L1 Porfil Minor Info choice 1

This UE is an introduction to linear algebra (formalized in S2), based on intuition from plane and space geometry. It includes an introduction to matrix calculus.

The UE also introduces the basic language of polynomials.

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In this module we introduce the basic concepts of algorithms (notion of problem, problem instance, instance size, notion of complexity, termination, proof of validity).

The algorithms presented will deal with problems related to sorting, stacks, queues, arrays.... 

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This course introduces the functional programming paradigm. First, we'll talk about lambda-calculus, the computational model on which functional languages are based. We then move on to teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following outline:
1. Basic types, definitions.
2. Function declarations.
3. Basic data structures (tuples, lists).
4. Advanced data structures (sum types, records).
5. Exceptions.
6. Higher-order functions, iterators on lists.

Time permitting, we'll also take a look at OCaml's module system, one of whose main motivations is to group together related definitions, but which also introduces reusability through the system of parameterized modules (functors).

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This UE aims to work on plane geometry and its objects, as well as demonstrations. It also introduces complex numbers. The geometry and complex numbers sections each account for half of the UE.

- plane geometry objects: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical demonstration

- introduction to complex numbers, geometric interpretation, calculating with complex numbers

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The aim of this course is to clarify the notions of limits of sequences and functions, to deepen the study of sequences and functions, and to study the notions of continuity and derivability of functions, as well as to introduce the main "usual" functions.

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