Semestre 1

Algebra is a key module that covers fundamental and advanced topics in algebra, focusing on vector spaces, linear applications, and matrix theory. It is divided into two parts:

• Algebra 1:

  • Chapter 1: Polynomials and Rational Fractions Studies the properties of polynomials, rational fractions, and their factorization.
  • Chapter 2: Vector Spaces Introduces vector spaces, their subspaces, basis, and dimension.
  • Chapter 3: Linear Applications Explores linear tapplications, their properties, kernel and image.

• Algebra 2:

  • Chapter 1: Matrix Calculation and Linear Systems Introduces matrix operations and their application in solving linear systems of equations.
  • Chapter 2: Matrices and Linear Applications Examines the connection between matrices and linear applications, along with their properties.
  • Chapter 3: Endomorphism Reduction Focuses on endomorphisms, diagonalization, and simplifying linear operators.

This module provides a solid foundation in algebra, which is critical for applications in mathematics and computer science.

The Formal Logic course introduces students to the principles of logical reasoning and the formal methods used to represent and evaluate logical statements. The course explores the structure of arguments, the validity of reasoning, and the application of formal systems to solve problems. It lays the foundation for understanding how logical systems are applied in computer science.

Analysis is a comprehensive module that provides essential mathematical tools for understanding sequences, functions, series, and differential equations. It is divided into two parts:

• Analysis 1:

  • Chapter 1: Real Sequences Studies the properties of sequences, including limits, monotonicity, and convergence.
  • Chapter 2: Functions of a Real Variable Covers limits, continuity, and differentiability of real functions.
  • Chapter 3: Primitives and Integrals Introduces indefinite and definite integrals, fundamental theorems of calculus, and integration techniques.
  • Chapter 4: Limited Developments Explores function approximations using Taylor expansions and asymptotic behaviors.

• Analysis 2:

  • Chapter 1: Numerical Series Examines series convergence, absolute vs. conditional convergence, and convergence tests.
  • Chapter 2: Power Series Explores Taylor series, radius of convergence, and function approximations.
  • Chapter 3: Functions of Several Variables Focuses on two-variable functions, including differentiability, gradients, and optimization techniques.
  • Chapter 4: Linear Differential Equations Introduces first-order and second-order linear differential equations with solution methods.

This module builds a strong foundation in mathematical analysis, essential for applications in physics, engineering, and data science.

Ce cours permettra aux étudiants de

• Analyser un problème donné et définir l'algorithme
• Traduire la solution du problème de manière rigoureuse et optimisée et prête à être traduite en utilisant n'importe quel langage de programmation.