Mathematics

There is no real frontier for me between Pure and Applied Mathematics.

Pure Mathematics

  • Algebra :
    • Groups Rings, Fields, Modulus, Dio├»ds Theories
    • Linear and Multi-Linear-Algebra.
  • Tensorial Algebra and Analysis.
  • Algebraic, General and Metric Topologies.
  • Standard and Functional Analysis.
  • Differential Calculus and Geometry.
  • Fourier and Wavelets analysis.
  • Probability Theory and Statistics.
  • Set methods, Interval and Fuzzy Calculations.
  • Tropical Mathematics :
    • Idempotent Algebra.
    • Idempotent Analysis.
  • Graph Theory & Algorithms.

Applied Mathematics

  • Numerical Analysis and Scientific Computing algorithms.
  • Combinatorial and Continuous Optimization.
  • Evolutionary Programming, Genetic Algorithms.
  • Gradient-based methods.
  • Automatic Differentiation.
  • Free-derivatives methods.
  • Operations Research.
  • Eigen modes analysis.
  • Finite Elements, Volumes, Differences.
  • Signal Processing.
  • Artificial Neural Networks.
  • Monte-Carlo Simulations.
  • Linear and non-linear wavelets (min,+).
  • Inverse Set methods, Interval and Fuzzy Calculations.
  • Monte-Carlo and probabilist methods..