinants - Functions of several variables - Partialderivatives - Total differentiation - Implicit functions - Level curve and their tangent

Methods of proof.4 Topology in RN. Continuous functions.4 Differentiable functions in RN. Taylor approximations.3 Convexity.2 Separation theorems.2 Fixed point theorems.1 Linear algebra. Eigenvalues and eigenvectors. Quadratic forms.3 Unconstrained optimization.2 Constrained optimization: equality constraints.2 Constrained optimization: inequality constraints.2 Constrained optimization: mixed constraints.2 Kuhn-Tucker conditions.3 The meaning of multipliers. The envelope theorems.4 Convex programming.

ECONOMETRICSOverview of basic probability and inferential concepts (Otranto)4 Classical linear regression model (Otranto)3 Multiple Regression (Otranto)4 Endogeneity and instrumental variables (Di Pino)2 Two-Stage least squares (Di Pino)5 Discrete regression models (Di Pino)4 Introduction to time series: stationarity, covariance matrixestimator and VAR (Distaso)3 Nonstationary time series and asymptotic theory (Distaso)4 GMM and Panel data models (Distaso)