Mathematics for Ai
A.Y. 2024/2025
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: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Online lessons and practicals with the possibility of following in streaming or using recordings.
Course syllabus
Linear Algebra and applications. Real vector spaces. Linear combination, dependence and linear independence. Basis and dimension in R^n. Algebra of vectors, inner product and Norm. Matrix algebra (inverse, rank, derivatives, eigenvalues, diagonalization and factorization).
Introduction to Graph theory and applications.
Basic Calculus for Real functions on Rn.
Optimization. First and Second order conditions for unconstrained problems. Constrained optimization: equality constraints and Lagrange Multipliers. Inequality constraints. Linear programming. Discrete and continuous dynamical systems with applications.
Discrete Probability.
Introduction to Graph theory and applications.
Basic Calculus for Real functions on Rn.
Optimization. First and Second order conditions for unconstrained problems. Constrained optimization: equality constraints and Lagrange Multipliers. Inequality constraints. Linear programming. Discrete and continuous dynamical systems with applications.
Discrete Probability.
Prerequisites for admission
Prerequisites for this course include a good knowledge of the mathematical tools presented in a basic Calculus course and a Basic Linear Algebra course.
Teaching methods
Frontal Lessons and practicals
Teaching Resources
As a complement to the notes of the teachers, we suggest the following books:
David C. Lay, Steven R. Lay and Judi J. McDonald, Linear Algebra and Its Applications, Pearson, 2016
K. Sydsaeter, P. Hammond, A. Strom, A. Carvajal, Essential Mathematics for Economic Analysis, Pearson, 2016
E. Salinelli, F. Tomarelli, Discrete-Dynamical Models, Springer, 2014, ISBN: 978-3-319-02290-1
Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong (2020), Cambridge University Press
MyAriel web site
David C. Lay, Steven R. Lay and Judi J. McDonald, Linear Algebra and Its Applications, Pearson, 2016
K. Sydsaeter, P. Hammond, A. Strom, A. Carvajal, Essential Mathematics for Economic Analysis, Pearson, 2016
E. Salinelli, F. Tomarelli, Discrete-Dynamical Models, Springer, 2014, ISBN: 978-3-319-02290-1
Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong (2020), Cambridge University Press
MyAriel web site
Assessment methods and Criteria
Assignments (not mandatory):
Assignments using exam.net: maximum 2 points.
P% = percentage of points compared to total points (considering all homework)
It is necessary to have done at least half of the homework
P% >= 75% 2 points
P% >= 45% and < 75% 1 points
P% >0 and < 45% 0.5 points
-----
Written test
6 multiple choice answers = 2 points for each correct answer;
2 multiple choice answers = 4 points for each correct answer;
2 open answers = 6 points for each correct answer.
Minimum (threshold) =18 points
maximum = 32 points
........................................................................................
Project (not mandatory)
3 points if basic requirements are met
Assignments using exam.net: maximum 2 points.
P% = percentage of points compared to total points (considering all homework)
It is necessary to have done at least half of the homework
P% >= 75% 2 points
P% >= 45% and < 75% 1 points
P% >0 and < 45% 0.5 points
-----
Written test
6 multiple choice answers = 2 points for each correct answer;
2 multiple choice answers = 4 points for each correct answer;
2 open answers = 6 points for each correct answer.
Minimum (threshold) =18 points
maximum = 32 points
........................................................................................
Project (not mandatory)
3 points if basic requirements are met
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Lessons: 48 hours