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MATG 635 Probabilistic Methods

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This MATG 635 Probabilistic Methods course may be a graduate-level introduction to the probabilistic methodology, an elementary and powerful technique in combinatorics and theoretical engineering. The essence of the approach is to point out that some combinatorial object exists and prove that a definite random construction works with positive likelihood. The course focuses on methodology moreover as combinatorial applications.

Course layout:

  • The mathematical formulation of random processes
  • Ito's formula
  • Probabilistic methodology in Dirichlet downside
  • Additional topics of Dirichlet downside and Probabilistic methodology in the heat equation
  • Additional topics of Probabilistic methodology in the heat equation
  • Richard Phillips Feynman Kac formula
  • Random differential equations

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