MAT475 Problem Solving Seminar
Spring of 2017
Recommended Topics
(under construction: more topics and descriptions are coming)
References are provided only for initial familiarity with the subject.
Distributions
Sections 11.1, 11.2
Applications of distributions to PDE and weak solutions
Sections 11.3, 11.4
Burgers equation
Section 12.1
Variational calculus of one variable
Sections 10.1, 10.2
Variational problems of several variables
Sections 10.1, 10.2
Classical mechanics: Lagrangian formalism
Section 10.3
Classical mechanics: Hamiltonian formalism
Section 10.3
Physics: Lagrangian & Hamiltonian formalism
Section 10.4
Variational theory of the eigenvalues for PDE
Section 13.1
Asymptotic distribution of eigenvalues for PDE
Section 13.2
Properties of eigenfunctions
Section 13.3
Spectra of PDEs
Section 13.4
Continuous spectrum and scattering
Section 13.5
Basic probability topics
Laws of large numbers, central limit theorems, martingales, Brownian motion, Markov chains and processes, basic ergodic theorems
Applications of probability in other fields
Using the probabilistic method in combinatorics, using random walks or Brownian motion to get results in PDE/complex analysis, probabilistic results in number theory etc.
Specific probabilistic models
Random walks on groups/graphs, random graphs, percolation, random polymers, various interacting particle systems etc.