##### Mathematics and computer science dual major explores the technical side of computer graphics

A love of video games and a desire to create them led **George Armah ’08** (Accra, Ghana) to pursue a B.S. in mathematics and an A.B. in computer science. In the fall semester, he undertook an ambitious independent study in each of his majors in preparation for his honors thesis.

The first independent study explored how a computer renders graphics. Armah worked with **Ge Xia**, assistant professor of computer science. He learned the theory and implementation of computer graphics using standardized OpenGL commands. He also worked with 3-D models that demonstrate the math and physics behind how the graphics are generated on the computer.

His second independent study was a deeper exploration of a branch of mathematics that combines ideas from theoretical computer science with another field of mathematics known as group theory. Armah explains that group theory is the study of symmetry using mathematical structures known as groups. It is applied in robotics, computer vision, medical image analysis, and certain branches of chemistry and physics.

He worked with **Louis Zulli**, associate professor of mathematics, to study a relatively new branch of mathematics called automatic group theory. Automatic group theory describes certain types of groups (automatic groups) by representing them as machines known as finite state automata. These automata can easily be represented and manipulated using a computer. By working with these automata on a computer, one is able to manipulate and better understand the groups they represent.

“I studied how to construct these automata on a computer when given a mathematical description of the group,” Armah explains. “Since these finite automata uniquely describe the groups they represent, once I had the automata constructed, I knew everything about the group. Another advantage of using these automata was that they give finite descriptions of groups that might be infinite in size.”

Armah will use the knowledge he gained from these independent studies for his thesis under the guidance of **Elizabeth McMahon**, professor of mathematics, which will focus on ways of rendering graphs of certain classes of groups on a computer screen.

Automatic group theory caught Armah’s attention during a special topics course on infinite groups he took with **John Meier**, professor of mathematics. It is a relatively young branch of mathematics having been discovered in the 1980s.

“I’m lucky that it is such a recent theory because the mathematicians who uncovered it are still alive,” Armah says. “I have been able to contact some of them with questions and this has been extremely helpful.”

Though, Armah says the theory’s age also proved to be a disadvantage.

“Because automatic group theory is recent, there aren’t that many books written about it yet, at least not at an undergraduate level,” says Armah. “One of the texts I used was actually a collection of academic research papers turned into a textbook. So, the reading was still very challenging to get through.”

After graduation, Armah looks forward to working in the software industry and later attending graduate school. He believes that Lafayette has prepared him well for what lies ahead.

”Career Services has been very helpful in that they have enabled me make some good contacts through programs like externships. As for the academics, many of the answers to questions posed by potential employers have come directly from my classes. Lafayette has also given me a chance to work very closely with my professors. Opportunities like EXCEL research and traveling and participating in conferences have been deciding factors for me in my education and vocational direction,” says Armah.

In the fall of 2006, Armah performed EXCEL research with **Robert Root**, associate professor of mathematics, on developing a mathematical model to help investigate vertebrae evolution. Last summer, he worked with **Rexford Ahene**, professor of economics and business and coordinator of Africana studies, to develop a critical evaluation of preliminary design proposals for a national Land Information System network in Uganda. Along with working for ITS, Armah is a McKevly Scholar, serves as treasurer for ACACIA (Africans Creating African Consciousness and Interest Abroad), vice president of MSE (Minority Scientists and Engineers), and was a member of the Tech Clinic in 2006.

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- Computer Science
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- Creative Projects
- EXCEL/Undergraduate Research
- Career Services