Courses:

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Linear Algebra (18.700) or Algebra I (18.701)

van Lint, J. H., and R. M. Wilson. A Course in Combinatorics. Cambridge, U.K.: Cambridge University Press, 1992. ISBN: 0521422604. (Reprinted 1994, 1996.)

Stanley, R. P., Sergey Fomin, B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak, and B. Simon. Course notes on Topics in Algebraic Combinatorics.

———. Enumerative Combinatorics. Vol. 1 and 2. Cambridge, U.K.: Cambridge University Press, 2001. ISBN: 0521789877.

• Catalan Numbers, Triangulations, Catalan Paths, Noncrossing Set Partitions
  
  
• Symmetric Group, Statistics on Permutations, Inversions and Major Index
  
  
• Partially Ordered Sets and Lattices, Sperner's and Dilworth's Theorems
  
  
• Young's Lattice, Tableaux, and Schensted's Correspondence
  
  
• q-Binomial Coefficients, Gaussian Coefficients, and Young Diagrams
  
  
• Partitions, Euler's Pentagonal Theorem, Jacobi Triple Product
  
  
• Noncrossing Paths, Lindstrom Lemma (Gessel-Viennot Method)
  
  
• Matrix-Tree Theorem, Electrical Networks, Walks in Graphs
  
  
• Lattice Paths and Continued Fractions
  
  
• Transportation and Birkhoff Polytopes, Cyclic Polytopes, Permutohedra
  
  
• Matching Enumeration, Pfaffians, Ising Model, Domino Tilings

Based on the 4 assignments.