Des·erts·edge (dez ûrts ej′), n. 1. the transition between dry, barren wilderness and lush, forested land.   2. the frontier between my ignorance and my understanding.

Contact me: mark@desertsedge.net

I tutor calculus, statistics, differential equations, physics, chemistry, and computer programming at the university level. I have helped hundreds of students in dozens of classes over my 12+ years experience as a professional tutor. I enjoy reading about the foundations of math and logic. I've studied set theory, group theory, differential geometry, and some number theory.

Recent Books:
Meta Math, The Quest for Omega, Gregory Chaitin. This book provides another way of looking at incompleteness in mathematics. The author develops the idea of randomness and constructs a maximally random, incompressible number, Ω. The idea is that the digits of this number can never be described by an algorithm. There is no way to compress this number into a smaller data set. Numbers like π and e, although transcendental, can still be described concisely with small formulae; therefore they are not truly random. The idea of compressing data into smaller sets is carried over to formal axiomatic systems. The only reason to have systems of axioms is so that the set of theorems represents a smaller data set than the results derived from those theorems.

The Road to Reality, Roger Penrose. Reviews the mathematics used in theoretical physics.

Latest math forays:
The Encyclopedia of Triangle Centers site lists thousands of triangle "centers", along with their homogeneous and barycentric coordinates. Very interesting. The first several have been known since antiquity.

The AT&T Integer Sequences Research site is an online encyclopedia of integer sequences. For example, if you enter "1,3,6,10,15,21", the result would be the triangular numbers. I've found this to be a useful resource.

The Stanford Encyclopedia of Philosophy has a lot of mathematics, logic, and the history thereof.

Some of my work:
My investigation of truth tables between 2 independent Boolean variables.

The coat problem: A large number of people enter a room and check their coat at the door. Later, upon exiting, everyone is given a coat at random.
Question: What is the probability that everyone gets the wrong coat?  Answer: 1/e

The Counterfeit Penny Problem: There are ten stacks of pennies, each with ten pennies. One of the stacks is known to contain all counterfeit pennies. Assume all good pennies weigh the same amount, X. Also assume that all the counterfeit pennies weigh a little less; each weighing the amount, Y. If you're allowed one weighing on a conventional scale, how should you proceed to determine the counterfeit stack? Answer: