Mathematics
Math Dept. Overview Overview Mission Faculty and Staff Faculty Positions News and Events Scholarships Majors Minors Student Organizations
Placement Choosing First Course
Advising Freshman Fall 2011 or After All Other Years
Undergraduate Research Overview Student Resources Faculty Resources Projects News and Events Additional Resources
Arts and Sciences Dept. Listing Other Departments
spacer

Projects

Faculty Research Interests

Dr. Abney's research interests include preservice teachers’ models of students’ mathematics, effectiveness of preservice teacher education, mathematical knowledge for teaching, mathematical knowledge needed for teaching teachers and keeping women and minorities in the mathematical pipeline.

Dr. Allen’s areas of interest include number theory and cryptography.  Previous projects have included examining a collection of proofs of the infinitude of the primes and investigating why primes are important, investigating the impact of ciphers on World War I and World War II, researching a modern day application of Euler’s Theorem, and considering applications of primitive roots and discrete logarithms in cryptography.  A student desiring to work on a project with Dr. Allen should exhibit a strong work ethic, be highly self-motivated, be fluent in mathematical writing, and be proficient in LaTeX.  In addition, to conduct research in number theory, a student should have successfully completed MATH 4110, and to conduct research in cryptography, a student should have taken or concurrently be taking MATH 4110 while enrolled in MATH 4989.

Dr. Brown’s research interests lie in two primary areas: applied algebraic geometry and Andean mathematics. As the name suggests algebraic geometry is a branch of mathematics that connects (abstract) algebra and geometry. Algebraic geometry is often described as the study of those geometric objects whose points correspond to the common solution set of a system of polynomial equations. Polynomials naturally arise in many areas of economics, the sciences, and mathematics. Many projects involve using tools from algebraic geometry to solve systems of polynomial equations and interpret results. Pre-Columbian Andean cultures had very interesting mathematical systems. The most widely studied is the khipu system of the Incas. A khipu consists of a collection of knotted strings attached to a single larger cord. There are many open questions about how khipus can be use to encode information. There are several projects that involve mathematical examinations of khipus and trying to decipher the information. Pre-Columbian cultures also demonstrated sophisticated geometric understanding in textiles, metalwork, and ceramics. There are several projects that involve characterizing the geometry and symmetry of artifacts of the Wari, Nazca, Chimu, Inca, and Moche. Other projects involving Inca architecture, engineering, and astronomy are available. Students interested in pursuing projects related to Andean mathematics should plan to enroll in the study abroad program New World Mathematics in Peru.

Dr. George Cazacu’s research interests include general topology, dynamical (poly)systems and stability theory, as well as algorithm complexity. He is tackling the P vs. NP problem in the hope that one day he will be able to fully understand it. A student interested in research under his guidance would have a considerable pool of topics to pick from, varying from rigorous understanding of abstract topological notions to attacking open problems or special, less explored cases of attractors in dynamical (poly)systems, or the study of some NP problems.

Dr. Chiorescu's research interests are in commutative rings, coding theory and the art of mathematics.

Dr. Mohr’s research interests lie in optimization, mathematical modeling, numerical analysis, and quantitative analysis in sports. Optimization problems arise in many areas of science such as physics, geology, economics, chemistry, and engineering. Finding solutions to optimization problems is an active research area for many companies. Quantitative analysis in sports involves using mathematics to make informed decisions about teams or players in a particular sport. Past projects have included creating new metrics to evaluate batter and pitcher performance in baseball, finding optimal evacuation routes in the Arts & Sciences building at Georgia College, and developing a healthy, lowest-cost meal plan at Georgia College. Students interested in any project with Dr. Mohr should be comfortable and willing to program and should be open to learning new mathematics and its applications.

Dr. Sadhu's research interest is in dynamical systems (differential equations) and its applications. More specifically, her research can be broadly classified into two sets: (i) studying and interpreting the behavior of solutions of nonlinear boundary value problems (which are ordinary differential equations with certain boundary conditions imposed on them), (ii) qualitatively analyzing and geometrically visualizing solutions of systems of differential equations that model some physical, biological or ecological phenomena. A student interested in learning classical theory of differential equations or interested in studying a problem that model an  ecological or a biological process should be comfortable with the material from one of the above sets. Mathematical tools such as Maple, MATLAB, XPPAUT will be frequently used and will be taught to the student. Programming capabilities are desirable, though not required.  Interested students are strongly encouraged to look at some undergraduate journals to get a sense of the nature of research done in this field.  Some possible papers to browse through are : "A predator prey model with disease dynamics" (Rose-Hulman Undergraduate Math Journal, vol 4, issue 1, 2003), "Long term dynamics for two three-species food web" (Rose-Hulman Undergraduate Math Journal, vol 4, issue 2,  2003), and "Introducing a scavenger onto a predator prey model" (Applied Math E-Notes, 2007), etc.

Dr. Samples areas of interest include representation theory (representing objects using methods of linear algebra), abstract algebra, number theory, graph theory, and mathematics education. A student wanting to work on a project with Dr. Samples in the pure mathematics setting should be interested and comfortable with material from at least a subset of the above mentioned branches of mathematics. A search of undergraduate mathematics journals (Rose-Hullman, College Math Journal, etc.) should allow the student to generate some possible topics. Previous projects have included topics coming from the study of Lie algebras associated to finite groups, combinatorics of finite graphs, generalized Fibonacci sequences, and generalizations of the Frobenius problem in number theory. A student wanting to work on a project within the realm of mathematics education should have thought about potential topics and searched the literature to get an idea of a possible framework. To get started, the student should have already looked at some mathematics education papers to get a sense for the nature of mathematics education research. Previous projects have included an analysis of conceptual versus procedural understanding in the context of story problems as well as assessing the efficacy of various teaching manipulatives at the undergraduate level.

Ms. Santarone's research interests lie in the areas of mathematical knowledge for teaching of inservice and preservice teachers, the mathematics content knowledge of preservice and inservice teachers, the mathematical knowledge needed for preservice teacher educators, and the evaluation of projects and programs for mathematics preservice teacher education.

Dr. Tchamna-Kouna’s primary area of interest is abstract algebra. He is interested in topics in commutative algebra.  Commutative algebra is the area of mathematics that studies commutative rings and other related topics such as module theory. Many areas of modern mathematics such as number theory, homological algebra, algebraic geometric, etc., use results from commutative algebra. A student wanting to work with him should complete (with at least a grade C) the two courses Math 3030 (Foundations of Mathematics) and Math 4081 (Abstract Algebra). He is also available to work with students wanting to explore topics in statistics. He is interested in techniques of collecting data to make predictions. In this case, the student should complete the two courses Math 1262 (Calculus I) and Math 2600 (Probability and Statistics).

Dr. Yue’s research interests lie in harmonic analysis related to function spaces, differential equations, fractal geometry and problem solving. Students who want to work on a project with Dr. Yue should have taken the course MATH 3030, Foundations of Mathematics. Also, if they are interested in a project in the setting of pure or applied mathematics, they should have taken​ at least one of courses MATH 4340, Differential Equations and MATH 4261, Mathematical Analysis. It is also encouraged that the students are good at a computer language or mathematical software, in particular, if they are interested in a topic in differential equations or fractal geometry.

Past Projects

2013 Student Projects

Jodeci Wheaden

R. Brown

An Application of Algebraic Geometry in Control Theory

Sally Gilbreth

D. Mohr

Using Mathematics to Find Optimal Evacuation Routes 

Tanner Mortensen

D. Mohr

Mathematics and Baseball: Rethinking Slugging Percentage

Brittany Tharpe

K. Westbrook

Talk Your MATH Off: Communicating in the Mathematics Classroom

Lydia Ozier

K. Westbrook

Effective Teaching Strategies for Students with Autism

Peggy Kimmons

A. Abney

Connections Throughout the Standards

Michael Eubanks

R. Brown

Machu Picchu and the Rising Sun

Juliana Martins

R. Brown

An Astronomical Analysis of an Inca Quipu

Amanda Schmidt

R. Brown

Mathematics in Knots: Quipus Then and Now

Lindsey Harrison

M. Allen

From Euclid to Present: A Collection of Proofs Regarding the Infinitude of Primes

Katelyn Callahan

M. Allen

The Impact of the Allied Cryptographers on World War II: Cryptanalysis of the Japanese and German Cipher Machines

Rujeko Chinomona

M. Chiorescu

Equilibrium, Stability, and Dynamics of Magnetocapillary Swimmers

Zachary Monaco

B. Samples

Olympic Coloring: Go for the Gold

Katy Hill

B. Samples

Classifying Lie Algebras for Abelian Groups Zn and Zm × Zn

Tricia Swift

B. Samples

Algebraic Understanding of College Algebra Students through Story Problems

Miles Daly

R. Brown

Symmetry Analysis of Inca Textiles and Ceramics

Matthew Hilliard

H. Yue

Investigation of the Interactions of Argon Particles in a Closed Container

Monica Pescitelli

S. Sadhu

Lotka Volterra Predator-Prey Model with a Predating Scavenger

2012 Student Projects

Student

Mentor

Project Title

Brandon Witta

D. Mohr

Optimization in the Airline Industry

Aubrey Kemp

L. Huffman

Cantor: The Mathematician and the Set

Kara Jackson

R. Cazacu

Metric Spaces and Continuity in Topology

Kelsey Davis

K. Westbrook

Use of Effective Questioning in the Mathematics Classroom

Rachel Waldron

A. Abney

Making Our Partial Fractional Understanding of Fractions Whole

Alexandra Cain

K. Westbrook

Inquiry Based Teaching Today Reflects the Moore Method

Kendyl Wade

R. Brown

Visualizing Mathematics Through the Lens

Laura Leon

R. Brown

Quipus and their Influence Seen through Mathematical Analysis

Eric Cardoso

D. Mohr

Chick-fil-A nutrition plan

Elizabeth Carpenter

K. Westbrook

Demonstrating Knowledge and Understanding through Mathematical Writing

Joseph Swearingen

A. Abney

Conceptual Understanding of Mathematics in America

Ashley Madden

B. Samples

Investigating What Constitutes an Effective Math Teacher

Chelsea Davis

J. Stover

Software Engineering for Computational Science and Engineering

Jackie Merriman

R. Brown

The Rationality Theorem for Multisite Post-translational Modification Systems

Joseph Scott

D. Mohr

Implicitly Defined Baseball Statistic

Catherine Stein

K. Westbrook

Hearing Impairment and ADHD: How they Affect Students' Ability to Learn Math

Katherine Austin

A. Abney

Investigating Student Centered Teaching

Megan Maxey

M. Allen

A Modern Day Application of Euler's Theorem: The RSA Cryptosystem

 

Georgia College
CONNECTING WHAT MATTERS
A-Z Sitewide Index
About the site
Georgia College • 231 W. Hancock St. • Milledgeville, GA 31061 • 1-800-342-0471 ; 478-445-5004 • admissions@gcsu.edu