Mathematics for Ai
A.Y. 2025/2026
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
Course syllabus
Summary of calculus in 1 variable. (Functions, graph of a function, tangent and derivative, elementary examples)
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.
Probability. Introduction to elementary probability, conditional probability, Bayes theorem and applications.
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). Principal components analysis (PCA) 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.
Probability. Introduction to elementary probability, conditional probability, Bayes theorem and applications.
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). Principal components analysis (PCA) and applications.
Prerequisites for admission
Prerequisites for this course include a knowledge of basic mathematics (fractions, manipulation of polynomials, solution of equations and inequalities of first and second order). Basic tools for the solution of linear systems.
Teaching methods
Lectures and exercises
Teaching Resources
Some material is given below. More material will be presented during the lectures.
For the part on probability I am using the text book that you can find here:
https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/edit
It is part of a larger project on probability that you can find here:
https://projects.iq.harvard.edu/stat110/
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In addition to the book used in course, PCA is very well explained in wikipedia:
https://en.wikipedia.org/wiki/Principal_component_analysis
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For what concerns the part on free optimization, I suggest the following text
https://www.lboro.ac.uk/media/media/schoolanddepartments/mlsc/downloads/HELM%20Workbook%2018%20Functions%20of%20Several%20Variables.pdf
Sect. 1,2,3.
It also contains several exercises of the kind that will be presented in the exam.
For the part on probability I am using the text book that you can find here:
https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/edit
It is part of a larger project on probability that you can find here:
https://projects.iq.harvard.edu/stat110/
%%%%%%%%%%
In addition to the book used in course, PCA is very well explained in wikipedia:
https://en.wikipedia.org/wiki/Principal_component_analysis
%%%%%%%%%
For what concerns the part on free optimization, I suggest the following text
https://www.lboro.ac.uk/media/media/schoolanddepartments/mlsc/downloads/HELM%20Workbook%2018%20Functions%20of%20Several%20Variables.pdf
Sect. 1,2,3.
It also contains several exercises of the kind that will be presented in the exam.
Assessment methods and Criteria
Written examination.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Lessons: 48 hours
Professor:
Bambusi Dario Paolo
Educational website(s)
Professor(s)