More ideas (maybe):
- The mathematics of rotation in
and representing the orientation of a k-dimensional polytope in
(related to the Hyper screen saver)
- The most interesting mathematical subject I’ve encountered since graduation: geometric algebra
- The noncentral t-distribution and the noncentral χ2-distribution
- Introduction to the most basic concepts of topology and measure theory (leading to continuous functions and measurable functions)
- Some math related to the problem of unbiased sampling of particulate material (and laboratory subsampling) — For a lot consisting of n particles, the sampling schemes that are guaranteed to be unbiased can be represented as a convex polytope in a high-dimensional real vector space (but how many vertices does this polytope have?)
Problem 1: Tom, Dick, and Harry competed in a track-and-field meet where points were awarded for first, second, and third place in each event. At the end of the meet, Tom had 22 points, Dick and Harry had 9 points each, and nobody else had any points.
If Dick won the javelin throw, who finished second in the 100-yard dash?
- The scoring was the same for all events.
- More points were awarded for first place than second, and for second place than third.
- No fractional points were awarded.
Problem 2: The following algorithm calculates the first several terms (0 through n) of a well-known integer sequence. Can you determine which one?