Older stuff
- Here is a review sheet for the material covered since the third exam. Here are solutions to the review problems.
- The paper on the history of combinatorial game theory that I mentioned can be found here.
- Solutions to Exam 3 can be found here.
Exam 3 stats: The mean is around 54. The approximate letter grade cut-offs are as follows. A+: 100+, A: 90-99, A-: 77-89; B+: 62-76, B: 56-61, B-: 48-55, C: 36-47; D: 29-35; R: 0-28
Stats over the average of all 3 exams (among students still enrolled): The mean is around 62. The approximate letter grades are as follows. A: 90+, A-: 78-89, B+: 73-79, B: 59-72, B-: 52-58, C+: 49-51, C:45-48, C-: 41-44, D: 37-40, R: 0-36
For the computation of your exam letter grade over all three exams (which I will use in computing your final letter grade in the course), I will take the maximum of {the average of your 3 exam letter grades, the letter grade computed in the second paragraph above}. - Here's a review sheet (updated on 11/19 to reflect that Sprague-Grundy theorem is NOT on the exam) for Exam 3, which takes place 11/21. If you have a documented need for extra time on exams, please arrange this directly with EOS by the beginning of next week!
- Here is the combinatorial game theory e-text.
- Please note that for exam 3 and the final, there will be absolutely no make-up times except for emergencies (such as serious illness or family emergency). Interviews and other non-emergency travel plans are not valid reasons.
- Solutions to Exam 2 can be found here.
Exam 2 stats: The mean is around 71. The approximate letter grade cut-offs are as follows. A+: 100+, A: 92-99, A-: 84-91; B+: 77-83, B: 71-76, B-: 66-70, C+: 63-65, C: 56-62, C-: 51-55; D: 47-50; R: 0-46
If you got a C- or lower, it may be a good idea to come talk to me, but this is up to you. - Here are solutions to the review exercises for Exam 2.
- Your midsemester grades are based on the exam, HWs 1-3, and quizzes 1-5. Specifically: exam 1 (60%), homework average (30%), and attendance (10%).
- Here is a good source for more probability background, for those of you who'd like an extra resource.
- Here is a good source to look at if you're not quite sure what is meant by a combinatorial argument. This guide serves as a review of material learned in Concepts.
- Solutions to Exam 1 can be found here.
Exam 1 stats: The mean is around 58. You got an e-mail from me if you got a C- or lower. The approximate letter grade cut-offs are as follows. A+: 97-100, A: 91-96, A-: 80-90; B+: 73-79, B: 61-72, B-: 50-60, C: 40-49, C-: 35-39; D: 25-34; R: 0-24 - Here are solutions to the review exercises for Exam 1.
- Exam 1 is coming up on 9/24. I recommend looking at this review sheet and this paper on the DIE method. Terse solutions to the review sheet problems will be posted on Monday, 9/22. You should try to do the problems before looking at the solutions.
- Here is Herb Wilf's book, generatingfunctionology.
- Here is a nice proof of Lucas' Theorem, which covers everything we did of the proof in class on 8/29, as well as the details of the generating functions stuff we omitted.
- For more on the correspondence between Towers of Hanoi, the Sierpinski triangle, and Pascal's triangle, see:
- Pascal's Triangle and the Tower of Hanoi by A.M. Hinz.
- The Towers and Triangles of Professor Claus by D.G.Poole.
- The Tower of Hanoi -- Myths and Maths by A.M. Hinz, S. Klavzar, U. Milutinovic, and C. Petr.
- We saw that Pascal's triangle modulo 2 looks like the Sierpinski triangle. Check out what happens when you look at it mod bigger primes:
Pascal's triangle mod 3