What is this math good for, anyway? –Every student, everywhere I am a professional applied mathematician, yet many of the mathematical and statistical techniques that I use every day are not from advanced university courses but are based on simple ideas taught in high school or even in grade school.

## Tag: **Math**

The eigenvalues of a matrix are not easy to compute. It is remarkable, therefore, that with relatively simple mental arithmetic, you can obtain bounds for the eigenvalues of a matrix of any size. The bounds are provided by using a marvelous mathematical result known as Gershgorin's Disc Theorem. For certain

Last week I compared the overhand shuffle to the riffle shuffle. I used random operations to simulate both kinds of shuffles and then compared how well they mix cards. The article caused one my colleague and fellow blogger, Rob Pratt, to ask if I was familiar with a bit of

Given a rectangular grid with unit spacing, what is the expected distance between two random vertices, where distance is measured in the L1 metric? (Here "random" means "uniformly at random.") I recently needed this answer for some small grids, such as the one to the right, which is a 7 x 6

Continued fractions show up in surprising places. They are used in the numerical approximations of certain functions, including the evaluation of the normal cumulative distribution function (normal CDF) for large values of x (El-bolkiny, 1995, p. 75-77) and in approximating the Lambert W function, which has applications in the modeling

My colleague Robert Allison recently blogged about using the diameter of Texas as a unit of measurement. The largest distance across Texas is about 801 miles, so Robert wanted to find the set of all points such that the distance from the point to Texas is less than or equal

Back in high school, you probably learned to find the intersection of two lines in the plane. The intersection requires solving a system of two linear equations. There are three cases: (1) the lines intersect in a unique point, (2) the lines are parallel and do not intersect, or (3)

This article uses graphical techniques to visualize one of my favorite geometric objects: the surface of a three-dimensional torus. Along the way, this article demonstrates techniques that are useful for visualizing more mundane 3-D point clouds that arise in statistical data analysis. Define points on a torus A torus is

Last week I blogged about how to draw the Cantor function in SAS. The Cantor function is used in mathematics as a pathological example of a function that is constant almost everywhere yet somehow manages to "climb upwards," thus earning the nickname "the devil's staircase." The Cantor function has three

A moving average (also called a rolling average) is a statistical technique that is used to smooth a time series. Moving averages are used in finance, economics, and quality control. You can overlay a moving average curve on a time series to visualize how each value compares to a rolling