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

This second-year course deepens the study of algebra (vector spaces, matrices, symmetric groups), analysis (integration, sequences and series, differential equations), and probability.

The objective is to consolidate and extend first-year knowledge by emphasizing rigor, modeling, and the resolution of complex problems.

The second-year computer science program focuses on the Python language, with an in-depth study of programming methods, including recursion, induction, and sequential and hierarchical data structures.

Students also study advanced algorithms (exhaustive search, graphs, problem decomposition), formal logic, regular languages, as well as resource management such as memory and files.

The course covers the formal definition and construction of a Markov chain, fundamental properties such as the Markov property, absorbing states, and communication classes.

It also includes key theorems like the ergodic theorem, convergence to a stationary distribution, and absorption times. This course prepares students for in-depth analysis of chains and their various applications in probability, statistics, and more generally in data science.

This course is an introduction to the principles of language interpretation. The following topics are covered:

The different phases of language interpretation: lexical, syntactic, and semantic analysis, and execution;

Regular expressions, finite automata;

Algebraic grammars, word recognition using the CYK algorithm, LL top-down parsing;

Abstract syntax trees;

Simple semantic rules for scope, typing, and evaluation.

This course, based on the second-year curriculum of the BCPST preparatory classes, deepens the study of human biology, physiology, and health, also integrating genomics, development, and cell communication.

It develops understanding of major physiological processes (immunity, reproduction, nervous system, hormonal regulation), the impact of environmental factors, and addresses evolution and phylogeny.

Practical work and document studies aim to strengthen the analysis of the main functions of the organism in relation to health.

This second-year course deepens the study of social mechanisms by focusing on the processes of inequality construction, transformations of family structures, social and political institutions, as well as issues of globalization and social change.

Students are required to analyze case studies, apply more complex sociological theories, and refine their critical methods to prepare for competitive exams, with an emphasis on rigorous interpretation of contemporary social phenomena.

Building on the first-year course, this course aims to deepen the understanding of contemporary economic mechanisms.

The program notably covers economic and financial globalization, economic imbalances, regulation, and public intervention. It also integrates theoretical and sociological foundations to analyze societal developments and prepare students for critical essays in the entrance exams of top business schools.

The objective of this course is to deepen statistical inference methods, including point and interval estimation, hypothesis testing, and analysis of variance (ANOVA). It also covers simple linear models, multivariate statistics, and basic stochastic processes.

This course combines theory and practical applications using statistical software, enabling students to design, analyze, and interpret quantitative studies in biology or economics.

This course deepens the fundamental techniques of data processing, analysis, and modeling. It introduces advanced statistical methods, basic machine learning algorithms, as well as computer tools for managing and exploiting large datasets.

The emphasis is on practical implementation and critical interpretation of results in various contexts.

This course offers an advanced approach to statistical methods, supervised and unsupervised learning techniques, and the management of large databases.

It emphasizes the rigorous application of models, critical evaluation of results, and interpretation of complex data. Students develop strong programming skills and use specialized software to address real-world problems in various fields.

The objective of this course is to acquire basic knowledge in biology, enabling students to understand biological issues and the nature of the data they will encounter.

The following topics are covered: Life: from the cell to the organism; Unity of the living world: replication, transcription, and translation; Genome and sequencing; Regulation of gene expression; Evolution in biology; Metabolism and its regulation.

This introductory course to R and R-Studio offers a first introduction to the R language and its working environment. Students learn to manipulate datasets, perform basic statistical analyses, and produce clear and reproducible visualizations.

The course uses datasets related to biology.

Students must choose one course from:

• Politics, crises, communication
• Convictions, data and emotions: how to build a sustainable business
• Social issues and social policies
• Labor law
• The challenges of the energy transition
• The pharmaceutical industry: its health issues, risks, and opportunities

This course offers a practical introduction to data modeling applied to social sciences and management, focusing on advanced use of Excel.

Students learn to efficiently organize, analyze, and represent data, while being introduced to formula logic (HLOOKUP, VLOOKUP, SUMIF, SUMIFS) and pivot tables.

This course explores the links between entrepreneurship and sustainable development, analyzing how startups integrate social and environmental issues into their business models.

This course follows an action-oriented approach across the five skills (listening and reading comprehension, written expression, continuous and interactive oral expression), with a focus on the pronunciation of vowel sounds.

Interaction takes place through written and/or audiovisual documents centered on environmental and sustainable development issues, as well as a communication scenario within a year-long project. Intercultural communication may also be addressed as part of the project.

The Solidarity Project aims - over the first two years of the program - to introduce students to managing projects with a social, civic, or community dimension. Through the implementation of concrete and sustainable actions serving a community, students develop practical skills in project management, teamwork, and communication.

This course introduces students to the main methods and tools used by entrepreneurs.

Students learn how to turn an idea into a viable project, structure a business model, and manage the development of an innovative startup in a competitive environment.

Physical, sports, and artistic activities chosen by the student, or language instruction.

The main objective of this SPOC is to help students understand the mechanisms and consequences related to global warming and biodiversity loss, as well as their connections to our lifestyles and consumption habits.

More broadly, it aims to provide a cross-disciplinary perspective for understanding global changes, particularly in relation to the United Nations' Sustainable Development Goals and the concept of planetary boundaries.