en:mat1a []

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=== Mathematics 1A ===
** 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

** <color red> This course unit is offered twice a year. </color> ** 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

==== Brief description ====

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)

==== Learning outcomes ====

  * tba

==== Prerequisites ====
  * 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

==== Assessment ====
  * Final exam: 50%
  * Continuous assessment: 50% (project, quiz, lab report)

==== Course content ====
  - Mathematical analysis
    * Differential calculus
    * Optimization
    * Lebesgue integral
    * Fourier transform and Fourier series
    * Hilbert spaces
  - Numerical analysis
    * tba
  - 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
==== Bibliography ====