The oral exam will be 1/2 hour at a time we've agreed upon during finals week.

Here is a summary list of topics we've worked on in the problems. You should be familiar with the problems we did in class related to these topics.

  • Ramsey numbers
  • Binomial theorem, Pascal's triangle
  • Pigeonhole principle
  • Catalan numbers and lattice paths
  • Basic graph terminology (connected, degree, vertex, edge, walk, path, complete graph, tree, etc.)
  • Trees, labeled trees, Prüfer codes
  • Minimum spanning trees
  • Eulerian paths
  • You should be able to derive and explain the counting formulas in the rows and columns listed below in Table 3.2 (p. 76). (You may be asked to work through one of the other situations in the table as part of a problem, but I won't assume that you've seen it before)
    • row 1, distinct recipients
    • row 7, identical recipients
    • rows 2, 4, 8, 9, 10; both columns
  • Compositions
  • Partitions (I will assume you understand the problems we did in class, but the things Steve Butler did was extra material that I won't assume you know already)

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