Génie industriel - Rubrique Formation - 2022

Mathematical and Computer Modeling - 3GUC0205

  • Number of hours

    • Lectures 19.5
    • Projects -
    • Tutorials 43.5
    • Internship -
    • Laboratory works 16.5
    • Written tests 4.0

    ECTS

    ECTS 6.0

Goal(s)

  • To understand the needs of numerical computing and its specificities; to know and understand the standard methods of numerical analysis (continuous optimization, differential equations, function estimation...)
  • To know the basic concepts and tools of Probabilities; to be capable of using them to model stochastic problems.

    • To understand the foundations of algorithmic and data structures; to know how to perform a top-down analysis of problems and design modular solutions based on the main concepts of object oriented programming; to be capable of implementing one's own programs using a programming language (Java).

Responsible(s)

Pierre LEMAIRE

Content(s)

Numerical analysis:

  • error control;
  • discretization, derivative evaluations, Euler method for differential equations;
  • continuous optimization (properties, gradien and Newton method);
  • continuous optimization with constraints (KKT conditions).

Probabilities:

  • discrete and continuous random variables;
  • independence, conditionnal probabilities;
  • pseudo-random number generation;
  • expected value and variance.

Computer science:

  • algorithmic formalism and the main concepts of object oriented programming;
  • top-down analysis of problems;
  • definition of an algorithmic language (variables, control structures);
  • data structures (tables, lists) and algorithmic techniques (recursion, divide and conquer)
  • simple complexity analysis
  • object oriented programming (objects, classes, attributes, encapsulation) and a programming language (JAVA).

Prerequisites

Mathematics

Test

CcM : continuous evaluation (maths)
CcI : continuous evaluation (computer science)
ExM : written exam (maths)
ExI : written exam (computer science)
Pro : project

S2 : exam session 2, maths and computer science

N1 = final result, session 1
N2 = final result, session 2

Note S1 = 0.4*Maths + 0.4*Informatique + 0.2*Problèmes

Note S2: un seul examen avec Maths /et/ Info, validé si note >= 10 avec au moins 3 en Maths et 3 en Info.

Calendar

The course exists in the following branches:

  • Curriculum - Engineer student Bachelor - Semester 5
see the course schedule for 2024-2025

Additional Information

Course ID : 3GUC0205
Course language(s): FR

You can find this course among all other courses.

Bibliography

  • L'Optimisation, J.B. Hiriart-Urruty, PUF, 1996.
  • Mathématiques numériques pour l'ingénieur, B. Radi, A El Hami. Ellipses, 2010.
  • Analyse numérique matricielle appliquée à l'art de l'ingénieur, P. Lascaux, R. Théodor. Masson (2 tomes).
  • Introduction to Probability Models, Sheldon M. Ross, Elsevier.
  • Introduction au calcul des probabilités, Gérald Baillargeon, 1999.
  • Probabilité, analyse de données et statistique, G. Saporta, 2006.
  • Calcul des probabilités : cours et exercices corrigés", D. Foata, A. Fuchs.
  • http://ljk.imag.fr/membres/Bernard.Ycart/smel/ (ce site propose un cours, des jeux de données, des articles de réflexion, et surtout beaucoup d'applications pour visualiser, tester et comprendre les différents concepts du cours)
  • Introduction to algorithms Ed. McGraw Hill. Thomas H. CORMEN, Charles E. LEISERSON, Ronald L. RIVEST.
  • Foundations of Computer Science. Ed. W. H. Freeman. Alfred V. Aho, Jeffrey D. Ullman.
  • Initiation à l'informatique. Ed. Eyrolles. Henri-Pierre Charles
  • Apprendre à programmer avec Python3, Gérard Swinnen, 2012
  • The Python Standard Library, https://docs.python.org/3/library/index.html