.|[ articles ]|. home

these are small articles i've written for classes, the riddle forum or other purposes. ultimately i'd like to turn this section into a collection of expositions for various puzzles. i also realize some of the writeups are incomplete but i'm too lazy to fix them.

for my attempts to date at writing real papers, check out my professional site.
description download
Fejer's Theorem

8:09 AM 8/11/2004: A clearly written exposition of Fejer's Theorem for the (C,1)-convergence of Fourier series in C([-pi,pi],R). An application of Fourier series tacked on at the end.
PDF format
Sums of Order Statistic Densities

8:05 AM 8/11/2004: Something I stumbled upon proving recently: the sum of n order statistic densities sum to the underlying density, scaled by n. Intuitively obvious, but I couldn't find this identity online anywhere or in any books. There really should be a one-liner proof for this; hopefully I'll come to know it someday. I'd like to exploit this identity, but maybe it is too simple to warrant exploitation.
PDF format
Platonic Solids

8:01 AM 3/12/2004: An open investigation into the fascinating group structure of the platonic solids, for a group theory course. Toward the end I'm trying to discuss things I really don't know enough about; apologies to those readers who know what's going on.
PDF format
100 Prisoners And A Light Bulb

12/7/2002 5:36PM: Work in progress. Describes new algorithms for solving the fairly new 100 Prisoners and Light Bulb puzzle, which was making the rounds of Hungarian mathematicians' parties around the summer of 2002. The author suspects that the puzzle has applications to distributed networks. Applications lacking in the meantime, it would be nice to eventually submit this to a recreational mathematics magazine. Many forum members have contributed ideas toward solving this puzzle, and the author hopes to credit them all eventually should this semblance of a paper actually be published someday. Currently he does not know most of their real names (just online avatars). In the meantime, he wishes to cite Paul Hammond for first suggesting the use of multiple counters, and Alex Harris for suggesting binary stages. The article currently tries to summarize what has been accomplished in the forum. But I've been lazy so it hasn't been properly updated.
PDF format
Riddle Forum Online Community Study

8:35 AM 8/11/2004: Written by Carl Cox, a computer science student at Georgia Tech, for a class project. Investigated the puzzle forum as a model online community, and conducted interviews with me and some of the regular members. It was a neat thing to be a part of!
DOC format
Expected Runtime Of 2-SAT Random Local Search

9/24/2002 4:53AM: Demonstrates that the expected number of iterations till the 2-sat random local search algorithm completes is n2, where n is the number of boolean variables. A standard thing to show in most randomized algorithms courses.
PDF format
PS format
page last modified Monday, 09-Dec-2002 16:30:05 PST

William Wu © ocf.berkeley.edu/~wwu | home | intro | chinese | psychology | riddles | truth | e-mail: wwu at ocf.berkeley.edu