Department of Mathematics
College of Arts and Sciences
University of Tennessee at Chattanooga
415 EMCS Building (Mail Stop 6956)
615 McCallie Avenue
Chattanooga, Tennessee 37403-2598
Office 417F EMCS Building
Telephone +1 423 425 4019
Facsimile +1 423 425 4586
I came to the University of Tennessee at Chattanooga in August 2011 from Boston College, where I had been on faculty for a little over a year, and currently work as an assistant professor of mathematics. After earning my doctor of philosophy degree in May 2007 under the direction of Professor Alexandru Zaharescu at the University of Illinois at Urbana-Champaign, I worked as a visiting assistant professor/post-doctoral faculty at the University of Rochester until June 2010. Professor Steven M. Gonek, my post-doctoral mentor, influenced my reading and helped to direct my thought toward some interesting problems that have preoccupied me in my work. Together, we investigated the zeros of the partial sums of the Riemann zeta-function. Our research is ongoing, as there are gaps in our study so far that need to be filled and other directions to be explored. During this time, I also studied the distribution of prime numbers with Professor Daniel A. Goldston at San José State University. In December 2010, we resolved how the Hardy-Littlewood prime k-tuple conjecture determines the jumping champions. Memories!
Area of Research
My area of research is in number theory. My favorite topics are L-functions, prime numbers and Farey fractions. I also study probability theory, especially random polynomials. I am currently seeking to be more actively involved in the mentoring of young mathematicians. Undergraduate and graduate students who are looking for a thesis adviser are encouraged to contact me. Come by my office for a meeting anytime!
I am dedicated to promoting significant learning experiences among all my students. I love learning, teaching mathematics on various levels, and advising students. In the spring term of 2015 I will be teaching the following courses:
MATH 1830: Calculus for Management, Life, and Social Sciences (2 sections)
MATH 4999/5910: Financial Mathematics (2 sections)
Here is the course description for MATH 4999/5910: Mathematical aspects of finance; theory of pricing derivatives of financial instruments; options in Black-Scholes model; portfolio optimization; capital asset pricing model. (The prerequisite for MATH 4999/5910 is MATH 3100 or MATH 4130 with a minimum grade of C, or department head approval.)
Students can access all my course materials by logging in to the UTC Learn system.
Here are my graduate students and their research topics:
Ashley Holcombe, The index of a Farey sequence (May 2014)
Gentry Jones, Option valuation using the Fourier transforms (December 2014)
Benjamin Kimsey, The prime number theorem and its applications (December 2014)
Here is my undergraduate student and her research topic:
Melissa Miller, The simple zeros of the Riemann zeta-function (Brock Scholars Program, Departmental Honors thesis, May 2016)
Professor Stan Byrd's Student Problem Competition
The Student Problem Competition is an ongoing competition for mathematics majors. Mathematics minors and mathematics enthusiasts are welcome to participate. Every few weeks Professor Stan Byrd creates an interesting and challenging problem for students to ponder and solve. His problems and puzzles are currently posted as flyers in the Main Office and on the office doors of several faculty members. A prize of $20.00 is awarded to the student who successfully solves the problem and provides the best correct solution with all assertions proved. The winning solution and other solutions will receive honorable mention in the next flyer. The current problem is:
Research Experiences for Undergraduates
Recently, the department received very generous financial support from the National Science Foundation to organize and set up a Research Experiences for Undergraduates (REU) Site in Differential/Difference Equation Models and Number Theory for the academic years 2013-2015 (National Science Foundation Grant DMS-1261308).
In the summer of 2013, nine undergraduate students participated in the REU program. I mentored the following students in number theory:
Kathryn Crosby (Oral Roberts University)
Jordan Eliseo (University of North Carolina at Greensboro)
David Mazowiecki (William Paterson University)
Our paper on the zeros of partial sums of the square of the Riemann-zeta function has been accepted for publication in Springer Proceedings in Mathematics and Statistics.
In the summer of 2014, we have another group of nine energetic undergraduate students. I was delighted to mentor the following students in analysis and probability theory:
Katrina Ferrier (University of Tennessee at Chattanooga)
Micah Jackson (Georgia Southern University)
Dhir Patel (Rutgers University)
Huong Tran (Georgia Institute of Technology)
August 1, 2014: Dhir and Huong have been invited to present a 20 minute report talk on their joint work at the forthcoming Young Mathematicians Conference (YMC) at Ohio State University, August 22-24, 2014. This wonderful conference for undergraduate student researchers has a very competitive review process with over 40 mathematics faculty reviewers. Only 50 abstracts out of 140 abstracts submitted by 200 students were selected for invitation to YMC. Congratulations, Dhir and Huong!
October 11, 2014: Katrina presented a 20 minute talk at Western Kentucky University's 34th Annual Mathematics Symposium!
January 7, 2015: Katrina will be presenting a research poster at the 7th Annual UTC Research Day, April 14, 2015.
February 10, 2015: Katrina will be presenting a research poster at the Emory University-Laney Graduate School STEM Research and Career Symposium, March 25-27, 2015.
March 8, 2015: Micah Jackson will pursue his Ph.D. in Statistics in the fall term of 2015 at the University of California at Irvine.
April 13, 2015: Dhir Patel will pursue his Ph.D. in Mathematics in the fall term of 2015 at the Ohio State University.
April 17, 2015: Huong Tran will pursue his Ph.D. in Mathematics in the fall term of 2015 at Duke University.
Travel and Meetings
You can find me presenting talks at the following meetings and conferences:
SERMON 2013 (SouthEastern Regional Meeting on Numbers), High Point University, High Point, North Carolina, April 13-14, 2013
INTEGERS 2013 (The Erdős Centennial Conference), University of West Georgia, Carrollton, Georgia, October 24-27, 2013
Mathematics Colloquium, University of Alabama at Birmingham, Birmingham, Alabama, April 17, 2015
Links and Miscellany
Here are some of my favorite links:
From the Top (I absolutely love this radio show!)
‘And gladly wolde he lerne, and gladly teche.’
Geoffrey Chaucer, The Canterbury Tales