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

Pure Mathematics

• Algebra :
  • Groups Rings, Fields, Modulus, Dioïds 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..