Principles of Mathematics and Computer Skills
A.Y. 2026/2027
Learning objectives
The course aims to provide students with basic knowledge of mathematical analysis and descriptive statistics. One of its main objectives is to develop the ability to analyze the behaviour of a real-valued function and determine its graph in a Cartesian coordinate system by applying the basic principles of differential calculus. Another important learning objective is to provide students with skills in the processing of experimental data through the introduction of commonly used statistical descriptors.
The course also aims to provide a clear, accessible, and conceptually rigorous understanding of the foundations of Artificial Intelligence and generative AI, establishing a shared vocabulary and intuitively explaining how machine learning models and language models operate. The course introduces the fundamentals of generative AI, from the role of data and embeddings to an understanding of the capabilities and limitations of these models. It also explores the main ethical, social, and regulatory risks, promoting transparency, accountability, and the responsible use of AI tools through practical case studies, prompt engineering, and professional applications.
The course also aims to provide a clear, accessible, and conceptually rigorous understanding of the foundations of Artificial Intelligence and generative AI, establishing a shared vocabulary and intuitively explaining how machine learning models and language models operate. The course introduces the fundamentals of generative AI, from the role of data and embeddings to an understanding of the capabilities and limitations of these models. It also explores the main ethical, social, and regulatory risks, promoting transparency, accountability, and the responsible use of AI tools through practical case studies, prompt engineering, and professional applications.
Expected learning outcomes
Through this course, students will acquire the main concepts of mathematical analysis as applied to the study of a real-valued function. In particular, they will understand the meaning of the domain of a function, the continuity of a function over an interval, and the derivative of a function at a given point. They will also be expected to demonstrate knowledge of the main statistical descriptors used to interpret a set of experimental data. Students will be able to interpret the behavior of a function and describe data from a statistical perspective. By applying the knowledge acquired, they will be able to interpret trends in the behavior of variables relevant to their research.
With regard to AI literacy, by the end of the course students will be able to define Artificial Intelligence and generative AI, distinguishing between rule-based symbolic approaches and systems that learn from data, while understanding how generative models operate. Students will be able to describe the role of data in machine learning processes, from data collection and encoding to their transformation into numerical representations, and to interpret embeddings and vector spaces as tools for representing texts, images, and concepts in computational form.
Students will gain a conceptual understanding of neural networks, deep learning, and language models, recognizing the statistical principles underlying prediction and generation. They will also be able to critically analyze the structural limitations of such models in terms of approximation, generalization, opacity, and dependence on training data. In addition, they will be able to identify bias and ethical risks, applying principles of explainability, transparency, and accountability, also in light of the main regulatory frameworks, and to use generative AI tools responsibly in professional and educational contexts.
Finally, students will be able to formulate effective prompts and develop coherent and responsible use cases, integrating technical competence, critical thinking, and ethical awareness for the strategic use of generative AI.
With regard to AI literacy, by the end of the course students will be able to define Artificial Intelligence and generative AI, distinguishing between rule-based symbolic approaches and systems that learn from data, while understanding how generative models operate. Students will be able to describe the role of data in machine learning processes, from data collection and encoding to their transformation into numerical representations, and to interpret embeddings and vector spaces as tools for representing texts, images, and concepts in computational form.
Students will gain a conceptual understanding of neural networks, deep learning, and language models, recognizing the statistical principles underlying prediction and generation. They will also be able to critically analyze the structural limitations of such models in terms of approximation, generalization, opacity, and dependence on training data. In addition, they will be able to identify bias and ethical risks, applying principles of explainability, transparency, and accountability, also in light of the main regulatory frameworks, and to use generative AI tools responsibly in professional and educational contexts.
Finally, students will be able to formulate effective prompts and develop coherent and responsible use cases, integrating technical competence, critical thinking, and ethical awareness for the strategic use of generative AI.
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
Mathematics Program
- Review of fundamental prerequisites: number sets, algebra review, equations, inequalities, logarithms, and exponentials.
- Functions and graphs. Domain, codomain and function study. Properties of functions: injective, surjective, and bijective functions. Even and odd functions. Periodic functions. Inverse function and composite function.
- Graphs of elementary functions: lines, powers, parabolas, exponentials, logarithms, and trigonometric functions.
- Concept of limit. Limits of elementary functions. Scale of infinities. Calculation of limits.
- Continuous and discontinuous functions.
- Derivatives: derivative of a functions at a point and its geometric interpretation. Tangent line to the graph of a function at a point. Points of non-differentiability.
- Differentiation rules. Operations with derivatives: sum, product, quotient, and composition of functions.
- Higher-order derivatives.
- Theorems of differential calculus and application of derivatives to the study of the graph of a function.
- Elements of statistics: random variables, measures of central tendency and variability, correlation, and linear regression.
AI Literacy Program
The AI Literacy course is delivered online through the platform https://ailiteracy.unimi.it/.
The course is structured into three modules, divided into 12 sections. Each section includes a variable number of lessons, each lasting no more than 10 minutes. The course also includes interactive learning activities based on AI tools, designed to support students through personalised learning pathways.
The topics covered are detailed below.
MODULE 1 - Foundations of Generative Artificial Intelligence
1.1 Introduction to Artificial Intelligence
1.2 Data, Encoding and Representation
1.3 Data Operations
1.4 Neural Networks and Deep Learning
1.5 Embeddings, Language Models and Generative Artificial Intelligence
MODULE 2 - Interpretability, Regulation and Ethical Issues
2.1 Hallucinations and Explainability
2.2 Bias, Stereotypes and Cultural Homogenisation
2.3 AI Regulation in Europe and Italy
MODULE 3 - Generative AI (GenAI): Tools, Applications and Use
3.1 Types and Evolution of Generative AI Models
3.2 Model Evaluation and Main Applications
3.3 Prompt Engineering
3.4 GenAI Use Cases
- Review of fundamental prerequisites: number sets, algebra review, equations, inequalities, logarithms, and exponentials.
- Functions and graphs. Domain, codomain and function study. Properties of functions: injective, surjective, and bijective functions. Even and odd functions. Periodic functions. Inverse function and composite function.
- Graphs of elementary functions: lines, powers, parabolas, exponentials, logarithms, and trigonometric functions.
- Concept of limit. Limits of elementary functions. Scale of infinities. Calculation of limits.
- Continuous and discontinuous functions.
- Derivatives: derivative of a functions at a point and its geometric interpretation. Tangent line to the graph of a function at a point. Points of non-differentiability.
- Differentiation rules. Operations with derivatives: sum, product, quotient, and composition of functions.
- Higher-order derivatives.
- Theorems of differential calculus and application of derivatives to the study of the graph of a function.
- Elements of statistics: random variables, measures of central tendency and variability, correlation, and linear regression.
AI Literacy Program
The AI Literacy course is delivered online through the platform https://ailiteracy.unimi.it/.
The course is structured into three modules, divided into 12 sections. Each section includes a variable number of lessons, each lasting no more than 10 minutes. The course also includes interactive learning activities based on AI tools, designed to support students through personalised learning pathways.
The topics covered are detailed below.
MODULE 1 - Foundations of Generative Artificial Intelligence
1.1 Introduction to Artificial Intelligence
1.2 Data, Encoding and Representation
1.3 Data Operations
1.4 Neural Networks and Deep Learning
1.5 Embeddings, Language Models and Generative Artificial Intelligence
MODULE 2 - Interpretability, Regulation and Ethical Issues
2.1 Hallucinations and Explainability
2.2 Bias, Stereotypes and Cultural Homogenisation
2.3 AI Regulation in Europe and Italy
MODULE 3 - Generative AI (GenAI): Tools, Applications and Use
3.1 Types and Evolution of Generative AI Models
3.2 Model Evaluation and Main Applications
3.3 Prompt Engineering
3.4 GenAI Use Cases
Prerequisites for admission
Basic knowledge of arithmetic and algebra: literal calculations, first and second-degree numerical equations in R; first and second-degree inequalities in R.
No prior knowledge is required for the AI Literacy course.
No prior knowledge is required for the AI Literacy course.
Teaching methods
Mathematics: interactive lectures.
AI Literacy is delivered in a blended learning format. In order to acquire the knowledge covered by the course, students are required to study the course content through the e-learning platform available at https://ailiteracy.unimi.it/.
The content is organised into learning pathways, including: (i) Foundations of Generative Artificial Intelligence; (ii) Interpretability, Regulation and Ethical Issues; and (iii) Generative AI (GenAI) Tools, Applications and Use.
Each pathway is divided into learning units, and a self-assessment test is provided at the end of each unit. Students are initially granted access to the first pathway. Access to subsequent pathways is released gradually and is conditional upon successfully completing the self-assessment tests for the units already available.
AI Literacy is delivered in a blended learning format. In order to acquire the knowledge covered by the course, students are required to study the course content through the e-learning platform available at https://ailiteracy.unimi.it/.
The content is organised into learning pathways, including: (i) Foundations of Generative Artificial Intelligence; (ii) Interpretability, Regulation and Ethical Issues; and (iii) Generative AI (GenAI) Tools, Applications and Use.
Each pathway is divided into learning units, and a self-assessment test is provided at the end of each unit. Students are initially granted access to the first pathway. Access to subsequent pathways is released gradually and is conditional upon successfully completing the self-assessment tests for the units already available.
Teaching Resources
Any high school mathematics textbook that mainly covers topics from the fourth and fifth years of secondary school.
The teaching materials for AI Literacy are available on the course webpage: https://ailiteracy.unimi.it/
The teaching materials for AI Literacy are available on the course webpage: https://ailiteracy.unimi.it/
Assessment methods and Criteria
Mathematics Written Test: exercises to be completed in 120 minutes on the practical and theoretical aspects discussed in the lessons. Evaluation is expressed in thirtieths.
The AI Literacy course is delivered online through a centralised service provided by UNIMI.
The final grade is the average of the individual positive evaluations obtained.
Assessment for the AI Literacy course takes place in two separate stages.
The first stage consists of a self-assessment carried out within the online course by completing closed-ended tests relating to the teaching units included in the learning pathways. Completion of all self-assessment tests is a prerequisite for admission to the subsequent assessment stage, namely the final examination.
The second stage, the final examination, takes place in a computer lab and consists of a computer-based test comprising closed-ended questions on all topics covered by the course syllabus. The questions are designed to assess whether students have acquired the knowledge specified in the course learning objectives. During the examination, students may not use printed materials or access any online resources other than those explicitly enabled on the computer used for the test.
Registration for the final examination and notification of the examination result are managed through the University's examination management system.
The AI Literacy course is delivered online through a centralised service provided by UNIMI.
The final grade is the average of the individual positive evaluations obtained.
Assessment for the AI Literacy course takes place in two separate stages.
The first stage consists of a self-assessment carried out within the online course by completing closed-ended tests relating to the teaching units included in the learning pathways. Completion of all self-assessment tests is a prerequisite for admission to the subsequent assessment stage, namely the final examination.
The second stage, the final examination, takes place in a computer lab and consists of a computer-based test comprising closed-ended questions on all topics covered by the course syllabus. The questions are designed to assess whether students have acquired the knowledge specified in the course learning objectives. During the examination, students may not use printed materials or access any online resources other than those explicitly enabled on the computer used for the test.
Registration for the final examination and notification of the examination result are managed through the University's examination management system.
INFO-01/A - Informatics - University credits: 3
MATH-01/A - Mathematical Logic - University credits: 3
MATH-01/A - Mathematical Logic - University credits: 3
Computer basics: 18 hours
Lessons: 24 hours
Lessons: 24 hours
Professor:
Biasibetti Luca
Professor(s)