Making Mathematical Connections

Math is the universal language. It is the underlying structure for what is occurring in the world and is present in everything from music to computers.

Cassidy Richmond, a senior math education major, is passionate about mathematics, so passionate that she wants everyone else to be also.

As a future teacher, her goal is to present math in such a way that the student in the back of the class who usually sleeps will instead say, “I learned something today.”

In the semester before student teaching Richmond finished up her undergraduate work, juggled her duties as wife and mother of three, and added another job, that of researcher.

Richmond plans to continue on with a master’s degree and eventually a PhD. Dr. Denise Dawson, associate professor of mathematics, advised she would need research experience. Richmond and Dawson applied for and received a research grant from South Carolina Independent Colleges and Universities to look for a connection between matroids and buildings.

“It’s been exciting, hard, exhausting,” said Richmond. She thinks about the research while driving and has white boards in her home filled with definitions. She flies out of bed in the middle of the night, flipping on lights and throwing pens and papers, much to the dismay of her husband.

Richmond explains that math is so much more than formulas. It is a chance to make connections.

Richmond and Dawson were looking for a connection between matroids and buildings. Richmond said, “With a Fano plane, we know it has a matroid. We also know it has a building. We overlapped 28 Simplices and 28 maximal independent sets. What is the connection? Between 28 and 28, where is the overlap? One day it finally clicked. We built 28 points and realized those points are a direct connection. That day was such a high.”

They have worked on the research separately and together. “The times we meet in Dr. Dawson’s office we make the biggest breakthroughs,” said Richmond. “We are able to ask, what if we approached it this way? How do we make it work?”

Richmond and Dawson presented their research findings to SCICU in February on Richmond’s birthday. Even though they have proven for themselves that a Fano plane is a building, they still have questions they want to research further.

“In presenting our research, we have to explain complex math concepts to nonmath people,” said Richmond. This ability is preparing Richmond for the classroom and further education. To present these complex concepts, Richmond and Dawson use plenty of visuals. “Visuals matter a lot in trying to explain these concepts,” said Richmond.

“The purpose of math research is math,” said Richmond. “Both buildings and matroids have uses. Some may ask why you would want to find a connection. We don’t know if we don’t do the research. It may just be there for someone else to come along and say, that’s what I was looking for,” she said.

For example, Number Theory is the basis for computers. It was originally thought to have no application. The world as we know it wouldn’t exist if someone hadn’t made that connection, someone like Richmond, who is passionate about making a complex mathematical world understandable to all.

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