Mathematics Recreations and Seminar Notes

Standing Waves in a Sphere.

This recreation gives a mathematical description of sound waves in a sphere, aiming to describe for example the sound a basketball makes when it bounces. It has not been completed, and in the future I will add a Java applet that demonstrates the wave form of a point disturbance.

Physics of Bowling.

This recreation gives a mathematical description of the trajectory of spinning balls rolling on the ground. The main application discussed is the bowling ball, but applications to billiard balls and golf balls (on a putting green) are also mentioned. It is incomplete and in the future I will add a Java applet that computes the predicted bowling average or outcome given a ball trajectory.

Computing Total Orders in Free Groups.

This note describes a seminar that I plan to give discussing the work I did for my dissertation on total orders on free groups and monoids.

Clustering Compounds by Mode of Action.

This note applies some basic formulas for a variance statistic that can be applied to a database of toxicities to group compounds by a hypothetical common mode of action.

Quadratic Forms in Normal Variates.

Some derivations related to the distribution of quadratic forms of normally distributed random variables. One is elementary for a specific form and the other uses moment generating functions for the most general case. This referenced from the page Clustring Compounds by Mode of Action.

Hilbert Functions in Free Associative Algebras.

This is a list of collected notes on the (unsolved) problem of the bounds on the Hilbert Function for free associative algebras, analogous to Macaulay's theory for polynomial rings. It is likely that this problem has been solved and published, but I could not find anything in a literature search.

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