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LVC Mathematicians Conduct Number Theory Research through Arnold Experiential Grant Program
07.01.13 | Share This Article
A trio of Lebanon Valley College mathematicians has spent the early part of their summer poring over data, applying their knowledge of number theory while trying to find number patterns that weren’t known to exist before. Isaac Lu ’15, Christina Doran ’15, and Dr. Barry Smith, assistant professor of mathematics, are hoping that the patterns they proved to exist might one day apply to a future science.

“Number theory is the purest area of mathematics and is only currently known to apply to cryptology – the science of secure communications,” Smith said. “Prior to the discovery of its application to cryptology, the people who worked in number theory did so for the joy of discovering patterns and logically establishing their validity. We hope the patterns will be elegant, surprising, and make us view numbers in a new way. If one day researchers discover an application for these patterns, then that’s just an added bonus.”

“The Foundations of Mathematics class provided the basics of this research,” said Lu, an actuarial science and mathematics double major from China. “We found patterns in quotients and learned how to generalize the pattern to apply to all types of numbers.”

“It’s really exciting for us,” said Doran, an actuarial science major from Warminster, Pa. “This was our first research project and having the chance to do research is a huge résumé builder. I’ll be completing an actuarial science internship next summer, so this is my chance to get real experience in applying what I’ve learned in the classroom.”

Smith, Lu, and Doran will co-author two papers that they will submit for journal consideration. Because the principle of patterns and number theory is among the most basic and widely understood in the mathematics field, they are hoping that one of their papers will be published in one of the most disseminated research journals in the world – the American Mathematical Monthly. They will spend the next month finalizing their drafts for submission. In addition to publishing a peer-reviewed research article, Lu and Doran are encouraged to present poster sessions at various academic events over the next year.

“If you’re thinking about graduate school, undergraduate research is a must,” Lu said. “It’s a worthy experience for students to further their education. Few people know how to do this type of mathematical science, and I feel very accomplished having completed this project.”

“Research is so much better than spending a summer working in a grocery store,” Doran said. “It’s a more relevant experience that gives me a taste of what I’ll actually be doing in my career.”

The research project, “Sequences of Quotients and Remainders in the Euclidian Algorithm,” was funded by the spring 2013 Edward H. Arnold and Jeanne Arnold Program for Experiential Learning research grants. It is one of 13 research and internship awards presented to Lebanon Valley College faculty and students this year.

“This project has spawned many other research ideas that we won’t have time to finish this summer,” Smith said. “We have many more ideas that would be great to start with additional funding to support collaborative student-faculty research.”


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