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 |
|---|
| 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 |