Falling asleep in your next math class could be more costly than you might think.

Mark Meloon, from the Goleta-based Toyon Corporation,, a defense systems and government contracting company, gave a lecture titled “Working as a Mathematician in the Private Sector” in the Girvetz Theater on Oct 30. The lecture discussed the real world applications of mathematics and the career possibilities in private businesses for math majors.

Meloon, who has a degree from the University of Wisconsin and a Ph.D. from the California Institute of Technology, both in applied mathematics, has been a senior analyst for Toyon since 1997. The company concentrates on the development and prototyping that are required before mass production can begin for defense systems and other technology. Due to its focus on development, Toyon is more academic and less industrial than other technical companies who may hire mathematicians, Meloon said.

Meloon started by showing slides of a complex cat door system to demonstrate applied mathematics. Designed by Quantum Picture, a private research company, the system uses a camera and a computer to monitor whether the approaching cat has something in its mouth – a bird, for example. The computer only allows entry if the cat has nothing in its mouth. The detection system was developed by taking a picture of the cat and translating the picture into numbers.

“If you apply math concepts to a new field, you’re often hailed as revolutionary,” Meloon said. “The math used in each [profession] may be the same; the job requirements differ significantly.”

Meloon said math is increasingly used in computer animated movies. Meloon described how in scenes where there is a herd of individual animated creatures, math equations can model the movements of individual creatures with the goal of making the herd move realistically. Doing this without mathematical modeling would be difficult for animators, Meloon said.

“If the resulting animation doesn’t look right, then the mathematician must improve the model,” Meloon said.

Meloon elaborated on how being a professional mathematician differs from being a math student.

“In school, the problems are given to you and it’s clear what you’re supposed to do,” he said. “In industry, you will often need to determine what solution methods are appropriate. Mathematicians need to explain their work clearly and succinctly to other team members. Managers do not want to see pages of algebra.”

Meloon told the story of a Toyon employee who was a skilled mathematician but could not make his results succinct and understandable to others. The employee was fired.

“What it means to get the right answer in the private sector is a nebulous thing,” Meloon said. “Being both fast and accurate are important.”

Meloon recalled a company motto at Toyon: “Mathematicians provide respectability to our ideas.” He explained that technical people are sometimes able to correctly formulate an idea, but lack the math to be able to prove its feasibility. Mathematicians provide the background and skills necessary to make an idea tenable, he said.

A high GPA is key for students looking for math internships, especially at small companies like Toyon, Meloon said.

“We tend to weight GPA very heavily,” he said. “3.0 bare minimum, 3.4 plus for small companies. It’s especially important for mathematicians. GPA is used not only to measure knowledge of coursework, but also ability to work hard.”