Department of Mathematics

University of Toronto

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.

  1. Distributions Sections 11.1, 11.2
  2. Applications of distributions to PDE and weak solutionsSections 11.3, 11.4
  3. Burgers equationSection 12.1
  4. Variational calculus of one variableSections 10.1, 10.2
  5. Variational problems of several variablesSections 10.1, 10.2
  6. Classical mechanics: Lagrangian formalismSection 10.3
  7. Classical mechanics: Hamiltonian formalismSection 10.3
  8. Physics: Lagrangian & Hamiltonian formalismSection 10.4
  9. Variational theory of the eigenvalues for PDESection 13.1
  10. Asymptotic distribution of eigenvalues for PDESection 13.2
  11. Properties of eigenfunctionsSection 13.3
  12. Spectra of PDEsSection 13.4
  13. Continuous spectrum and scatteringSection 13.5
  14. Basic probability topics Laws of large numbers, central limit theorems, martingales, Brownian motion, Markov chains and processes, basic ergodic theorems
  15. 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.
  16. Specific probabilistic models Random walks on groups/graphs, random graphs, percolation, random polymers, various interacting particle systems etc.