L2 - Double Major in Mathematics and Computer Science

This course introduces the basic principles of object-oriented modeling and programming. The primary languages covered are UML and Java, with some Python concepts possibly introduced at the end of the semester.

From a modeling perspective, this course focuses on static modeling, including class and instance diagrams. Through these diagrams, students will explore the concepts of classes, instances, attributes, operations, associations, interfaces, and specialization. Implementing these concepts in parallel in Java will provide concrete applications and, in particular, demonstrate how associations are represented in a programming language that does not natively support them. In Java, particular emphasis will be placed on the concepts of classes, instances, inheritance, instance variables, class variables and methods, visibility, organization into packages, and static and dynamic binding. Commonly used data collections in Java will be presented to represent certain associations (lists and associative dictionaries). These collections will introduce students to the use of generic classes. The implementation of object-oriented programming concepts using Python may be covered at the end of the semester, depending on the class’s progress.

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This course covers the design of business processes within an information system and the management of relational databases. We will cover the following topics:
(1) Information Systems: Introduction to the entity-relationship model, the relational model, and business process modeling (conceptual business process model, organizational business process model),

(2) Databases: Creating, Manipulating, and Querying Relational Databases.

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Building on the analysis course from the second semester, this course will cover the concepts of series with terms of arbitrary sign. The Riemann integral will be defined and applied to solve differential equations, particularly linear ones. The section on integration will be expanded to include generalized integrals.

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This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and continuous random variables, with an emphasis on modeling.

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This course will cover the concepts of symmetric groups and determinants, and will address the reduction of endomorphisms to finite dimensions (up to Jordan form) and its applications. It serves as an introduction to spectral analysis.

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- Formal syntax of propositional logic: symbols, connectives, well-formed formulas, syntactic trees, normal forms, and clause forms

- Semantics of propositional logic: interpretation, model, truth tables, satisfiability, validity, semantic equivalence, logical consequence

- Modeling: formalization of problems in propositional logic; expressive limits of propositional logic

- Formal proof: sequences, inference rules, axioms, theorems, the LK system, the resolution method

- Correctness and completeness of a system with respect to a semantics: proof of the correctness and completeness of the LK and the resolution method (reduced to the propositional case)

- Curry–Howard Correspondence

- Introduction to first-order logic (predicate calculus) without function symbols

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The objective of this learning unit is to describe the main concepts of operating systems, particularly Unix.

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In this course, we will cover the fundamentals of floating-point arithmetic and then discuss common basic numerical methods for solving nonlinear equations, interpolating functions, and approximating integrals. Students will learn how to implement an algorithm to solve a numerical analysis problem.

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This course will cover the concepts of sequences and series of functions, as well as various types of convergence. Integral series and Fourier series will also be discussed.

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This course will provide an introduction to the topology of R^n, the basic concepts of differential calculus of functions from R^n to R, and optimization. Parametric curves will also be covered.

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Students will learn to model and develop using advanced aspects of object-oriented programming and will have acquired best programming practices. They will be able to create UML diagrams that illustrate the dynamics of interactions within a system and will strengthen their knowledge of structural modeling.

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This course introduces the main statistical concepts (graphical representation of data, measures of central tendency and dispersion, the relationship between two variables, and confidence intervals).

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This course will cover numerical methods applied to linear algebra, with a particular focus on matrices. The concepts of conditioning, matrix decompositions, iterative methods, and eigenvalue calculation will be introduced.

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This course will introduce students to the various careers in mathematics through presentations on career opportunities, thematic lectures, and roundtable discussions.

For students with an AED contract as part of a pre-professional training program, the course unit supports their work at the school by providing resources designed to enrich their observations and help them gain perspective. It also aims to prepare them for the written assignment they will be required to submit.

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