This course is taught by Sergey Fomin. He is a really great professor/lecturer and this course is just fantastic.

As per instructor’s requirement, the notes will not be posted after the course is finished. Here are the contents of the course:

  • [Jan. 6, linear algebra prelim, adjacency matrices & eigenvalues]
  • [Jan. 11, eigenvalues inequalities and anti-diagonal block matrices]
  • [Jan. 13, eigenvalues of circulant matrices, Cartesian products]
  • [Jan. 18, random walks, domino tilings]
  • [Jan. 20, domino tilings]
  • [Jan. 25, spanning trees, diamond lemma]
  • [Jan. 27, diamond lemma with application in several games]
  • [Feb. 1, loop erasure, Wilson’s algorithm]
  • [Feb. 3, flow, potential]
  • [Feb. 8, solving Kirchhoff equations]
  • [Feb. 10, effective conductance]
  • [Feb. 15, effective conductance, squaring a square]
  • [Feb. 17, Laplace expansion]
  • [Feb. 22, matrix-tree theorem]
  • [Feb. 24, Cayley’s formula, Eulerian tours, the BEST theorem]
  • [Mar. 8, postman routes, De Bruijn sequences]
  • [Mar. 10, construction of De Bruijn sequences, partitions]
  • [Mar. 15, the dominance order, lattice $L(m, n)$]
  • [Mar. 17, the $q$-binomial coefficients]
  • [Mar. 22, identities of $q$-binomial coefficients, Sperner theory]
  • [Mar. 24, Sperner’s theorem]
  • [Mar. 29, rank-unimodality of $L(m, n)$]
  • [Mar. 31, Young lattice]
  • [Apr. 5, the hooklength formula]
  • [Apr. 7, the Frobenius-Young identity]
  • [Apr. 12, involutions]
  • [Apr. 14, Schensted’s insertion algorithm]