# Senior Capstone Projects

Graduating seniors majoring in Mathematics are required to complete the Capstone course. This is currently offered during the Fall semester. Students are strongly encouraged to that a Capstone Preparation course during the Spring of the Junior year to identify potential topics, investigate background material, and obtain practice with the proposal process.

As part of the Capstone course, each student proposes and carries out an individual research project under the direction of a faculty advisor. Examples of student projects are listed below.

#### Fall 2015

- Chang Xu, Analysis Basic Game Scheduling by TSP and Edge Labeling
- Clayton Craig, An Overview of Metrization Theorems
- Jamell Dorton, Orbits: A Look at the Symmetry of 4 by 4 Sudoku Puzzles
- Mark Drach-Meinel, Limiting the Size of Topological Spaces Through Cardinal Invariants and Arhangel'skii's Theorem
- Joshua Garrett, An Introduction to Translating Audio Signals into Wavelet Space
- Kim Gentzler, The History of and a Complex Analytic Proof of the Fundamental Theorem of Algebra
- Devyn Jeska, An Analysis fo 2015 Facultying Voting at California Lutheran University
- Matthew Johnston, Finding the Minimum Starting Values of a Sudoku Puzzle that Produces a Unique Solution
- Vivian Martinez, The Pythagorean Triple Tree and Its Many Branches
- George Nasr, Showing the Computational Complexity of Graph Coloring is NP-Complete
- Steven Nguyen, A Mathematical Approach to Analyzing Voting Power with California as 6 States
- Bradley Ryan Joshua Paté, How to Find Patterns of Elliptic Solutions Using Modular Arithmetic
- Yuri Pineda, Discovering Hyperbolic Functions Secret Identities through Trigonometric Functions
- Sherise Requiestas, Algorithms and Proofs of Three Graph Theoretic Problems
- Diana Salazar, Entries and Position Impact the Maximum Number of Solutions in a Sudoku Puzzle
- Jesús Villegas, Topological Homogeneity and the Hilbert Cube

#### Fall 2014

- Adriana Adler, Holling Function Responses: A Look Into Predator-Prey Modeling
- Jordan Card, An Array of Cryptosystems and Some Applications
- Tavish Dunn, Influence of Matrix Symmetries on Eigenvalues and Dressing Actions
- Courtney Hong, Mathematical Modeling of the Hypothalamic-Pituitary-Adrenal Axis
- Su Ji Hong, Duality of Invariants
- Kevin Howe, A Study of Pascal's Triangle, Square Pyramid, and Tetrahedron Fractal Dimensions and Patterns
- Sarah McKee, Game Theory and Dominion

#### Fall 2013

- Ashley Budfuloski, Polynomial Equations and The Fundamental Theorem of Algebra
- Jennifer Chavez-Lanza, Stability Analyses of Several Predator-Prey Models
- Maddy Christman, Lie Matrix Groups: An In Depth Look at the Flip Transpose Group
- Shawn Jackson, Linking Markov Chains
- Jim Meyring, The Dynamics of Newton's Method for Complex Polynomials
- Rebecca Peterson, Patterns of Pascal's Triangle and Pyramid with Combinatorics
- Ivan Sanchez, Conics and Their Zero Sets
- Brooke Swanson, Elliptic Curves Over Finite Fields

#### Fall 2012

- Casey Adams, The Zombie Apocalypse
- Andrea Cruz, The Sprague-Grundy Theorem
- David Reaves, Knot Theory: A Proof of Reidemeister's Theorem
- Justine Duke, Lansey's Hypothesis
- Lauren Toohey, Stochastic Optimization and the Newsboy Problem
- Trevor Milford, Steganography

#### Fall 2011

- Megan Ameche, Autonomous Robotic Movement Planning
- Alicia Costin, Burnside's Lemma and Polya's Theorem
- Christina Messer, Monopoly and Markov Chains
- Evan Reed, The Field of Cryptography Exposed
- Micheal Rodriguez,
*p-adic*Analysis, or, The Prime that Killed Calculus - Randee Smith, Evolutionary Game Thoery
- Travis Severt, Investigation into the Mathematical Framework of General Relativity
- Miguel Tenorio, Pinpoint: The Colors of Graph Theory and Adjacency Matrices

#### Fall 2010

- Lydia Cleveland, Wallpaper Groups- Euclidean and Hyperbolic
- Jonathan Davies, Describing the Pursuit Curve of Missiles en route to Destroy Satellites
- Samuel Lyche, Markov Chain Analysis of NFL Overtime
- Robert Spangler, Markov Applications to Soccer Formations
- Travis Wheaton, The Hunt for the Classification Theorem for Surfaces

**Spring 2010**

- Zach Gallen, The Real Line is Uncountable: A Topological Proof
- Elizabeth Caulkins, Rieman Zeta-Functions and Quadratic Fields
- Lauren Dakin, Mathematical Enigmas: Carroll's Guessing Game and a Strategy Puzzle
- Brian Kahovec, Public Key Cryptosystems

**Spring 2009**

- Kelsey Hart, An Investigation of Hyperbolic Triangles
- Alex Sherbetjian, Being Transcendental: Searching for Transcendental Numbers
- Katie White, Magic Square Rubik's Cubes
- Ashley Bentz, Explorations of the Four Color Theorem
- Kristina Klug, A Statistical Analysis of NASCAR Scoring Systems
- Katy Roller, Cellular Automata and Group Theory
- Christine Gaal, Logarithms in High School and Beyond
- Shannon Pesta, Modeling and Predicting Earthquakes with Markov Chains

#### Spring 2008

- Juan Ortiz, The Rank Number of Prism Graphs
- Graydon Pearson, Cracking the Code
- Marc Morris-Rivera, Deal or No Deal: Making Smart Choices Toward Fortune
- Terri Kimmel, Square Patterns in Rayleigh-Bénard Convection
- Joseph Rower, When Does a Product of Group Elements Equal Its Reverse?
- Greg Walker, Shut the Box
- Jessica Newville, Voting Theory
- Eric Wright, A Quantum Mechanical View of the Navier-Stokes Equations

**Fall 2008**

- Jeff Ackkerman, Quadratic Formula and Beyond! Solving Quadratic and Cubic Equations
- Jesse Sylvia, Voting Theory: A Look at Arrow's Theorem

#### Spring 2007

- Megan Donohue, What are the real numbers and how do we teach them in the middle/high schools?
- Brian Stanley, The Fibonacci Golf Ball
- Autumn Malloy, Teaching Logarithms
- Prudence Kjontvedt, Schwarzschild Geometry
- Meghan Pulte, Permutation Statistics on Generalized Derangements and Desarrangements

**Fall 2007**

- Marissa Predmore, Meta-Problems in Mathematics
- Danielle Alberti, Magic Squares

#### Spring 2006

- Matt Broussard, Portfolio Management with the Lagrange Multiplier Technique
- Mark Nishimura, Multi-Strain SIR Model Variations
- Larry Coaly, Julia Sets Over the Quaternions
- Julie Tukua, Solutions to Polynomial Equations: Their Role in High School and Beyond
- Jason Baehne, Potential Orderings of Polyhedra

#### Spring 2005

- David Barra, Mathematics Behind Patience Sorting
- Cheryl Clough, History and Role of Proofs in Secondary Mathematics Education: a Pedagogical Perspective, (website)
- Kristen Dronen, Course Scheduling via Network Flows
- Lucas Lembrick, Human Knot
- Marlene Merchain, Is God Rational?
- Katie Pabst, Analysis of the Current Math Placement Program at CLU
- David Parker, Blackjack: A Beatable Game
- Ryan Petitfils, On the Symmetries of Pascal's Pyramid (website)

#### Spring 2004

- Jason Counihan, Graph Pegging
- Tim Harding, Applying the Hungarian Algorithm to NFL Scheduling
- Andrea Katz, Voting Blocs in Academic Divisions of CLU: A Mathematical Explanation of Faculty Power
- Ryan Palmer, Mathematical Modeling: Stress Relaxation of Viscoelastic Materials (part 1, part 2)

#### Fall 2004

- Alejandra Cortez and Clara Rodriguez, Game Theory and Military Scenerios

#### Spring 2003

- Sara Bretana, Databases for City Planning
- Blaise Djeugoue, Graph Pebbling
- Karl Fedje, Number Theoretical Graph Pebbling
- Billy Harris, Techniques for Teaching Proofs in High School Geometry
- Chris Hall, Twin Primes: A Survey
- Jordon Long, Fractals
- Amanda Wilson, Program Scheduling

#### Spring 2002

- Chris Henderson, Scheduling a Scramble Golf Tournament
- Rafeal Marino, Algebraic Coding Theory
- Michael McDonald, Shooter's Advantage
- David Wirkkala, Comparing Craps Table Odds

#### Spring 2001

- Jennifer Bienstock, What Energy Bar is Best to Fit Your Daily Calorie Needs?
- Rachael Carver, Earthquakes in California
- Jermaine Dixon, Traffic Scenarios
- Nicole Imhof, Soccer Penalty Kicks: Are They Unfair to Goalkeepers?
- Nathan Miller, Batter Up: A Computer Simulated Look at Baseball
- Ann Monville, The Perfect Toss: How to Survive the MCM
- Dave Shafer, Voting Schemes
- Ron Scofano, Pin Action!

#### Spring 2000

- Sean Flaherty, Building a Zoom Lens: Matrix Methods in Optics
- Matt Hunwardwsen, Computational Fluid Dynamics
- James Tarver, Title IX and Cal Lutheran Athletics

#### Spring 1999

- Susan Bloomgren, When to Say When
- Nica Calderon, How to Get a Hit
- Gabe Chandler, Salaries of Starting Professional Baseball Pitchers
- Sarah Dyck, Buying a Home as a College Graduate
- Joshua McGee, Computers, Data, and the Future
- Ramon Orozco, Traffic Control
- Maggy Tomova, The Citric Acid Cycle
- Victoria Walker, The Tobacco Industry vs. the Health Industry