## Information on Capstones for Mathematics and Statistics Majors

*Remember that one of the prerequisites for the capstone is to attend four seminar/colloquium presentations in your junior and senior years prior to taking the capstone course.*

**Writing and Presenting Mathematics/Statistics
**

- Information on writing and presenting an expository paper in mathematics and statistics.
- Rubric for evaluating written math/stat papers.
- Rubric for evaluating math/stat presentations.

**Capstone Courses:**

**Spring 2017 Capstone Courses:**

- Applied Mathematics: Prof. Gevertz (Dynamical Systems)
- Mathematics: Prof. Curtis (Topics in Topology, Geometry, and Algebra)
- Statistics: Prof. Ochs (Data Analysis)

**Spring 2016 Capstone Courses:**

- Applied Mathematics: Prof. Clark (Partial Differential Equations)
- Mathematics: Prof. Hingston (Topics in Geometry and Topology)
- Statistics: Prof. Thayer (Data Analysis)

**Spring 2015 Capstone Courses:**

- Applied Mathematics: Prof. Conjura (Time Series)
- Mathematics: Prof. Clifford (Topics in Mathematics)
- Statistics: Prof. Thayer (Data Analysis)

**Spring 2014 Capstone Courses:**

- Applied Mathematics: Prof. Conjura (Time Series)
- Mathematics: Prof. Clifford (Topics in Mathematics)
- Statistics: Prof. Thayer (Data Analysis)

**Spring 2013 Capstones:**

- Applied Mathematics: Prof. Clark (Partial Differential Equations)
- Mathematics: Prof. Clifford (Topics in Mathematics)
- Statistics: Prof. Thayer (Data Analysis)

**Earlier Capstones** (**Spring 2012 Capstones and earlier:**)

Prior to the Spring 2013 semester, student capstones were done on an individual basis with faculty. Listed below titles of past capstone papers. The last name of the faculty advisor is indicated in the parentheses.

**Spring 2012 Capstones**

**Mathematics Majors**

- Joseph Aromando – “Gauss, Galois Theory, and the Construction of the 17-gon”
- Mary Ambrosino (Kardos) – “Theory of Integration”
- Mark Azic (Zheng) – “Gibbs Phenomenon”
- Chris Cooper (Benoit) – “The Mathematics of the Finite Element Method”
- Hunter Hageman (Harris) – “A Mathematical Study of HIV and AIDS”
- Emily Kaelblein (Alves) – “Cryptography: Expediting the RSA Algorithm and Attacks to Watch Out For”
- Amanda Klein (Clark) – “An Introduction to Climate Modeling with Ordinary Differential Equations”
- Michael Lee (Harris) – “A Mathematical Model to Analyze the Number of Ovulating Follicles”
- Sean Nath (Kardos) – “Ramsey Theory and Homotheties in Z
^{n}“ - Eric New (Hagedorn) – “Zero Divisor Graphs: Connecting Commutative Ring Theory and Graph Theory”
- Rachel Roesch – “Deriving the Effective Conductivity of a Composite Material”
- Lauren Somma (Kardos) – “Creating the Sierpinski Triangle”
- Jennifer Urban (Curtis) – “Studying Stick Knots: Part I”
- Calvin Woo (Clifford) – “The Mapping Class Group of the Torus”
- Matthew Ziminski (Wang) – “An Expanded View on the Genetic Algorithm”
- Jacob Ziefle (Curtis) – “The Schoenflies Theorem and the Alexander Horned Sphere”

**Statistics Majors**

- Ashley Carswell (Navard) – “Randomization: Bootstrap Method”
- Emily DeCarlo (Holmes) – “Probit and Logit Analysis”
- Kathryn Huff (Braaten) – “Reliability of Internet Survey Research”
- Louis Klein (Braaten) – “Bayesian Analysis and Model Uncertainty”
- Dan Leva (Navard) – “Randomization: Monte Carlo Simulation”
- Amanda Timlin/Danielle Aran (Holmes/Johnson) – “Structural Equation Modeling”
- Matt Wright/Leigh Mitchell (Holmes) – Multivariate Analysis of Variance”

**Fall 2011 Capstones**

**Mathematics Majors**

- William Franczak (Curtis) – “Compactifications of Hausdorff Spaces”
- R. J. Leiser (Clark) – Laminar Definition of Effective Conductivity”
- Julie Melzer (Navard) – “The Expectation Maximization Algorithm”
- Robert Moore (Clark) – “An Introduction to the Calculus of Variations”
- Shane Mullin (Hagedorn) – “How to Factor
*x*³ – 1: The LLL Algorithm and its Applications” - Anastasia Pastino (Navard) – “Computing Transition Probabilities with Markov Chains”
- Katharine Pelican (Gevertz) – “Bifurcation Diagrams of First Order Differential Equations”
- Michael Stefanelli (Gevertz) – “Nonlinear Systems and Limit Cycles”

**Mathematics Secondary Education (Electronic Portfolios)
**

- David Arva – “Increasing Students’ Abilities in Simplifying Complex Expressions”
- Patrick Catalano – “Evoking Frequent, High-Quality Questions in the Math Analysis Classroom”
- Amanda Huelbig – “Improving the Quality of Pre-calculus Students’ Written Responses to Mathematical Problems”
- Daniel Hughes – “Writing and Solving Word Problems – Mathematics in a Real Life Context”
- Andrea Krsnak – “The Effects of Teacher Expectation on Student Explanation”
- Marissa Maiello – “Improving Student Writing in Middle School Mathematics”
- Amanda Ruch – “Analyzing Students’ Problem-Solving Abilities”
- Daniella Teplinsky – “Algebra II Students’ Abilities to Symbolize Word Problems Through Algebraic Representations”

**Fall 2010-Spring 2011** **Capstones**