Detailed educational programme for the third year of the Paris-Saclay CPES

This third mathematics course offers an in-depth introduction to the topology of normed vector spaces, to duality, and to the study of quadratic and Hermitian forms. It also provides an introduction to differentiable optimization, as well as to fundamental algebraic structures: groups, rings, and fields.

This course introduces the foundations of measure and integration theory, with particular attention given to the construction of σ-algebras, the notion of measurability, and the Lebesgue integral. It explores functional spaces and their properties, in connection with the tools of modern analysis.

Applications to probability illustrate the scope of these concepts in modeling random phenomena and in the rigorous treatment of random variables.

This course offers an introduction to signal theory, in particular to the discrete Fourier transform and the Nyquist-Shannon theorem, which make it possible to analyze and reconstruct digital signals.

It then covers the fundamentals of discrete optimization and convex optimization, with or without constraints, emphasizing analytical and algorithmic solution methods.

This course deals with the solution of ordinary differential equations (ODEs) of order 1 and 2, as well as linear differential systems of order 1 and their extension to ODEs of order n. It covers the Cauchy-Lipschitz theorem, qualitative analysis of solutions, and offers an introduction to partial differential equations (PDEs).

The program provides the essential knowledge needed to understand and use the main tools of differential analysis.

This course covers the fundamental principles of Database Management Systems (DBMS), including data modeling, integrity constraints, persistence, concurrency control, and security. It also focuses on PL/SQL programming and database integration using general-purpose languages (PHP).

This course analyzes the design and evaluation of public policies: who decides, with what objectives, and how to measure their effects using micro- and macro-econometric tools. It also covers behavioral economics as applied to public policies and offers a critical assessment of interventions.

The second part explores economic and financial globalization: the opening of trade since the 19th century, analysis of international trade, regionalization and governance, as well as the formation and functioning of the global capital market.

This module offers a multidisciplinary approach to understanding the fundamental mechanisms of living organisms:

Microbiology: diversity of microorganisms, observation and culture in the laboratory.

Immunology: roles of the molecular and cellular actors of the immune system, vaccination strategies, and principles of antivirals.

Cellular differentiation: concept of stem cells, stages and control of differentiation, role in development and cell renewal.

Neuroscience: anatomo-functional organization of the central and peripheral nervous systems, complex functions, and pathologies, notably neurodegenerative diseases.

This module explores major contemporary issues through four key themes:

Sociology of risk: analysis of perceptions and social constructions of risk, prevention policies, and behaviors in the face of uncertainty.

Sociology of the family: study of family forms, transformations of roles, and intergenerational relationships in various contexts.

Sociology of sexuality (introduction): approach to norms, representations, and practices, in connection with social and cultural developments.

Sociology of social movements: understanding collective mobilizations, their actors, their strategies, and their impact on social change.

This course in Data Analysis and Modeling for Sciences introduces fundamental data analysis and modeling methods common to all scientific disciplines: basic sciences, natural sciences, humanities and social sciences. It covers data collection, visualization, and statistical analysis, as well as mathematical modeling and protocol modeling.

The course utilizes languages such as R, Python, and Julia to develop students' analytical and programming skills.

This introduction to clinical and epidemiological research presents the essential methodological foundations for designing, conducting, and analyzing studies in public health and clinical settings. It covers the key principles of epidemiology, the different types of observational and interventional studies, as well as statistical methods suited to the analysis of clinical data.

Particular attention is given to scientific rigor, research ethics, and the critical interpretation of results, with a practical approach that encourages the application of concepts in various biomedical contexts.

One elective selected from: Fairness in AI; Biological Data Analysis; Theoretical Computer Science.

The objective of this course is to introduce students to the analysis of social phenomena using quantitative data. It combines sociological concepts and statistical tools to measure behaviors, inequalities, and social dynamics.

Students learn to collect and process data, use analysis methods such as descriptive statistics and regression, and interpret the results for practical applications such as social mobility or inequalities.

This course in computational sociology explores quantitative and computational methods applied to the study of social phenomena. It introduces the fundamental concepts of modeling, social network analysis, and the processing of large databases resulting from human interactions.

The course highlights the use of digital tools for the collection, analysis, and visualization of social data.

The Capstone project is a synthesis project that concludes the program. It enables students to mobilize all the skills they have acquired to solve a concrete problem in data science. This project may take the form of an in-depth data analysis, the development of a predictive model, or the design of an innovative solution to address a real-world challenge.

Carried out over several months, it fosters autonomy, creativity, and the practical application of statistical methods, programming, and data visualization.

This English course aims to consolidate and deepen the five language skills (listening and reading comprehension, written expression, continuous and interactive oral expression) through an action-oriented approach. Emphasis is placed on fluency and accuracy, with work on pronunciation and intonation.

Activities are based on a variety of documents and collaborative projects around current themes such as the environment, sustainable development, and intercultural communication, in order to prepare students for professional and academic exchanges in an international context.

Physical Sports and Artistic Activities chosen by the student or language instruction.