Two of Indiana University East’s online students not only graduated with a B.S. degree in Mathematics, they are also proud co-authors of peer reviewed articles.

During the last academic year, students Chava Shawn and Carlos Garces Lopez had worked hard with their faculty mentors on solving difficult problems in mathematics. The results of their labor have been published in two peer-reviewed mathematical journals.

Chava Shawn collaborated with two faculty mentors on a difficult problem in partial differential equations. Their project considers a problem derived from the heat equation. Imagine a thin metal rod of finite length. The rod is initially heated up, so that some portions are hotter than others. The heat equation describes how the temperature distribution in this rod will change as it cools.

The researchers investigated the inverse problem: Suppose we take temperature measurements at a single location on the rod in specified time intervals. The researchers devised a formula by which they can reconstruct an estimate of the initial temperature profile of the entire rod from just this information. The results of the research will be published in the journal Mathematics in Applied Sciences and Engineering.

Carlos Lopez Garces and his faculty mentor investigated a problem from the world of computer graphics: It explores three innovative techniques that can be used to create realistic lighting effects in digital images. These techniques, called Monte Carlo estimators, are sophisticated algorithms that accurately capture the way in which light scatters in a virtual environment.

The researchers set out with two main goals: first, to make these complex ideas more user-friendly by seamlessly incorporating them into a popular image-rendering software called PBRT, and second, to see how well these techniques perform in real-world scenarios.

They used comparisons of generated images to validate their methods, ensuring they work reliably. The paper takes the reader through the step-by-step process of understanding, implementing, and testing the algorithms, aiming to enhance the ability to create stunning and lifelike computer-generated images. The results will be published in the journal Mathematics and Statistics.

Perhaps most surprising about the scholarly productivity is that the students and their faculty members never met in person. Shawn lives in Clarksville, Tennessee and Lopez Garces hails from Seattle, Washington.

The two students are part of a group of over 250 online mathematics students who enroll in Indiana University East’s program in order to earn their B.S. in Mathematics.

“We aim to offer the same opportunities to our online students as other universities offer in their face-to-face programs,” explained Markus Pomper, Dean of the School of Natural Science and Mathematics.

“In a digitally interconnected world, where working from home and online collaboration are the norm, education must follow suit. Our mathematics program is at the forefront of this digital revolution of our working lives. IU East offers a high quality online curriculum in mathematics, and we supplement it with an equally high quality co-curriculum”, Pomper continued.

“Our students have the opportunity to work alongside faculty who are not only great teachers but also moving their disciplines forward in new areas—and who are helping students be a part of that work. We do all this in a fully online environment.”

Student Chava Shawn agreed with Pomper’s assessment:

“I chose Indiana University East’s online mathematics program because it is flexible, and because it allows me to contribute to research with experts in the field.”

Chava’s faculty mentor is proud of their common achievement.

“Being listed as a co-author on a research paper in mathematics means that Chava has contributed significantly in the development of the proofs and ideas in this paper”, her faculty mentor Young You explained. “Having a published paper will provide a significant advantage to Chava as she applies for graduate school.”

The work of Shawn was supported by an internal grant of Indiana University East; Garces was supported by a grant from the Women’s Philanthropy Leadership Council.

References

Karki, R., Shawn, C., You, Y. (2024). Recovery of an initial temperature of a one-dimensional body from finite time-observations. Mathematics in Applied Sciences and Engineering. 1-7. 10.5206/mase/16723.

Garces, C., Kong, N. (2024). Derivation and Evaluation of Monte Carlo Estimators of the Scattering Equation Using the Ward BRDF and Different Sample Allocation Strategies. Mathematics and Statistics. 12. 55-62. 10.13189/ms.2024.120108.