These topics were chosen and presented by the students in the Fall 2006 class. Each year, each student signs up for 4 dates and is responsible for presenting a lecture in class on each of those dates.

Lecture notes files.SES # | TOPICS | KEY DATES |
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1 | Introduction | |

2 | Stable marriage problem | |

3 | Pattern-avoiding permutations, weighted Dych patterns | |

4 | Emergency response vehicles | |

5 | Game theory | |

6 | Conguences | |

7 | 4 and 5 color theorems | |

8 | Cake-cutting algorithms | |

9 | RSA encryption | |

10 | Extrapolated numerical integration | |

11 | Sorting algorithms | |

12 | Post correspondence problem (PCP) | |

13 | Ramsey theory and Van der Waals' theorem | Pick a topic for final paper project |

14 | Fibonacci numbers | |

15 | 4 color theorem | |

16 | Recursions | |

17 | Domino tilings | |

18 | Towers of Hanoi | |

19 | Pigeonhole principle and Ramsey theory | |

20 | Surreal numbers | |

21 | Matrix hamming codes and the hat game | Construct outline of final paper project |

22 | Juggling | |

23 | Zero-knowledge proofs | |

24 | Game theory: Repeated games | |

25 | Lewis Carroll's theorem for computing determinants | |

26 | Nash equilibrium | Submit first draft of final paper project |

27 | 5 proofs of the infinitude of primes | |

28 | Bridges of Konigsberg | |

29 | Time series analysis: GARCH model | |

30 | Rational recurrence relations | |

31 | Digital image compression | |

32 | Quantum computing | |

33 | Fundamental methods of numerical extrapolation with applications | |

34 | Infinities | |

35 | Markov chains | |

36 | Catalan numbers | |

37 | Election Theory | |

38 | Advanced counting techniques | |

39 | Class wrap-up | Submit completed final paper project |