Undergraduate Student Research

The Department of Mathematics is committed to providing undergraduate research opportunities to interested students.  The office of Undergraduate Research and Creative Activities at the College of Charleston offers financial support for undergraduate research experience thorugh several grant programs. Most of the time you will be able to attend conferences and present your research in front of your peers and other researchers. Such attendance at conferences, which are usually all paid for, also give you an opportunity for networking and to get valuable lessons in the art of communication. Many times participation can lead to research publications. Most importantly you get first hand experience about how Mathematics is "created". It is not really important whether you are a freshman or a senior or what is your background, just like any other art one can enjoy the stimulus and challenge at one's own level and be creative. The most important ingredients are enthusiasm and positive attitude with a bit of aptitude.

Here is what someone with the first hand experience has to say after participating in the research program at CofC.

"As a Freshman majoring in Mathematics, I did not initially anticipate much opportunity for myself in actual research. This illusion was soon cleared, however, as I began studying under the guidance of Dr. Dinesh Sarvate. Even with my limited background and experience, I was quickly able to make the transition into contemplating new, undiscovered ideas. My undergraduate research project this previous summer was invaluable, not only due to the research itself, but also the incredible amount of information and skill I acquired during such a short time frame. Through complete immersion in the realm of theoretical pure mathematics, I learned not only what is required of mathematicians who continue to Graduate School and beyond, but also the fundamental concepts of how mathematics is discovered and proven. This understanding has lead to great success in my current courses, as I now can fully appreciate the logic, methodology and intuitive reasoning behind the numerous definitions, theorems and proofs that are being covered. Nothing has increased my mathematical prowess as greatly as the few months I spent over this summer. I cannot emphasize how much Undergraduate Research is really a necessity for any student seriously interested in Mathematics."
-Sam Buelk

If you are interested in pursuing your own mathematics research, take the first step, talk with your favorite professor about academic year research or Summer research today!

Project Students Faculty
Modeling mental imagery Grier Jones Garrett Mitchener
Rational solutions to the matrix KdV equation Luiz Bossa Alex Kasman
Almost parallel and nearly circular vortex filaments Allison Conger and Danielle Masse Annalisa Calini and Stephane Lafortune
Dynamic models of targeted advertising competition Chloe Fletcher Jason Howell
A convex hull approach to solubility parameters Benjamin Stephens Jason Howell
Influence of neck width on the hemodynamics of intracranial aneurysms Allison Conger Jason Howell
Computational studies of abdominal aortic aneurysms Danielle Masse Jason Howell
GDDs with equal number of triples of configurations (0,3) and (1,2) Blaine Billings Dinesh Sarvate
GDDs with equal number of even and odd blocks of size 4 and two groups Issa Ndungo Dinesh Sarvate
GDDs with equal number of even and odd blocks of size 4 and three groups Brittney Johnson Dinesh Sarvate
Counting divisors Lauren Tubbs Dinesh Sarvate
A GDD construction using Mutually orthogonal latin squares Devin Henson Dinesh Sarvate
Algorithmic Complexity and Universal Prior Probability of Infinite Sequences via non-Halting Universal Turing Machines Prerna Bihani Jim Young
An Application of Symmetric Chains to Statistical Database Compromise Prevention Problem Kevin Miller Dinesh Sarvate
Chaotic Dynamics in Perturbed Nonlinear Equations Kelly Sweetingham Annalisa Calini
Comparison of Hospital Occupancy Patterns in American and English Hospitals Sonja Killian Gary Harrison
Comparison of Three Methods for Numerically Solving Stiff Ordinary Differential Equations Andrew Cornwell Gary Harrison
Continuous-Time Model of Inventory of Business Cycle Dimitre Milkov Annalisa Calini
Counting and Classifying Critical Points Prerna Bihani Tom Ivey
Difference Sets of Integers Mark Creech and Darryl Adams (graduate student) Oleg Smirnov
Faithful Enclosings of Group Divisible Designs Formed by Adding and Additional Group Tarsem Purewal Dinesh Sarvate
Integrable Dynamics of Vortex Filaments Jane Ilina and Kevin Young Annalisa Calini and Tom Ivey
Linear Codes through Latin squares modulo n Alex Strehl Dinesh Sarvate
Minimal Enclosings of Group Divisible Designs with Block Size 3 and Group Size 2 Tarsem Purewal Dinesh Sarvate
Nonstandard Methods in Kneser's Theorem for Upper Banach Density Prerna Bihani Renling Jin
Occurence of Epidemics in Isolated and Interacting Populations Kelly Geyer Gary Harrison
On group divisible designs with block size four and three groups Devin Henson Dinesh Sarvate
On the KdV Two Soliton Interaction Kevin Young and Nicholas Benes (graduate student) Alex Kasman
Predator Prey Systems with Differing Time Scales Hollie Pitman Gary Harrison
Simulation Model of Hospital Admissions and Occupancy Andrea Shafer and Melissa Hancock (graduate student) Gary Harrison
Slightly irregular Planar graphs I Adrienne Chisolm Dinesh Sarvate
Slightly irregular Planar graphs II Jesse Raab Dinesh Sarvate
Some necessary existence conditions, construction, and a list of partially balanced ternary designs Jaideep Mirchandani Dinesh Sarvate
Two block size PBDs with a maximum number of triples Sam Buelk Dinesh Sarvate
p-adic interpolation of the Fibonacci sequence via hypergeometric functions Prerna Bihani and Wendy P. Sheppard (graduate student) Paul Young
Universality of Rank 6 Plücker Relations and Grassmann Cone Preserving Maps Amy Reiszl and Kathryn Pedings Alex Kasman
Measure Theory Kirk McMullan Herb Silverman
Using Statistical Game Theory to study Tactical Approach Problem for Air Force Pilots Mark  Jones Martin Jones
Ternary codes through ternary designs Alexander Strehl Dinesh Sarvate
Investigations of Periodic Orbits in Triangular Billiards Cassel Sloan Anna Calini
Integrable Dynamics of Knotted Vortex Filaments Kelly Epperson Anna Calini
Analytical and Numerical Investigations of Fourier Knot Evolution under Vortex Filament Flow Kelly Epperson Tom Ivey
PBDs with block sizes three and k where k=4 or 5 Mathew King (GSSM) and Sam Buelk Dinesh Sarvate
Fractional and Trigonometric Decomposition of Supermatrices Stephen Yackey Ben Cox
Introduction to Fractals Bill McNeilts Sandi Shields
Modeling and Simulating Thin Molecular Films Barron Whitehead Brenton leMesurier
Modeling Occupancy and Admissions Fluctuations among Pediatric Patients Using Compartmental Flow Models Melissa Hancock Gary Harrison
Difference sets of Integers: the infinite case Darryl Adams Oleg Smirnov
New Measures of risk in financial markets Kirk McMullan Martin Jones
Numerical Simulation of 1/k Flow for Curves Ross Ingram Tom Ivey
A new type of block designs: Adesigns William Beam Dinesh Sarvate
Further results on Adesigns and t-designs William Beam Dinesh Sarvate
Construction of families of Mutually orthogonal Latin Squares Hau Chan Dinesh Sarvate
On the Large Sets of SB designs and the non-existence of t-SB designs Hau Chan Dinesh Sarvate
Beautifully ordered balanced incomplete block designs Hau Chan Dinesh Sarvate
Magic Squares and Cubes Vashtia Bennett Dinesh Sarvate
H-polynomials and their computation Caroline Copeland Tom Kunkle
A Variation on 3-GDDs with Blocks of Size 4 and 3 Groups
Aidyn Trubey Dinesh Sarvate
Embedding an n by n Knight’s Tour Solution in an (n+8) by (n+8) Knight’s Tour Path Aidyn Trubey Dinesh Sarvate
Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions John Cobb and Monique Sparkman Alex Kasman
Deep Learning Based Matrix Completion Terence Carey Mukesh Kumar
An Effective and Flexible Intrusion Detection System based on Deep Learning Carson Barber Mukesh Kumar
Isogeometric Collocation Methods on Phase Field Equations Michael Lanier Mukesh Kumar
An Automated System for Polyp Detection in Wireless Capsule Endoscopy Michael Lanier Mukesh Kumar
Numerical Techniques for Nematic Liquid Crystal  Tea Liu Mukesh Kumar

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