Student Research
There are many opportunities to pursue independent research projects in Mathematics and/or Computer Science at Denison, both during the summer and the academic year. One or more of these research experiences allows a student to explore in depth research questions that interest him or her. A research experience is also great preparation for graduate studies, which many of our students pursue after graduation.
Our Summer Scholar programs provide funding for students wishing to undertake a 10-week summer research project under the supervision of a faculty mentor. You can view a list below of Mathematics and Computer Science summer scholars to get a better idea about the kinds of projects on which our students have worked.
Occasionally, students will also work with a faculty member under a DURF grant.
A select group of senior students each year undertake a Senior Research Project or an Honors Thesis. These are normally year long research experiences that result in a written thesis and/or software project at the end of the year. You can view a list below of Mathematics and Computer Science honors projects.
Completed Student Research Projects
Summer Research Projects
Click on the title of a project to see more information (if available).
2012
Sketch Guided Sampling for measuring network traffic statistics.
Yuting Chen
Simulating MapReduce Application Performance on Scalable Clusters.
Jared Gray
A Web Tool for Detecting Riboswitches in Genomic Sequences.
Steven Johnson
Investigation of Hypergraphics in Coloring Complexes.
Nat Kell
Towards a More Realistic Metric for Online Ring Routing.
Andrew Quinn
Divergence in Network Traffics.
Edward Takahashi
Computer-based Kinetic Simulation of RNA folding.
Shiyao (Aaron) Wang
Developing Formally Specified, Verifiable Software with RESOLVE.
Dan Welch
Mosaic Numbers and Torus Knots.
Cheng (Gary) Wu
2011
Metric Linear Characterizations of Algebraic Structures.
Matt Gibson
Entanglement in a Modal Quantum Thoery.
Yige Li
A Generalized Computational Approach to Identify Novel Riboswitches.
J.D. Sheets
Generalized Online Malleable Job Scheduling on 3 Processors.
Nat Kell
Malleable Job Scheduling with Logarithmic Overhead.
Seth Lyles
Modular Program Design and Verification in RESOLVE.
Dan Welch
Analyzing and Modeling MapReduce Applications.
Kenny Wottrich
2010
Alternative Performance Metrics for Online Ring Routing
Neal Barcelo and Bryce Pioske
Exploring Knot Mosaics: Discovering Mosaic Numbers and Enumeration
Erica Evans and Joe Paat
A Combinatorial Exploration of a Kostka Matrix Identity for Partitions of Integers Less than or Equal to 8
Mary Kimberly and Beidi Qiang
M-uniformity and Error Correction in Data Transfer
Glen Sutula
Norm Characterizations of Operator Algebras
Nathan Zakahi
2009
Routing of Splittable Network Flows on Torus-Shaped Networks.
Joseph Buell
Game Theory and Social Networks.
Zachary Goldman
Implementation of a Robot Swarm.
Shaun McFall
Investigating Cluster Fault Tolerance-Web Interfaces, Simulation and Extension.
Sarah Mercier
Investigations of Quantum Knot Mosaics.
Joseph Paat
Game Theory and Social Networks.
Yuechao Pei
Investigations of Quantum Knot Mosaics.
Jacob Shapiro
Characterization of Entanglement in Quantum Systems.
Arjun Singh
Automated Generation of Verification Clauses for Formally Specified Software.
Yu-Shan Sun
2008
The Performance Cost of Virtual Machines in Compute Clusters
Neal Barcelo and James Nicholas Legg
Intrinsic Triple Linking in Straight Edge Embeddings of Complete Graphs
Samuel Behrend
Game Theory and Social Networks
Zachary Goldman
2007
Algorithms for Finding Links in Kn
Jeffrey Camealy
Getting the Most Out of 'Life': Private Key Encryption with 2-Dimensional Cellular Automata
Rob Flax
Knots in Straight-Edge Embeddings of K7
Rachel Grotheer
Modern Cryptology Conundrums: Efficient Factoring Methods for Large Integers
Joanna Krieselmann
Locked Linkages: Finding a Key
Amanda Moore
2006
Determining Links in Complete Graphs on Seven Vertices
Pamela Arbisi
Program Justification: Verifying Code Semantics with Mathematics
Samuel Behrend
Classifying Projections Formed from m-Uniform (n,k)-Frames
Amanda Moore
Knotted Hamiltonian Cycles in Straight Edge Embeddings of Complete Graphs on N Vertices
Evan Starr
2005
Automated Animation of the Human Hand Manipulating Deformable Objects
Andrew Hoffman
Optimal Frames for Erasures
Tarika Mansukhani
Quantum Distance Between Matrix Spaces
David Nassar
Constructing an Efficient and Easily Distributable Virtual Tour of Denison
Nathan Schmidt
Alliances in Graphs
Kati O'Neill
The Bus Driver's Sanity Problem
Jennifer Swank
Dimensionality Reducation in Reinforcement Learning
Dan Bucatanschi
Online Algorithms for Packet Routing on Rings
Mete Tuzcu
2004
The Ant Colony System for the Freeze-Tag Problem
Dan Bucatanschi
Online Packet Routing on Ring Networks
Pancham Gajjar
Geometric Characterizations of Algebraic Systems
Patricia Garmirian
Language Support for Software Engineering Principles
Andrew Hoffman
Genetic Algorithms Applied to the Freeze Tag Problem
Blaine Hoffman
Straight Edge Embeddings of the Complete Graph on Six Vertices
Colleen Hughes
Analysis and Development of a M-209 Field Converter Simulator
Evan Lewis
Open Content Addressable Storage Expanded to Include Peer to Peer Networks
Nathan Schmidt
Mathematical Modeling in Population Dynamics (Discontinuous Case)
Kaythi Soe
Computerized Distorted Text Recognition Reloaded
Zhenyu Wu
2003
Design and Construction of a Stored Program Computer
Kevin Connor
An Operator Space Classification of Mixed Injective Hilbert Spaces
Robey Holderith
Computerized Distorted Text Recognition-a Trial Against CAPTCHA
Zhenyu Wu
Automatic Service Discovery for Content Addressable Storage
Rahul Parikh
Content Addressable Storage (CAS) Providers and Clients
Stoyan Paunov
Cylindrical (or Periodic) Geometry
Elizabeth Ehret
Integer Construction by Induction
Elizabeth Ehret
Evaluation of Formal Specification Languages: UML, Z and RESOLVE
Nalini Iyer
Abstract
Evaluation of Formal Specification Languages: UML, Z and RESOLVE
Nalini Iyer
Summer 2003
Mathematics and Computer Science Department
Denison University
Advisor: Dr Joan Krone
Abstract: In today's world of heavy dependence on computer software applications in both domestic households and industries, accuracy and reliability of software systems are key issues. Software malfunctions in monitoring and control systems could lead to crippling blackouts brining life in urban regions to a grinding halt. In medical facilities, space programs and other organizations where safety-critical or mission-critical systems are used, an error could cost billions of dollars and even loss of human lives. Hence in order to ensure the smooth error-free running of operations and to avert catastrophe, it is extremely essential to guarantee that the required software specifications communicated by the client are understood and met with utmost precision by the software engineers. For this purpose the use of natural language alone is inadequate resulting in miscommunication and specifications that are often incomplete, inconsistent and ambiguous.
During the past decade new languages called 'specification languages' have been developed primarily to formalize the process of software specification, and to enable programmers to precisely and unambiguously write software specifications. The Formal Methods approach of Software Engineering uses mathematical notations and theories as a basis for its specification languages to accurately and unequivocally describe system properties and also verify their implementation. Currently two widely used formal specification languages in industry and academia is UML (Unified Modeling Language) and Z. RESOLVE is a newer, less well-known formal specification language that combines both specification and executable constructs into one language. But how successfully do UML, Z and RESOLVE meet the ultimate goals of formal specification languages and Formal Methods? In this research I explored and examined the syntax and semantics of UML, Z and RESOLVE. I then evaluated the capabilities and limitations of each language to specify and verify software system properties.
2002
Parallel Reinforcement Learning: Extending the Concept to Continous Multi-State Tasks
Daria Antonova
Online Algorithms for Routing and Scheduling on Ring Networks
Rohit Bansal
Scheduling Jobs on Parallel Machines with Overhead
Vesselin Dimitrov
Topological Logics
Anthony Fressola and Stoyan Paunov
The Additivity Question in Quantum Channel Capacity
Michael Khoury
Generics in Java Using Objects and Interfaces
Jason Roberts
Algorithm Analysis for the Object Oriented Programming Paradigm
Molly Tawney
2001
Convergence of Real Infinite Series
Michael Khoury
Algorithms for Deriving Zero-Divisor Graphs of Commutative Rings
Vesselin Dimitrov
GPSS and the Testing of Random Number Generators
Jared Schuetter
Online Discovery of Subgoals in Reinforcement Learning
Rohit Bansal
2000
Algebra and Integers
Michael Khoury
Derivation Scheme in Twin Open Set Phase Space Logic Under Cofinite Topology
Rohit Bansal
Multiple User-Defined Data Types in C++ and Related Issues
Jeffrey Amos and Barnaby Nardella
1999
Using Neural Networks to Find Seagrass in Satellite Data
David Michael
Indeterminate Propositions in Twin Open Set Phase Space Logic
Eng Siang Tan
Zero Divisors in Cayley-Dickson Algebras
Jacob Tawney
1997
Classifications for Algorithm Implementation
Laura Eilar
Properties of Twin Open Set Phase Space Logic
Zhu He
Conceptualization of Strategies for Writing Algorithms
Mark Ward
Evolutionary Programming
Peiyong Weng
1996
Application of Adaptive Critc Reinforcement Learning Algorithm
Jason Mihevic
Formal Methods in Computer Security
Mark Ward
Honors Theses
A Lower Bound on the Competitive Ration of Online Torus Routing
Joseph L. Buell, V., 2010 (supervised by Dr. Havill)
Entanglement in Finite Fields
Arjun Singh, 2010 (supervised by Dr. Westmoreland)
Triple Linking in Complete Graphs
Samuel J. Behrend, 2009 (supervised by Dr. Ludwig)
Investigating TPP Riboswitches in Archaea Using Computational Algorithms
Chinmoy I.S. Bhatiya, 2009 (supervised by Dr. Havill and Dr. Thompson)
Implementation of Fast Factoring Algorithms
Joanna R. Kreiselman, 2009 (supervised by Dr. Feil)
The complete story of stick knots in K7
Rachel Grotheer, 2008 (supervised by Dr. Ludwig)
Diffusion of technologies through social networks with continuous strategy spaces
Nicole Scholtz, 2008 (supervised by Dr. Wexler)
Arc presentations: the (p,q)-torus knot
Matt Steinke, 2008 (supervised by Dr. Ludwig)
Links in straight-edge embeddings of K7
Pamela Arbisi, 2007 (supervised by Dr. Ludwig)
Kernel Methods for Image Processing
Dan Bucatanschi, 2006 (supervised by Dr. Kretchmar)
Encoding Algebra as Affine Geometry
Patricia Garmirian, 2005 (supervised by Dr. Neal)
A New Axiomatic Geometry: Cylindrical (or Periodic) Geometry
Elizabeth Ehret, 2004 (supervised by Dr. Westmoreland)
Integer Construction by Induction
Tony Fressola, 2004 (supervised by Dr. Krone)
Mobile Room Condition Inventory System
Rohit Bansal, 2003 (supervised by Dr. Havill)
Content Addressable Storage Provider in Linux
Vesselin Dimitrov, 2003 (supervised by Drs. Bressoud and Havill)
Applications of AI in Natural Language Generation: An Object Oriented Approach
Alex Harris, 2003 (supervised by Dr. Krone)
The Additivity Question for Classical Capacity of Quantum Channels: Perspectives on a Problem in Quantum Information
Michael Khoury, 2003 (supervised by Dr. Westmoreland)
Algorithm Analysis for the Object Oriented Programming Paradigm
Molly Tawney, 2003 (supervised by Dr. Krone)
Using Genetic Algorithms to Evolve Successful Task Completion Strategies in Robots
Tom Groff, 2001 (supervised by Dr. Kretchmar)
Application of Reinforcement Learning Algorithms to Solve a Track Following Task
David Michael, 2001 (supervised by Dr. Kretchmar)
The Affine Reflection Groups Ãn
Jake Tawney, 2000 (supervised by Dr. Blanchard)
Mathematical Foundations for Performance Analysis
Mark Ward, 1999 (supervised by Dr. Krone)
Design Principles to Support Evoluationary Software
Tedd Dawson, 1998 (supervised by Dr. Krone)
Application of a Critic Reinforcing Learning Algorithm Using a Radio Controlled Car
Roshan Navagamuwa, 1998 (supervised by Dr. Feil)
Bell's Theorem and Quantum Mechanics
Jay Neidermeyer, 1998 (supervised by Dr. Westmoreland)
CS 272 Projects (Spring 2004)
CS 272 Projects (Spring 2004)
This is a collection of research papers written by students in CS 272, Data Structures and Algorithm Analysis II, during the Spring 2004 semester. (All papers are in pdf format.)
- Triangulation of a Simple Polygon by Dan Bucatanschi [pdf]
- Convex Hull Algorithms by Eric Eilberg [pdf]
- The Freeze Tag Problem by Pancham Gajjar [pdf]
- Approximate String Matching by Brad Harris [pdf]
- Euclidean Steiner Tree Problem by Michael Herring [pdf]
- Distributed Shortest Path Algorithms by Andy Hoffman [pdf]
- Maximum Flow Problem by Ian Hudson [pdf]
- RSA Encryption by Jack Zhao Jin [pdf]
- Simulated Annealing by Nate Schmidt [pdf]
- Quantum Computing by Matthew St. John [pdf]
CS 334 class projects (Fall 2001)
CS 334 class projects (Fall 2001)
The list of projects done by Dr. Krone's CS334 class.
- Push Down Automata with 2 Stacks - Harsh Chandriani, Nalini Iyer, and Pankil Shah. [doc]
- Explorations of Two-Stack PDA - Barnaby Nardella and Jeff Amos. [doc]
- 2-Tape Turing Machine - Josue Vazquez and Richard Mill?n. [doc]
- Turing Machine with Deque - Ed Hunsinger, Kris Niswander, and Slater Overbey. [doc]