Undergraduate Seminar in Discrete Mathematics
18.204, Fall 2015
List of topics for the first talk
Your first talk will be a lecture on a major theorem in Discrete Math. I highly
recommend the last two chapters of “Proofs from the book” by Aigner and Ziegler,
available online through the MIT library. Each section can be presented as a single
40-minute lecture.
In addition, I have collected a list of topics that may be suitable. As Discrete Math
is a very broad subject, this list is far from complete. Please consult with me if you
would like to present a topic not on the list.
1. Voting theory:
• Arrow’s impossibility theorem
2. Graph theory:
• Chromatic polynomial
• Electrical networks and “squaring the square”
• Perron-Frobenius theorem
• Lindström-Gessel-Viennot lemma
• Probabilistic method
3. Posets:
• Möbius inversion
• Dilworth’s theorem
4. Enumeration:
• Cayley’s theorem
• Burnside’s lemmma
• Catalan numbers
• The exponential formula for generating functions
• Partition identities
• Robinson-Schensted-Knuth correspondence
5. Algorithms and computability/complexity:
• Djikstra’s algorithm
• Linear programming
• Regular languages and rational generating functions
• Knapsack problem
1
6. Discrete Geometry:
• Helly’s theorem
• Sperner’s lemma, Tucker’s lemma
• Ham-Sandwich theorem
• Art gallery theorem
• Delaunay triangulations
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