Differentiated paths

To give students entering 1A the necessary grounding (language and culture) to be able to follow courses in computer science, mathematics, psychology, human biology and neurobiology.

Mathematics (resp.: J. Saracco): basic probability calculus, matrix calculus, complex numbers.
Computer science (resp.: F. Placin): variables, functions, algorithms.

Psychology (supervisor: V. Lespinet-Najib): cognitive psychology, cognitive functions, theoretical models, methods in psychology.

Fundamentals of human biology and neurobiology (resp.: F. Faita)

Procedure:

The three courses then take place over two to three weeks, at the very start of the academic year. These courses are not assessed.

Mathematics (Speakers: Jérôme Saracco, Jean-Marc Deshoulliers, Christophe Jauze)

Themes A and B will be covered during the differentiated pathway at the start of semester 5, to prepare students for the probability and data science modules in semesters 5 and 6.

A) Basics of probability calculus (8h00 Speaker: Jérôme Saracco)

During these 8h00, the first three chapters of the 1A Probability course (Semester 5) will be covered:

Chapter 1: Axiomatic foundations 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 spaces

1) Real numbers, complex numbers

2) Vector spaces. Vector subspaces

3) Linear combinations. Bases. Dimension

4) Linear applications

5) Canonical norm in R^n.

II. Matrix calculation

1) Families of p vectors in an n-dimensional e.v.

2) Linear applications, associated matrices

3) Sum of two matrices. Multiplication of two matrices

4) The vector space Ln,p(R)

5) Multiplying two matrices

III. Square matrices

1) Special matrices (identity, diagonal, triangular...)

2) Inverse matrices3

) Determinant in dimensions 2 and 3

4) Solving an n × n linear system

5) Practical calculation of the inverse

IV. Proprietary items

1) Eigenvectors, eigenvalues

2) Characteristic polynomial

3) An example: spotlights

4) Diagonalizability

5) Change of bases, similar matrices

V. Symmetrical bilinear forms, symmetrical matrices

1) Symmetrical bilinear forms

2) Positive forms, positive definites, Cauchy-Schwarz

3) Symmetrical matrices

C) Bases of complex numbers (4h00 Speaker: 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 transforms: definition, some useful examples

4) Continuous and discrete convolution product: definition and some useful examples

 Computer science

History of computer science
Boolean calculus
Integer encoding
Real number encoding
Basics (instructions, variables, etc.)
Algorithm basics
Algorithm interface
Variables
Read/Write

Psychology (10h TD - Lecturer: Véronique Lespinet-Najib)

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

Practical workshop

Fundamentals of human biology and neurobiology (resp.: F. Faita) 

Understand the foundations of life and the levels of organization of the human body,

Know the main tissue families and cellular communication mechanisms, 

Understand the basic anatomy and physiology of the nervous system.

- Definition, challenges and fields of application

- Notions of evolution and organization of living organisms

- Cells: structure, functions, differentiation

- Tissues: classification, roles and examples

- Functional anatomy of the brain

- Anatomy of the central and peripheral nervous system Motor control: spinal cord, brain stem, motor cortex

- Neurons: structure, action potential, synapses

- Neurotransmitters and neuromodulation

- Neuronal plasticity

- Introduction to biological neural networks and analogies in AI".

Computer science / Mathematics / Psychology