## Past Projects

### 2021 Student Projects

Student | Advisor | Title |
---|---|---|

Caleb Gill | R. Epstein | The Cornerstones of Algorithmic Randomness |

Morgan Grey | D. Santarone | Mind Over Math |

R. Seth Rozelle | J. Mijena | COVID-19 and the Effect On Grades |

### 2020 Student Projects

Student | Advisor | Title |
---|---|---|

Hanwen Chen | J. Mijena | Modeling Grade Distribution |

Caroline Drummond | B. Samples | Deepening Understanding of Quadratics Through Bruner’s Theory of Representation |

Sam Eichel | J. Mijena | What determines WAR in Baseball |

Kristen N. Hartley | D. Santarone | Comparing Virtual and Concrete Manipulatives Effect on the Conceptual Understanding of the FOIL Method |

Justin Hockey | D. Santarone | The Effectiveness of Middle and High School Math Inclusion Classes |

Emily Howe | G. Biyogmam | Lie-derivations of three-dimensional non-Lie Leibniz algebras |

Stephen Mosley | J. Mijena | Resampling Methods in Inferential Statistics |

Dawson Shores | M. Allen | The Evolution of Cryptography Through Number Theory |

### 2019 Student Projects

Student | Advisor | Title |
---|---|---|

Joshua Ballard-Myer | R. Cazacu | Deterministic Greedy Algorithm for Maximum Independent Set Problem in Graph Theory |

Laurel Brodkorb | R. Epstein | The Entscheidungsproblem and Alan Turing |

Amy Beth Edwards | J. Mijena | Derivative Security Pricing with the Binomial Asset Pricing Model |

Bayley Perkins | A. Abney | Reasoning with Fractions as Measures and Rational Expressions |

Ashleigh Romer | J. Mijena | Modeling FICO Score and Loan Amount |

Christopher Williams | D. Santarone | Understandings and Misunderstandings of Trigonometry |

Matthew Emmerling | J. Mijena | Partial Least Squares Path Modeling to Determine the Success of College Football Teams |

Clayton Gilchrist | S. Tchamna | Some Results on Fuzzy Matrices |

Brooke McDonald | B. Samples | The Importance of Equity in Mathematics Education |

Stella Oliver | A. Abney | Get "Gritty" With It: The Impact of Effort on Mathematical Achievement |

Charles Quinn | J. Mijena | Applications of Regular Markov Chains |

### 2018 Student 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 |

## 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).