C8835 - MATEMATICA PER L'INTELLIGENZA ARTIFICIALE

Learning outcomes

The course aims to provide students with the mathematical foundations necessary for the study of Artificial Intelligence. It will review key topics from various areas of basic mathematics, including linear algebra, mathematical analysis, and statistics. The course is designed to address any gaps in prior knowledge and to strengthen the essential skills required for continuing studies in more advanced subjects.

Course contents

Linear Algebra

1. Vector spaces, subspaces; linear combinations and bases.
2. Coordinates with respect to a basis, dimension; operations among subspaces.
3. Linear mappings and their matrices.
4. Linear systems, rank theorem, and affine subspaces.
5. Change of basis, isomorphisms, and determinants.
6. Eigenvalues, eigenvectors, and diagonalization of endomorphisms.
7. Symmetric bilinear forms, scalar products, and orthogonality.
8. Orthonormal bases, orthogonal matrices, isometries. Summary exercises.

Calculus

1. Functions of multiple variables: limits and continuity.
2. Partial derivatives, directional derivatives, and gradients.
3. Differentiability, differential, and Jacobian matrix.
4. Second derivatives, Schwarz’s theorem, and Hessian matrix.
5. Optimization: maxima, minima, and Weierstrass’s theorem.
6. Multiple integrals and multivariate probability density.
7. Change of variables and distribution transformations.
8. Summary exercises and applications.

 

Probability and Statistics

Basic concepts of combinatorics and discrete probability spaces. Random variables, expected value, and variance. Dependence and independence of random variables. Continuous probability spaces, cumulative distribution functions, and density functions. The Central Limit Theorem. Basic concepts of inferential statistics: confidence intervals and statistical tests.

 

 

Office hours

See the website of Fabrizio Caselli

See the website of Luca Moci