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Dr. Bathi Kasturiarachi is an associate professor in mathematics based primarily at �鶹ӰԺ’s Stark Campus. Apart from teaching mathematics, Dr. Kasturiarachi also teaches computer science courses. Dr. Kasturiarachi is actively involved with undergraduate research, and states that “undergraduate research is a critical component of any undergraduate program.” Dr. Kasturiarachi explains that completing undergraduate research allows students to apply what is taught in the classrooms in a productive and hands-on way, better preparing students for their careers after graduation.

Dr. Kasturiarachi was paired with �鶹ӰԺ’s recent alum Cameron Gmitra through Choose Ohio First, which is a scholarship program for Ohio residents geared toward STEM majors. Gmitra graduated from �鶹ӰԺ with a degree in actuarial mathematics and a minor in computer science. Together, Dr. Kasturiarachi and Gmitra discovered a way to visually depict geometric series.

Dr. Kasturiarachi explained that occasionally a concrete answer can be found in the infinite geometric series, and that other times the answer will be infinity. In order to visually depict geometric series, Dr. Kasturiarachi and Gmitra selected geometric series with definitive answers and began with the question How can we picture this?

Taking that initial question, Dr. Kasturiarachi and Gmitra began to formulate how they could develop a visual portrait of the result. The pair discovered that geometry was the proper medium to depict the geometric series, and Dr. Kasturiarachi tasked Gmitra with developing a visual representation as her research. To do so, a series of circles were utilized to express numerical values within the geometric series. The portrait consisted of numerous circles within a larger circle, with smaller circles indicating fractions generated in the series. The circles were then shaded according to their significance in the portrait.

With Dr. Kasturiarachi’s guidance, Gmitra completed a series of these visual portraits and titled the project “Portraits of Infinite Geometric Series.” The visual portraits can be explained as “proof with a picture,” and Dr. Kasturiarachi compares the pictures to artwork that one might see in a museum, saying “there’s this geometrical picture and you have to stare at it for a moment, and we have the result written underneath, like a title. And then you say ‘ohh, this is actually showing this particular result in a pictorial way.’”

Gmitra went on to receive second place with “Portraits of Infinite Geometric Series” at the Undergraduate Symposium on Research in 2022.

However, “Portraits of Infinite Geometric Series” was not the only research project that Dr. Kasturiarachi and Gmitra completed together. Gmitra joined Dr. Kasturiarachi again for the Summer Undergraduate Research Experience (SURE) program, where they worked to explore mutual funds through a technique called “Bollinger Bands.” The “Bollinger Bands” technique that Gmitra and Dr. Kasturiarachi worked with used moving average and standard deviation in order to model the prices of mutual funds. Gmitra wrote the program herself and was ultimately successful in predicting the fluctuations for two months into the future. Gmitra presented this research at the Undergraduate Symposium on Research in 2023.

Partnerships between undergraduate students and faculty mentors are crucial for successful undergraduate research. Dr. Kasturiarachi recalls that working with Gmitra was enjoyable, stating that “she was very good at working independently,” and that Gmitra was also very good with deadlines. Gmitra’s research with Dr. Kasturiarachi made her stand out in the job market and helped her find a job after graduation with Western and Southern Financial Group in Cincinnati.

As a research mentor, Dr. Kasturiarachi believes in providing the starting point and necessary information, and then allowing the researcher to go out on their own to work through the problem with guidance as needed. Dr. Kasturiarachi recommends that all students, and STEM students especially, partake in undergraduate research.

Written by Lenore Kohl