Semester S1


  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Algorithmic complexity
    • Hash table (hash map)
    • Tree data structure:
      • Map search (eg. red/black tree),
      • search/localization in R^d (e.g. region-tree or kd-tree)
      • search in strings;
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Database theory introduction
    • Database systems introduction
  • ECTS: 3
  • Time (hours): 26
  • Notes: Functional analysis bases for scientific computing and engineering mathematics
  • keywords
    • Measure theory
    • Convex analysis
    • Finite dimension Hilbert spaces
    • Weak convergences
    • Distributions
  • ECTS: 3
  • Time (hours): 26
  • Notes: C++ programming introduction and practice
  • keywords:
    • Standard library (STL, C++14)
    • Inheritance
    • Patterns
    • Generic programming
    • Functional programming
    • object and meta programming
    • Scientific programming applications
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Parallel architectures
    • Parallel algorithms
      • Domain decomposition
      • Parallel reductions
      • Sort
    • Scientific computing examples
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Numerical analysis reminder based on PDEs
      • Physics examples
      • Biology examples
      • Economy examples
    • Approximation methods
      • Finite element methods (FEM)
      • Finite difference methods (FDM)
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Definitions and generalities
    • Convex graph
    • Trees and forests
    • Eulerian graph
    • Hamiltonian graph
    • Plane tree
    • Chromatic number
    • Five colors theorem
  • Connector.

    Languages

    Supervisor: CRL

  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • English sessions
    • Defense (oral) for the project EU
  • ECTS: 3
  • Time (hours): 26
  • Notes: Informatic side of Graph 1
  • keywords:
    • Data mining
    • Networks
    • Big sized data search
    • Famous algorithm: Google pagerank, etc… using graph type representation
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Law of large numbers
    • Central limit theorem
    • Monte Carlo method
    • Rejection method
    • Scale invariance
    • Isotropic and homogeneous stochastic process
    • Random walk
    • Brownian motion
    • Diffusion and stochastic differential calculus
    • Markov chains
    • MCMC
    • particle systems and simulated annealing

Semester S2


  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • 1D signal (sound)
    • 2D signal (image)
    • Sampling
    • Fourier series
    • FFT filtering
    • Time-frequency analysis and aliasing phenomenon
    • Chromatic and quantification spaces
    • Contour detection
    • Smothing and compression
    • Textures generation
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Project management and tools introduction
    • Cemosis projects (can eventually prepare to the internship)
    • Final defense in english (oral)
  • Connector.

    Numerical methods PDE 1

    Supervisor: Bopeng RAO

  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Approximation of linear elliptic PDEs using finite elements
    • Sobolev spaces
    • Compactness theorem
    • Trace theorem
    • Lax Milgram theorem
    • Variational form
    • Galerkin approximations
  • ECTS: 6
  • Time (hours): 52
  • keywords:
    • Convex analysis
    • Existence and uniqueness of solution
    • Optimality condition
      • Euler equations and inequality
      • Lagrange multipliers
      • Kuhn-Tucker relations
      • Saddle point and duality theory
    • Numerical algorithm
      • Gradient methods
      • Relaxation methods
      • Newton and quasi-Newton methods
      • Penalization methods
      • Uzawa
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Python programming introduction
    • Scientific computing applications
    • Graphic interface
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • OS components
    • File systems
    • Process
    • Threads
    • Concurrency and synchronization
    • Memory management
    • Virtual memory
    • Virtualization
  • ECTS: 3
  • Time (hours): 26
  • keywords:
    • Finite element application
    • Parabolic PDEs
    • Stabilization methods
    • Extend to hybrid models
    • Applications
  • Connector.

    Internship

    ECTS: 6

  • ECTS: 3
  • Time (month): 2
  • keywords:
    • 2 month internship (enterprises, research laboratory or research center)