Dreams. Made Real.
Krop Plus Ermakov Plus Contractor Equals Success
Clayton State Associate Professor of Mathematics Dr. Elliot Krop + 19th Century Russian mathematician V.P. Ermakov + Clayton State double major (Math and Computer Science) Aziz Contractor = Success.
Contractor, a native of India who came to the U.S. 10 years ago, was a student in Krop’s calculus class this past summer, wherein Krop posed a challenge problem about the convergence/divergence of a special infinite series.
“In the latter half of Calculus 2, we learned about infinite sums,” explains Contractor. “These are just sums of sequences that increase or decrease in a specific pattern. 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 challenge 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 Contractor, warming to the subject of advanced calculus. “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 Calculus 2 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 he 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 Ermakov's Test.”
Ultimately, success for Contractor means solving unsolved problems.
“Dr. Krop showed me that math could not only be as challenging as computer science but also just as rewarding,” he 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.”
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