L2 - Double Mathematics Computer Science

The teaching unit presents the basic principles of modeling and object-oriented programming. The supporting languages are UML and Java, with possible elements of Python at the end of the semester.

From a modeling perspective, the teaching unit focuses on modeling static views, using class and instance diagrams. These diagrams will be used to explore the concepts of classes, instances, attributes, operations, associations, interfaces, and specialization. Their parallel implementation in Java will provide a concrete application and demonstrate, in particular, how associations are translated into a programming language that does not have them. In Java, particular emphasis will be placed on the concepts of class, instance, inheritance, instance variable, class variable and method, visibility and organization into packages, and static and dynamic linking. Data collections widely used in Java will be presented to translate some of the associations (associative lists and dictionaries). These collections will introduce students to the use of generic classes. The implementation of object-oriented programming concepts with Python may be covered at the end of the semester, depending on progress.

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This teaching unit presents the design of processes in an information system and the management of relational databases. We will cover the following topics:
(1) Information systems: Introduction to the entity/association model, Relational model, Process modeling (Conceptual process model, Organizational process model),

(2) Databases: creation, manipulation, and querying of relational databases.

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This course will build on the S2 analysis course by covering the concepts of series with terms of any sign. Riemann integrals will be defined and applied to solve differential equations, particularly linear ones. The integration section 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 density 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 in finite dimensions (up to Jordan form) and its applications. It is a first step toward 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: sequents, inference rules, axioms, theorems, LK system, resolution method

- Correctness and completeness of a system with respect to semantics: proof of correctness and completeness of 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 course is to describe the main concepts of operating systems, particularly Unix.

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This course will cover the particularities of floating-point arithmetic, then detail common elementary numerical methods for solving nonlinear equations, interpolating a function, and approximating an integral. Students will learn how to implement an algorithm for solving a numerical analysis problem.

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This course will cover the concepts of sequences and series of functions and various types of convergence. Entire series and Fourier series will also be discussed.

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This course will cover 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 discussed.

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Students will learn how to model and develop using advanced aspects of object-oriented programming and will have acquired good programming practices. They will learn how to create UML diagrams expressing the dynamics of interactions in a system and will consolidate their knowledge of structural modeling.

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Introduction to the main statistical concepts in this course (graphical representation of data, measures of central tendency and dispersion, relationship between two variables, 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 and iterative methods, and eigenvalue computation will be introduced.

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

For students who have a pre-professional AED contract, the EU supports their activities at the institution by providing them with information designed to enrich their observations and give them perspective. This also involves preparing them to write the paper they will be required to submit.

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