Capstones

All TCNJ students fulfill a capstone experience as part of their major.  In the Department of Mathematics and Statistics, the Liberal Arts Mathematics and Statistics majors complete the capstone by researching and presenting an expository paper on a mathematics or statistics topic. The Mathematics – Secondary Education and Mathematics Education majors complete the capstone through their student teaching.

Seminar Requirement: All students are required to attend four departmental seminars in their junior and/or senior year before they can take the capstone course.   Both department seminars and School of Science colloquia (in which mathematics or statistics is presented) will count.

Information on Capstones for Liberal Arts Mathematics and Statistics Majors

Information and Advice on writing and presenting an expository paper in mathematics and statistics can be found here.    We have listed below titles of past capstone papers.  The last name of the faculty advisor is indicated in the parentheses.

Spring 2012 Capstones

Liberal Arts 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 Zn“
  • 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

Liberal Arts 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 x³ – 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”

Previous Capstones:

Fall 2010-Spring 2011