2025-2026
University of Limoges,
Department of Engineering

• Basic Concepts of Functions: L1 lectures and tutorials (45h).
  Introduction to real-valued functions of a real variable, limits, continuity and derivatives of functions, Taylor’s formula, inverse function.
  
• Algebra: L2 tutorials (55h).
  Fundamentals of logic, set theory, functions, binary relations, complex numbers, polynomials.
  
• Linear Algebra: L2 Tutorials and Practical Sessions with Maple (27h).
  Vector spaces, matrices, linear maps, systems of linear equations.
• Calculus of several variables: L2 tutorials (43h).
  Introduction to vector calculus in several variables, partial and directional derivatives, multivariable optimization, Lagrange multipliers, differential operators, Stokes’ theorem.
• Analysis: L1 tutorials (65h).
  Partial orders, numerical sequences, continuity of functions, convexity, integral.
• Probabilities: L1 tutorials (56h).
  Basic combinatorics, random variables, standard discrete distributions.

2024-2025
University of Bordeaux,
Department of Science and Technology

• Mathematical Tools: L1 tutorials (58h).
  spatial geometry, limits, derivative, circular, exponential, and logarithmic functions, scalar product, integrals, differential equations.
  
• General Math: L1 lectures and tutorials (66h).
  Fundamentals of logic, set theory, complex numbers, limits, continuity and derivatives of functions, integrals, differential equations.
  
• Discrete Mathematics: L1 tutorials (32h).
  Basics of counting and probability, conditional probability, random variable,
  Discrete distributions, Basics of graph theory.
  
• Calculus in several variables: L2 tutorials (34h)
  Norms and inner products, limits and continuity, elementary topology in normed spaces, Compactness and equivalent norms, directional and partial derivatives, differentiable functions, functions of class C^k, Taylor’s formula,
  relative extrema, Inverse function theorem, implicit function theorem, Constrained extrema.