Differentiated paths

To give students entering 1A the necessary foundations (language and disciplinary culture) to be able to follow courses in computer science, mathematics and psychology.
Keywords:

Mathematics: study of functions, derivation, continuity, sequences, limits, complexes, integration, matrix calculation.
Computer science: variables, functions, algorithms.
Psychology: cognitive psychology, cognitive functions, theoretical models, methods in psychology.

Procedure:A placement questionnaire enables each student to identify the disciplinary elements he or she is lacking.This placement takes place on the first day of the new academic year.The three courses then take place over two-three weeks, at the very start of the academic year.These courses are not subject to assessment.
Part 1: Mathematics (20h TD - Speakers: Jérôme Saracco, Jean-Marc Deshoulliers, Christophe Jauze): Jérôme Saracco, Jean-Marc Deshoulliers, Christophe Jauze)
Themes A and B will be covered during the differentiated course at the start of semester 5, in order to best prepare students for the probability and statistics modules in semesters 5 and 6 (CO5SFMA0 and CO6SFMA0).
A) Bases du calcul des probabilités (8h00 Lecturer: Jérôme Saracco)
During these 8h00, the first three chapters of the 1A Probability course (Semester 5) will be covered:
Chapter 1: Axiomatic bases of probability
Chapter 2: Random variables
Chapter 3: Usual laws of probability
The course material is available on Moodle (CO5SFMA0).
B) Basics of linear algebra (8h00 Lecturer: Jean-Marc Deshoulliers)
I. Vector spaces1) Real numbers, complex numbers2) Vector spaces. Vector subspaces3) Linear combinations. Bases. Dimension4) Linear applications5) Canonical norm in R^nII. Matrix calculus1) Families of p vectors in a n-dimensional e.v.2) Linear applications, associated matrices3) Sums of two matrices. Multiplication of two matrices4) The vector space Ln,p(R)5) Multiplication of two matricesIII. Square matrices1) Special matrices (identity, diagonal, triangular...)2) Inverse matrices3) Determinant in dimensions 2 and 34) Solving an n × n linear system5) Practical calculation of the inverseIV. Eigenelements1) Eigenvectors, eigenvalues2) Characteristic polynomial3) An example, projectors4) Diagonalizability5) Change of bases, similar matricesV. Symmetrical bilinear forms, symmetrical matrices1) Symmetrical bilinear forms2) Positive forms, positive definite forms, Cauchy-Schwarz3) Symmetrical matrices
C) Bases of complex numbers (4h00 Lecturer: Christophe Jauze)
This topic will be covered at the beginning of Semester 6 to prepare students for the Signals and Systems module (CO6SFSS0).
1) Complexes: definition, canonical writing, Euler writing, real and imaginary parts, modulus, argument, affix, Moivre and Euler formulas.
2) Laplace transform: definition, some useful examples
3) Continuous and discrete Fourier transform: definition, some useful examples
4) Continuous and discrete convolution product: definition and some useful examples
Part 2: Computer science (20h TD - Speakers: to be specified)

Historical background on computer science
Boolean calculus
Encoding integers
Encoding real numbers
Basic notions (instruction, variables, ...)
Basics of algorithms
Algorithm interfaces
Variables
Reading/Writing

Part 3: Psychology (10h TD - Presenter: Véronique Lespinet-Najib)

History of psychology
Cognitive psychology
Methods in cognitive psychology
Overview of the major cognitive functions

Practical workshop

"Philosophy of TDs" :
Part 1: Mathematics

The aim is to review certain mathematical concepts that will be used in training during semesters 5 and 6.

Part 2: Informatics

The aim of this course is to introduce students to the concept of algorithms.

Part 3: Psychology

The aim of this course is to enable students to understand what an experiment in cognitive psychology is all about.

Computer science / Mathematics / Psychology