Istanza di test Polo Economia

In order to make sure that all students do have the necessary quantitative background that is required to successfully attend the Master Program in Economics, we offer two short courses (24 hours each one of them) on the essentials of Mathematics and Probability.

The two short courses consist of on-campus lectures on 6-15 September 2021: every day 3 hours in the morning and 3 hours in the afternoon. In person classes are offered on-campus, at the School of Management and Economics, corso Unione Sovietica 218 bis, Torino, in classroom number 7, except for the lecture on Tuesday September 7, that will be online only.

The exact calendar of the courses follows below.

Essentials of Mathematics (24 hours)

Teacher: Alberto Turigliatto, email: alberto.turigliatto@unito.it

• Monday 6 September 2021: 9-12 a.m. and 2-5 p.m.
• Tuesday 7 September 2021: 9-12 a.m. and 2-5 p.m. -  on line only: Webex link
• Wednesday 8 September 2021: 9-12 a.m. and 2-5 p.m.
• Thursday 9 September 2021: 9-12 a.m. and 2-5 p.m.

Essentials of Probability (24 hours)

Teacher: Guillaume Kon Kam King, email: guillaume.konkamking@gmail.com

• Friday 10 September 2021: 9-12 and 2-5 p.m.
• Monday 13 September 2021: 9-12 and 2-5 p.m.
• Tuesday 14 September 2021: 9-12 and 2-5 p.m.
• Wednesday 15 September 2021: 9-12 and 2-5 p.m.

Attendance of the short courses is not strictly compulsory, but it is strongly encouraged. We expect that all students will consider the short courses and the personal study a good opportunity either to refresh their knowledge or to enlarge it, in order to be well equipped for the official lectures on the more advanced topics.

Topics Covered

Short course on “Essentials of Mathematics”

Functions. Global/local maximum and minimum. Infimum, supremum. Concavity and convexity of functions of one or more variables. Limits of functions of one and more variables. Continuity, derivability and differentiability of functions of one or more variables. Polynomial expansions (Taylor’s and Mc Laurin’s expansions) of functions of one or more variables. Necessary and sufficient conditions for local maxima and minima of differentiable functions of one or more variables. Criteria for concavity and convexity of differentiable functions of one or more variables. Constrained optimization, Lagrange multipliers. Numerical sequences, convergence and divergence criteria. Numerical series and series of functions, uniform convergence, radius of convergence. Riemann integral, integrability of continuous functions, and monotonic functions. Improper integrals. Mean value theorem for integrals. Fundamental theorem of calculus. Computation of indefinite and definite integrals by means of different methods such as: immediate integrals, integrals by parts, integrals by substitution, integrals of rational functions. Riemann-Stieltjes integral. Vector spaces and subspaces. Linear combinations and spans. Linear dependence/independence. Basis and dimension of a subspace. Matrices, operations on matrices, rank of a matrix, Gaussian elimination procedure. Determinant, inverse matrix. Solution to linear systems. Rouché-Capelli theorem and Cramer rule. Eigenvalues and eigenvectors.

Short course on “Essentials of Probability”

Classical approach, frequentist, subjectivist and axiomatic of probability. Conditional probability and independence. Bayes’ theorem. Probability distributions of discrete random variables: Bernoulli, binomial, Poisson, geometric, negative binomial. Probability density functions and distributions functions of the continuous random variables: uniform, normal, negative exponential, gamma, Weibull, lognormal, Pareto. Mixed random variables. Moments of a random variable, moment generating function and its existence. Monotonic function of a random variable. Multivariate probability distributions. Covariance matrix and correlation coefficients. Laws of large numbers and central limit theorem.