Algebra 37 ECTS
Taught by Lucas Gnecco Heredia.
Abstract algebra: integers and modular arithmetic, groups (cyclic and permutation groups, quotients, homomorphisms), and an introduction to rings, ideals, and polynomial rings.
Year 2
The second year deepens the mathematics and computer science of the first – algebra, analysis, advanced statistics, and programming taken as far as the theory of computation – and turns towards the methods that make current AI work: deep learning, statistical learning, bandits and reinforcement learning, and the mathematical optimization underneath all of them. Data analysis and web development put them to work on real data.
It is also the year in which the wider questions arrive in their own right, with courses on the ethics and philosophy of AI, its economics, and what cognitive science has to say about machines that are said to think; and the year of a personal project, carried out over the semester under supervision.
Semester 3 · September to January
8 courses · 30 ECTS · 378 contact hours in the timetabled courses · 1 optional course besides
Foundations of AI
Analysis 37 ECTS
Taught by Maja Ivkovic.
Analysis in several variables: continuity and compactness, differential calculus up to the inverse and implicit function theorems, extrema, and the Riemann integral in several dimensions, with Fubini’s theorem and changes of variables.
Computer Programming 37 ECTS
Taught by Pierre Senellart and Anton Gnatenko.
In two parts. The first is the theory of computation: computability, models of computation, complexity classes and NP-completeness, automata, and formal languages – what can be computed at all, and what can be computed efficiently. The second is software development as practised today: specification and testing, version control, code review and continuous integration, AI coding tools and their failure modes, and the release of open source software.
Advanced Statistics3 ECTS
Taught by Alice Lacan and Jonathan Chirinos Rodríguez.
Probability and statistics beyond the first year: multivariate distributions, probability inequalities, convergence of random variables, Markov chains; then statistical inference, with the properties of estimators, Fisher information and the Cramér–Rao bound, maximum likelihood, the bootstrap, and MCMC.
AI-focused courses
Deep Learning 13 ECTS
Taught by Changhong Wang and Octave Mariotti.
Neural networks and how they are trained, from the single perceptron up: backpropagation, optimization, and regularization, then convolutional networks for vision, recurrent networks for sequences, and transformers. Students implement a small deep learning library from scratch and run their own experiments with it.
Transverse courses
Ethics and Philosophy of AI1.5 ECTS
Taught by Ben White.
A discussion-based seminar on the philosophical and ethical questions raised by artificial intelligence: whether machines can think or be conscious, AI companionship, existential risk, the effects of AI on attention, cognition and creativity, privacy, algorithmic injustice, and the environment.
Economics of AI1.5 ECTS
Taught by Zichuan Li.
The economics of data, digital platforms, and artificial intelligence: how AI affects firms, consumers, and competition, its effects on productivity, employment, and inequality, privacy and algorithmic bias, and the questions it raises for regulation.
Digital Fresk0 ECTS
A one-off collaborative workshop on the environmental cost of digital technology: where the energy and the materials go, and what follows for the systems students will build.
Additional languageoptional0 ECTS
An optional language course taken at the language centre of PSL, at the Centre des Mines: French as a foreign language, or another language. It is not compulsory and carries no credit.
Semester 4 · February to June
10 courses · 30 ECTS · 354 contact hours · 1 optional course besides
Foundations of AI
Mathematical Optimization7 ECTS
Taught by Panagiotis Patsilinakos.
Convexity, gradient descent and its variants, duality and Lagrange multipliers, linear programming, and the optimization methods that training a model comes down to.
Analysis 43 ECTS
Taught by Maja Ivkovic.
Metric spaces, elements of topology, completeness and compactness, and normed vector spaces.
Ordinary Differential Equations3 ECTS
Taught by Nat Mathews.
Ordinary differential equations and dynamical systems, with the emphasis on what is useful in artificial intelligence: stability, flows, and continuous views of learning dynamics.
Data Analysis and Visualization3 ECTS
Taught by Octave Mariotti.
Working with real datasets end to end: cleaning and exploring data, choosing a representation, and building visualizations that show what is there rather than what one hoped to find.
Web Development3 ECTS
Web development in earnest, where the databases course of the first year stopped at a page over a query: HTTP and the client-server model, front-end frameworks and interfaces that react to their own state, the design of the interface between a front end and a server, sessions and authentication, the vulnerabilities a web application has to be written against, and what deploying one involves.
AI-focused courses
Statistical Learning3 ECTS
The theory behind supervised learning: risk and empirical risk, bias and variance, generalization bounds, kernel methods, and ensemble methods.
Deep Learning 22.5 ECTS
Taught by Shuyu Dong.
A second course in deep learning, built around a personal project supervised by the teacher: attention and transformer architectures, generative models, and representation learning.
Bandits and Reinforcement Learning1.5 ECTS
Taught by Changhong Wang and Octave Mariotti.
Learning by trial and error: multi-armed bandits and the exploration-exploitation trade-off, Markov decision processes, Q-learning, and applications to games and robotics.
Transverse courses
AI and Cognition1.5 ECTS
Taught by Edgar Dubourg.
What cognitive science and neuroscience say about perception, learning, memory, and motivation in humans, and what that means for machines built to do the same things.
Personal Project2.5 ECTS
Taught by Lucas Gnecco Heredia.
A project of the student’s own, carried out over the semester with regular supervision. It can take various forms: work for a non-profit, a piece of software, a research project.
Additional languageoptional0 ECTS
An optional language course taken at the language centre of PSL, at the Centre des Mines: French as a foreign language, or another language. It is not compulsory and carries no credit.
Course descriptions are written and maintained by the teaching team. Contact hours are hours of class per student; credits follow the European ECTS scale, 60 of them per year.
