General information

• Course name in French: Mathématiques 1A
• ECTS credits: 5
• Level : Undergraduate (Bachelor 3rd year)
• Teaching hours: 96 hours (Lectures = 36 hours, Tutorials = 36 hours, Self-study = 24 hours)
• Language of instruction: French
• Coordinator: Jacques Liandrat
• Instructor(s): Jacques Liandrat, Guillaume Chiavassa, Mitra Fouladirad, Frédéric Schwander, Jean-Marie Rossi, Thibaut Le Gouic, Chiheb Daaloul, Emmanuelle Sarrouy, Christophe Pouet
• Last update 18/02/2022 by C. Pouet

This course unit is offered twice a year. Students can attend this course during

• Fall-Winter Semester: from early September until end of January/early February
• Spring Semester: from early February until end of June

This course is a basic course in Mathematics for any student in engineering. It is divided into three equal parts:

• Mathematical analysis (Analyse théorique in French)
• Numerical analysis (Analyse numérique in French)
• Probability and statistics (Probabilités et statistique in French)

• tba

• Undergraduate level in
  • Mathematical analysis: Riemann integral, change of variable, derivatives, limits, sequences
  • Linear algebra: vector, matrix, vector space, scalar product, determinant, matrix diagonalization, change of basis

• Final exam: 50%
• Continuous assessment: 50% (project, quiz, lab report)

1. Mathematical analysis
   • Differential calculus
   • Optimization
   • Lebesgue integral
   • Fourier transform and Fourier series
   • Hilbert spaces
2. Numerical analysis
   • tba
3. Probability and Statistics
   • Sigma-algebra, probability measure
   • Real random variables (discrete and continuous)
   • Expectation, variance
   • Random vector, covariance, variance matrix
   • Independence
   • Strong and weak law of large numbers
   • Central Limit Theorem
   • Introduction to statistics: statistical experiment, quadratic risk, bias, pointwise estimation, Maximum Likelihood Method, confidence interval