Mathematics for Ai
A.Y. 2023/2024
Learning objectives
To introduce the main tools of mathematics for AI
Expected learning outcomes
At the end of the course students will be able to understand and use the main mathematical tools used in the domain of AI. They will be familiar with the basis concepts of algebra, optimisation amd modellization used in the context of artificial intelligence and machine learning
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
The first part of the course will be devoted to the introduction of the basic concepts of linear algebra and probability with the aim of introducing the PCA analysis allowing to extract a few meaningful data from a large set of data.
The second part will be devoted to optimization.
More topics will be discussed, depending on the time left and on the interests of the students
More in detail:
Linear algebra: matrices, vectors, eigenvalues and eigenvectors, diagonalization.
Basic probability: Gaussian distribution, covariance, PCA.
Calculus and optimization:
Recall of the main ideas of calculus for functions of one variable: derivatives, maxima and minima, a few algorithms for determining maxima and minima.
Partial derivatives of a function of more than one variable, gradient. Maxima and minima of a function of more than one variable. Constrained maxima and minima, Lagrange multipliers.
Convex optimization: Convex sets, convex functions. Subderivatives and subgradients.
The second part will be devoted to optimization.
More topics will be discussed, depending on the time left and on the interests of the students
More in detail:
Linear algebra: matrices, vectors, eigenvalues and eigenvectors, diagonalization.
Basic probability: Gaussian distribution, covariance, PCA.
Calculus and optimization:
Recall of the main ideas of calculus for functions of one variable: derivatives, maxima and minima, a few algorithms for determining maxima and minima.
Partial derivatives of a function of more than one variable, gradient. Maxima and minima of a function of more than one variable. Constrained maxima and minima, Lagrange multipliers.
Convex optimization: Convex sets, convex functions. Subderivatives and subgradients.
Prerequisites for admission
Basic of elementary mathematics, in particular computations with polynomials, elements of combinatorial calculus, to be able to read the graph of a function, elements of differential calculus
Teaching methods
Lectures
Teaching Resources
The main reference book is: Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong (2020), Cambridge University Press
Assessment methods and Criteria
Written and oral examination
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Lessons: 48 hours
Professor:
Bambusi Dario Paolo
Educational website(s)
Professor(s)