Page 13 - Laker Connection Spring 2015
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Krop + Ermakov + Contractor = Success
BY JOHN SHIFFERT
Success here comes in the form of presentations on double major (math and computer science) Aziz Con- tractor’s work on infinite series at two mathematics conferences; the Kennesaw Mountain Undergraduate Mathematics Conference, and the 10th Annual Univer- sity of North Carolina Greensboro Regional Mathemat- ics and Statistics Conference.
Contractor, a native of India who came to the U.S. 10 years ago and graduated from Fayette County High School, was a student in Assistant Professor of Mathe- matics Dr. Elliott Krop’s Calculus II class this past summer. In that class, Krop posed what he refers to as a “challenge problem” about the convergence/divergence of a special infinite series.
“In the latter half of Calculus 2, we learned about infi- nite sums,” explains Contractor. “These are just sums of sequences that increase or decrease in a specific pat- tern. Think of a sequence such as 1/k, where k starts at one and keeps growing. A sum of this sequence would simply add the consecutive terms.”
Sounds simple enough, doesn’t it? Well, Krop’s chal- lenge was anything but simple, and Contractor had to learn some advanced calculus tests, including the little- known Ermakov’s Test, developed by the Russian mathematician in 1871.
“We had to find a pattern which showed us how many logs we could take of a specific k value,” says Contrac- tor, warming to the subject of advanced calculus. “This alone was a tedious task. Second, this was an infinite product inside an infinite sum and it was the first time I
looked at something like this, let alone trying to solve it.
“I tried many tests and methods that I was familiar with but none of the tests and methods we learned in Calcu- lus II were meant to deal with such a complex infinite series. Then, we came across Ermakov’s Test. It tests for convergence and divergence and is meant to be used on infinite series that contain logarithms.”
“In order to solve the series Aziz had to learn a few more advanced tests as well as proof techniques from analysis to understand why those tests are true,” adds Krop. “Eventually, he solved the problem by using Er- makov’s Test.”
Ultimately, success for Contractor means solving un- solved problems.
“Dr. Krop showed me that math could not only be as challenging as computer science but also just as re- warding,” Contractor explains. “I see the work I do with him here at Clayton State as my first step on a long ladder toward success. The professors here at Clayton State, not just in the math department but also in computer science, English and other departments, have always guided me in the right way and taught me to keep moving forward and learning more things.
“Since solving the challenge problem from Dr. Krop, I have been working with him to solve some unsolved problems in the field of Graph Theory. We believe we have already solved one and written a paper about it, and I hope to solve a few more before I graduate.”
SPRING 2015
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