Projects

Past Projects

2015 Student Projects

 

Student
Advisor
Title
     

Keri Spetzer

R. Brown

Sequences of Soddy Circles

     

Brian Minter

R. Brown

Multi-Way 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

Discovering Discovery Learning

     

Dylan Hogan

R. Brown

Modeling the Game Plinko with Random Walks

     

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

Children’s Understanding of the Equal Sign

     

Elijah Jordan

A. Abney

Investigating the Content Knowledge Teachers Need to be an Effective Mathematics Teacher

     

Misty Kent

D. Santarone

The Mystery of Mixed Number Addition and Subtraction

 

2014 Student Projects

 

Student
Advisor
Title
     

Andrew Pangia

M. Allen

A Matrix Extension of the RSA Cryptosystem 

     

Lindsay Yates

M. Chiorescu

Linear Algebra of Pascal Matrices

     

Moriah Gibson

B. Samples

Various Properties of the Fibonacci Number Sequence

     

Wayne Cook

R. Brown

Using Groebner Bases to Find Nash Equilibria

     

Suzanne Frank

B. Samples

Generalizations of the Postage Stamp Problem

     

Matthew Heath

J. Mijena

Regression and Tree Based Models: Georgia Unemployment

     

Taylor Smoak

B. Samples

Student’s Perception of Interactive Teaching Aids in the Core Mathematics Classroom

     

Lauren Stephansen

A. Abney

Comparing Perspectives of Mathematics and Special Education

     

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-Kouna

Forecasting Median Home Price Using Regression Analysis

     

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

Mathematics Taking the Stage

     

Katie Hodgson

A. Abney

Culturally Responsive Mathematics Teaching

     

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

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
Advisor
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   

     

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   

 

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 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. 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 research interests are in commutative rings, coding theory and the art of mathematics.

Dr. Rachel Epstein’s primary area of research interest in mathematical logic, and in particular, computability theory.  Computability theory is the study of what is computable by a theoretical idealized computer (or Turing machine) and what isn’t.   Within the realm of the non-computable, 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. Epstein is also interested in the connections between mathematics and origami.

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" (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. 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 (Rose-Hulman, 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-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. 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 1-29  |  Campus Box 17
Milledgeville, GA 31061
Phone: (478) 445-5213
Fax: (478) 445-2606