Projects

Past Projects

2017 Student Projects

 

Student	Advisor	Title
Emily Andriano	A. Abney	Content Knowledge vs. Pedagogical Knowledge
Jasmine Gray	J. Mijena	Modeling Grade Distribution
Christopher Kline	S. Tchamna	Eigenface for Face Detection
Olivia Lindsey	D. Santarone	Increasing Students' Understanding of Multiplying Binomials through Manipulatives
Kendal McDonald	J. Mijena	Comparative Analysis of Students' Performance Between Online and on Campus in an Introductory Statistics Course
Jaclyn Pescitelli	S. Sadhu	Turing Instability in a Predator-Prey Model for Zooplankton Grazing on Competing Phytoplankton Species
Patrick Pruckler	S. Sadhu	A Reaction Diffusion Model of Acid Mediated Tumor Invasion with Chemotherapy Intervention
Brian Skoglind	H. Yue	The Helix Conjecture: A Study of Fractional Derivatives of Sinusoidal Functions by Means of Fourier Transform
Shannon Smith	B. Samples	Music Through a Mathematical Lens
Calvin White	S. Tchamna	Application of Linear Algebra to Image Processing

 

2016 Student Projects

 

Student	Advisor	Title
Cassidy Amason	R. Brown	Deterministic and Probabilistic Approaches to Card Shuffling
Darby Bagwell	D. Santarone	The Benefits of Writing in a Mathematics Classroom
Savanna Cash	D. Santarone	The Two Types of Assessment Tasks and What They Tell a Teacher
Samantha Clapp	B. Samples	Lie Algebras of Generalized Quaternion Groups
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	An Exploration of Function-Order Derivatives
Elyse Renshaw	J. Mijena	Analyzing the Weight Lifting Performance on the 2000-2016 Olympics Games
Henry Rowland	M. Allen	The Role Of Prime Numbers in RSA Cryptosystems
Cuyler Warnock	M. Allen	Investigating Proofs of the Quadratic Reciprocity Law
Kelsey Windham	M. Chiroescu	Unique Visualizations: Exploring Symmetries with Complex-Valued Functions and Group Theory

 

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	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. Guy Biyogmam's research interests lie mainly in the field of non-associative 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 BCK-algebras, 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), 19-27) and "Centers of some non relativistic Lie algebra" (Rose-Hulman 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 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. 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’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