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 ====