MIA – The Mathematics of Artificial Intelligence: Understanding Large Language Models for Teaching

The Teaching and Learning Centre and the Department of Mathematics at the University of Turin are offering MIA, a course that links the study of the mathematical foundations of Artificial Intelligence to the teaching of mathematics and physics.

Using simplified yet rigorous models, the course explores the mathematical and computational principles of Large Language Models (LLMs): numerical representation of language, neural networks, training and text generation. The simplifications will be explicitly explained and compared with the characteristics of real-world systems.

The course continues with the use of generative AI in instructional design and the preparation of materials, exercises and activities, culminating in an analysis of how students utilise it. Lectures will alternate between theoretical frameworks, guided examples and practical sessions, with a focus on the opportunities, limitations and reliability of the generated responses.

Target audience and requirements

The course is aimed at secondary school teachers of mathematics and physics, including those on temporary contracts. To be eligible for admission, candidates must hold specific master’s degrees, specialist degrees or V.O. degrees in the fields of science, technology, engineering, architecture, finance and statistics. The full list of eligible degree programmes is set out in the Rector’s decree.

Registration

Pre-registration is open from 9.30 am on 14 October 2026 until 3.00 pm on 4 December 2026 via the members’ area of the website www.unito.it.

• Course Registration Manual👈🏻

There will be a minimum of 25 and a maximum of 40 participants. Should the maximum number of eligible participants be exceeded, admission will be based on a comparative assessment of CVs.

The list of successful applicants will be published on this page on 11 December. Enrolment will be finalised when successful applicants register for the course between 11 and 18 December 2026.

Learning objectives

The course aims to provide tools to:

• understand the fundamental mathematical principles of modern Artificial Intelligence systems and Large Language Models (LLMs);
• distinguish the roles of data representation, training and generation in the functioning of a model;
• critically assess the potential, limitations and reliability of generative AI tools;
• make informed use of AI to support design and teaching activities;
• design activities that address students’ use of AI in a critical and informed manner.

Programme

Mathematical Foundations of LLMs – 6 hours

• Data, representations and models.
• Training as an optimisation process.
• Generation as the application of the trained model.
• From educational simplifications to real-world systems.

AI as a tool for teachers – 2 hours

• Use of generative AI tools in instructional design.
• Production and review of materials, exercises and activities.
• Potential, limitations and reliability of generated responses.

AI and students – 2 hours

• Impact of generative AI on study and problem-solving practices.
• Opportunities and challenges in the learning of mathematics and physics.
• Analysis and design of teaching activities that integrate the use of AI in an informed manner.

Lessons timetable

All sessions will be held in person at the Department of Mathematics, Via Carlo Alberto 10, Turin. The course is worth 2 CFU credits in the MATH-03/A subject area. The course consists of five sessions, each lasting two hours. Attendance of at least 80 per cent of the sessions is required, equivalent to four out of five sessions. Enrolled students will be informed of the lecture theatre shortly before the course begins.

Registration fee

The fee is 100 euros per participant, plus an additional charge of €16.00 for government stamp duty and €1.50 for SIAE fees.
Payment can be made using the Carta Docente.