Jeff Hollon, who is working on his Ph.D. in Interdisciplinary Applied Science and Mathematics (IASM), has been working with Professor K.T. Arasu on research that applies sequences to things like radar systems.
Radar systems, error correcting codes, cell networks applications and data security all use sequences of numbers. Mathematicians call these strings of numbers sequences, engineers call them signals and computer scientists would call them codes.
Hollon earned a Bachelor of Science and a Master of Science in Mathematics at Wright State University. He completed his thesis on weighing matrices. While growing up in Wilmington, Ohio, he always had an interest in computer science. But after taking chemistry and physics he discovered how math is involved in everything.
Hollon has been working with Professor Arasu since 2008 as his research assistant while pursuing his masters. As a teacher, he would travel back to Wright State University to assist Arasu with his research groups because he loved the subject matter. The connection has lasted through the years and they are still working together on sequences research.
A sequence is a string of numbers - usually using a binary or ternary alphabet. For example, {0,1} or {-1,0,1} are the letters that are used to make them. A "nice" sequence shows a consistent pattern, referred to as a correlation and can be used in a computer or a signal such as radars, and in erroring correcting codes. In radars, the sequence itself is what is transmitted to the target and its reflection is measured. The reflection makes a shifted waveform. The shifted waveform is compared to the original waveform and a correlation is made.
All computers use codes and with the ability to encode messages and detect errors. Mathematicians, like Hollon, can mathematically form a sequence to fix codes, usually before the user notices. The errors in stored data can be detected and corrected because the code is fixed.
“I enjoy working with sequences because it combines both traditional mathematical theories and challenging computational problems into one research topic. Plus, once found, these sequences can be used for something in the real world!” said Hollon.
