Past Projects
2016 Student Projects
Student 
Advisor 
Title 
Cassidy Amason 
R. Brown 
Deterministic and Probabilistic Approaches to Card Shuffling 
Darby Bagwell 
D. Santarone 

Savanna Cash 
D. Santarone 
The Two Types of Assessment Tasks and What They Tell a Teacher 
Samantha Clapp 
B. Samples 

Sarah David 
A. Abney 
Investigating Spatial Visualization van Hiele Levels and Early Experiences 
Megan McGurl 
S. Tchamna 
A Comparative Study of the Mathematical Curricula of France and the State of Georgia 
Matthew Pearson 
H. Yue 

Elyse Renshaw 
J. Mijena 
Analyzing the Weight Lifting Performance on the 20002016 Olympics Games 
Henry Rowland 
M. Allen 

Cuyler Warnock 
M. Allen 

Kelsey Windham 
M. Chiroescu 
Unique Visualizations: Exploring Symmetries with ComplexValued Functions and Group Theory 
2015 Student Projects
Student 
Advisor 
Title 
Keri Spetzer 
R. Brown 

Brian Minter 
R. Brown 
MultiWay Contingency Tables in Baseball: An Application of Algebraic Statistics 
Emily Baum 
B. Samples 
Effectiveness of a Supplemental Instruction Program in a Statistics Classroom 
Kirsten Morris 
M. Chiorescu 
On the Rank of a Kronecker Sum of Similar Matrices 
Austin McTier 
J. Mijena 
Fractional Calculus Fundamentals and Applications in Economic Modeling 
Kendall Brown 
D. Santarone 

Dylan Hogan 
R. Brown 

Matthew Mitchell 
S. Sadhu 
Models Involving Interactions between Predator and Prey Populations 
Jordan Orlandini 
J. Baugh 
How Conceptual Understanding Can Improve Mathematical Intuition 
Sue Prestwood 
A. Abney 

Elijah Jordan 
A. Abney 
Investigating the Content Knowledge Teachers Need to be an Effective Mathematics Teacher 
Misty Kent 
D. Santarone 
2014 Student Projects
Student 
Advisor 
Title 
Andrew Pangia 
M. Allen 

Lindsay Yates 
M. Chiorescu 

Moriah Gibson 
B. Samples 
Various Properties of the Fibonacci Number Sequence 
Wayne Cook 
R. Brown 

Suzanne Frank 
B. Samples 

Matthew Heath 
J. Mijena 

Taylor Smoak 
B. Samples 
Student’s Perception of Interactive Teaching Aids in the Core Mathematics Classroom 
Lauren Stephansen 
A. Abney 

Madii Davis 
B. Samples 
Creatively Disrupting the Mathematics Classroom with the Humanities 
Joel Rapkin 
R. Cazacu 
Introducing Students to the Projective Plane Using the Dynamic Geometry Software Sam 
Marcie McBride 
S. Tchamna 

Ryan Lawson 
J. Mijena 
Modeling Student Achievement using Linear and Nonlinear Models 
Alex Reid 
H. Yue 
The Principle of Mathematical Induction: A Viable Proof Technique for High School Students 
Emily Harper 
A. Abney 

Katie Hodgson 
A. Abney 

Nassim Talbi 
D. Mohr  Optimization of Formula 1 Racing 
Michael Seligman 
G. Cazacu  Introduction to Stability Theory of Dynamical Systems 
2013 Student Projects
Student 
Advisor 
Title 
Jodeci Wheaden 
R. Brown 

Sally Gilbreth 
D. Mohr 

Tanner Mortensen 
D. Mohr 

Brittany Tharpe 
K. Westbrook 
Talk Your MATH Off: Communicating in the Mathematics Classroom 
Lydia Ozier 
K. Westbrook 

Peggy Kimmons 
A. Abney 

Michael Eubanks 
R. Brown 

Juliana Martins 
R. Brown 

Amanda Schmidt 
R. Brown 

Lindsey Harrison 
M. Allen 
From Euclid to Present: A Collection of Proofs Regarding the Infinitude of Primes 
Katelyn Callahan 
M. Allen 

Rujeko Chinomona 
M. Chiorescu 
Equilibrium, Stability, and Dynamics of Magnetocapillary Swimmers 
Zachary Monaco 
B. Samples 

Katy Hill 
B. Samples 

Tricia Swift 
B. Samples 
Algebraic Understanding of College Algebra Students through Story Problems 
Miles Daly 
R. Brown 

Matthew Hilliard 
H. Yue 
Investigation of the Interactions of Argon Particles in a Closed Container 
Monica Pescitelli 
S. Sadhu 
Lotka Volterra PredatorPrey Model with a Predating Scavenger 
2012 Student Projects
Student 
Advisor 
Title 
Brandon Witta 
D. Mohr 

Aubrey Kemp 
L. Huffman 

Kara Jackson 
R. Cazacu 
Metric Spaces and Continuity in Topology 
Kelsey Davis 
K. Westbrook 

Rachel Waldron 
A. Abney 
Making Our Partial Fractional Understanding of Fractions Whole 
Alexandra Cain 
K. Westbrook 

Laura Leon 
R. Brown 
Quipus and their Influence Seen through Mathematical Analysis 
Eric Cardoso 
D. Mohr 

Elizabeth Carpenter 
K. Westbrook 
Demonstrating Knowledge and Understanding through Mathematical Writing 
Joseph Swearingen 
A. Abney 

Ashley Madden 
B. Samples 

Chelsea Davis 
J. Stover 
Software Engineering for Computational Science and Engineering 
Jackie Merriman 
R. Brown 
The Rationality Theorem for Multisite Posttranslational Modification Systems 
Joseph Scott 
D. Mohr 

Catherine Stein 
K. Westbrook 
Hearing Impairment and ADHD: How they Affect Students' Ability to Learn Math 
Katherine Austin 
A. Abney 

Megan Maxey 
M. Allen 
A Modern Day Application of Euler's Theorem: The RSA Cryptosystem 
Faculty Research Interests
Faculty in the Georgia College Mathematics Department have research interests in variety of branches of mathematics and mathematics education. The following faculty descriptions offer students a glimpse at these interests relative to directing senior capstone projects.
Dr. Angel 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. Martha 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 selfmotivated, 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. Guy Biyogmam's research interests lie mainly in the field of nonassociative algebras, combined with the areas of Leibniz Algebras, Algebraic Topology, Leibniz (Co)Homology, Invariant Theory and Homological Algebra. Possible projects will consist of using the Pirashvili spectral sequence to detect (non) relativistic invariants, which may be useful in the calculation of the Leibniz (co)homology of abelian extensions of semisimple Leibniz algebras. He also has some interest for BCKalgebras, Racks, Fuzzy set theory, and multilinear Lie algebras. These fields can generate several undergraduate projects. Some projects under my supervision to browse through are: "A study of subracks" (American Journal of Undergraduate Research, 13(2) (2014), 1927) and "Centers of some non relativistic Lie algebra" (RoseHulman Undergraduate Mathematics Journal, Vol. 16, Issue 1, 2015).
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. Marcela Chiorescu's areas of research interest are in abstract algebra and its applications (in particular commutative algebra), in the history of mathematics (in particular the history of mathematics in Japan and China) and in the connection between mathematics and art (in particular the connection between mathematics and temari). A student desiring to work on a project on any of these areas should have successfully completed at least MATH 3030 and be proficient in LaTeX.
Dr. Rachel Epstein’s primary area of research interest is mathematical logic, and in particular, computability theory. In addition, she is interested in the connections between mathematics and origami, the history of mathematics around the world, and the application of mathematics to social issues such as gerrymandering and voting. To say more about computability theory, it is the study of what is computable by a theoretical idealized computer (or Turing machine) and what isn’t. Within the realm of the noncomputable, we can classify mathematical objects such as real numbers by how much information they contain. Computability theory can be applied to many areas of mathematics, such as abstract algebra or graph theory, as well as studied on its own. To work on problems in computability theory, the only prerequisite would be Foundations of Mathematics (MATH 3030). A subfield of computability theory that is closely linked to computer science is the study of randomness. To work on randomness, Probability (MATH 4600) would be useful. Other topics in mathematical logic include set theory, model theory, and Godel’s Incompleteness Theorems. Students with an interest in computer science, philosophy, psychology, or physics could work on topics that combine computability theory or mathematical logic with those disciplines.
Dr. Susmita 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" (RoseHulman Undergraduate Math Journal, vol 4, issue 1, 2003), "Long term dynamics for two threespecies food web" (RoseHulman Undergraduate Math Journal, vol 4, issue 2, 2003), and "Introducing a scavenger onto a predator prey model" (Applied Math ENotes, 2007), etc.
Dr. Brandon 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 (RoseHulman, 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.
Dr. Doris 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. Simplice Tchamna’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. Hong 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.
Department of Mathematics
Arts & Sciences Room 129  Campus Box 17
Milledgeville, GA 31061
Phone: (478) 4455213
Fax: (478) 4452606