We are growing a Google Pittsburgh office on CMU's campus. We are hiring creative computer scientists who love programming, and Machine Learning is one the focus areas of the office. We're also currently accepting resumes for Fall 2008 intenships. If you might be interested, feel welcome to send me email: awm@google.com .
Central limit theorem. The central limit theorem has a number of variants.

In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions, given that they comply with certain conditions. In more general probability theory, a central limit theorem is any of a set of weak-convergence theorems.
Benford's law. The distribution of first digits, according to Benford's law.

Each bar represents a digit, and the height of the bar is the percentage of numbers that start with that digit. Frequency of first significant digit of physical constants plotted against Benford's law Benford's Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data.
Magician-turned-mathematician uncovers bias in coin flipping. By ESTHER LANDHUIS Persi Diaconis has spent much of his life turning scams inside out.

In 1962, the then 17-year-old sought to stymie a Caribbean casino that was allegedly using shaved dice to boost house odds in games of chance. In the mid-1970s, the upstart statistician exposed some key problems in ESP research and debunked a handful of famed psychics.
Hypercube Projection.

Calculus

Programing. Fundamentals of Mathematics. Fractals. Number Theory.