L2 - Double Computer Mathematics

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

From a modeling point of view, this course focuses on static view modeling, using class and instance diagrams. These diagrams cover the notions of classes, instances, attributes, operations, associations, interfaces and specialization. Their parallel implementation in Java will give them a concrete application, and show in particular the translation of associations in a programming language that doesn't have them. In Java, particular emphasis will be placed on the notions of class, instance, inheritance, instance variable, class variable and method, visibility and package organization, and static and dynamic binding. 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. Implementation of object-oriented programming concepts with Python may be tackled at the end of the semester, depending on progress.

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This teaching unit introduces the design of processing in an information system and the management of relational databases. We will cover the following points:
(1) Information systems: Introduction of the entity/association model, Relational model, Processing modeling (Conceptual processing model, Organizational processing model),

(2) Databases: creating, manipulating and querying relational databases.

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Following on from the analysis course in S2, this course deals with the notion of series with terms of any sign. The Riemann integral will be defined and applied to linear and other differential equations. The integration section will be extended to generalized integrals.

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This course introduces probability spaces, the concepts of probability and independence, and defines discrete and density random variables, with an emphasis on modeling.

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This course will cover the notions of symmetric group, determinants and will deal with the reduction of endomorphisms in finite dimension (up to Jordan form) and its applications. This is a first step towards spectral analysis.

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

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

- Modeling: formalizing problems in propositional logic, expressiveness limits of propositional logic

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

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

- Curry-Howard correspondence

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

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The aim of this course is to describe the main concepts of operating systems, particularly Unix.

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In this course, we'll look at the particularities of floating-point calculus and then go into detail on the most common elementary numerical methods for solving non-linear equations, interpolating a function and approximating an integral. Students will learn how to implement an algorithm to solve a numerical analysis problem.

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This course covers the notions of function sequences and series, and the various convergences. Integer and Fourier series will also be developed.

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This course covers an introduction to the topology of R^n, the basics of differential calculus for R^n functions in R and optimization. Parametric curves will also be covered.

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

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

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This course deals with numerical methods applied to linear algebra, and more specifically to matrices. The notions of conditioning, matrix decompositions and iterative methods, and the calculation of eigenvalues will be introduced.

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This course includes presentations on career opportunities, themed lectures and round-table discussions on the various mathematical professions.

For students with a pre-professionalization AED contract, the UE accompanies their activity in the establishment, providing a few elements to enrich their observation and give them perspective. It also prepares them for the written work they will be required to submit.

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