Students majoring in mathematics complete a capstone project during their senior year to fulfill the Senior Comprehensive Requirement. The capstone project is either a Senior Comprehensive Project or, for honors students, an Honors Project in mathematics. The capstone project is an opportunity for the student to deeply explore a mathematical topic under the guidance of a faculty member and share their insights with others.

Senior Comprehensive Projects

For a Senior Comprehensive Project, the student works with a professor to select a topic that relates to but goes beyond the usual scope of a 300- or 400-level mathematics course, writes a paper on the topic, and gives a talk based on the paper to students, faculty, and guests. 

Students often select topics that relate to their interests beyond mathematics. For example, a student minoring in finance may choose a mathematical topic that relates to finance.

The student takes the one-credit course MATH 492 during their graduation semester.

Honors Projects

The Honors Project is a year-long endeavor in which an honors student works intensively on the definition and solution of a scholarly problem, or on the development of a creative work. The honors student’s work is guided by an adviser and submitted to two readers for approval. Upon completion, it is publicly presented to interested faculty, students and guests.

An Honors Project in mathematics with a grade of C or better fulfills the Senior Comprehensive Requirement.

An honors student takes the three-credit course HON 498/499 during their senior year. Further details about a Degree with Honors are provided in the Honors Program website.

2021–2022

• Teddy Bishop: “Data Analytics in Baseball.”
  Mentor: Dr. Michael Klucznik.

  Teddy played catcher for the Bonnies baseball team, so it was natural that his project applied math to his favorite sport. He explained that in recent years the technique of data analytics has become ubiquitous in Major League Baseball. Teddy used the method and the program R to show how pitchers can refine their strategies against different types of batters. Each attendee of Teddy's talk was treated to a box of Cracker Jacks.

• Erica Low: “Elliptic Curve Cryptography: An Efficient Cryptosystem and Its Applications.” (Honors Project)
  Mentor: Dr. Chris Hill.

  Erica began by providing background on private and public key cryptography and on elliptic curves. She then described in detail the elliptic curve cryptosystem (ECC) and explained how ECC is more "efficient" than the more commonly used RSA. Erica concluded her project with applications of ECC to e-commerce. She noted that Best Buy and Home Depot use ECC on their websites, but not yet SBU...

• Ben MacConnell: “Symmetries of Noncommutative Algebras.”
  Mentor: Dr. Christine Uhl.

  Ben's work was inspired by open questions posed in a paper by Chelsea Walton. He found the symmetries of a three-dimensional q-polynomial algebra and investigated the symmetries of the split-quaternion algebra. Ben described the connections of this material to quantum mechanics, nicely tying together his dual majors in math and physics.

• Gillian MacNeil : “Orthogonality in Sudoku Latin Squares.”
  Mentor: Dr. Maureen Cox

  Gillian observed that Sudoku grids—solutions to the wildly popular Sudoku puzzles—are special cases of Latin squares. She then applied group theory to count pairs of mutually orthogonal Sudoku grids.

2020–2021

• Alison Garlock: “Understanding the Rubik's Cube through Group Theory.”
  Mentor: Dr. Christine Uhl.

  Alison used group theory to analyze the moves of the classic Rubik’s puzzle. Her project culminated with a theorem characterizing which “states” of the cube could be reached by legal moves. (Side note: Alison can solve a Rubik’s cube in under two minutes, which proved invaluable to a certain mentor.)

• Sarah Kone: “Oscillation and Continuity.”
  Mentor: Dr. Maureen Cox.

  Sarah characterized the set of points of continuity and the set of points of discontinuity of a real-valued function defined on a closed interval. Using a detailed analysis of the oscillation of a function, she showed that the set of points of continuity is always a countable intersection of open sets and that the set of points of discontinuity is always a countable union of closed sets.

• Hannah Schifley: “Coronavirus in New York State.”
  Mentor: Dr. Maureen Cox.

  Hannah employed the SIR model of three differential equations and real-world data to analyze the spread of the virus in New York. Her timely project predicted possible outcomes of the pandemic in our state.

2019–2020

• Ethan McKeone: “What do turtles, the cube root of 2, and paper folding all have in common? The Beloch Fold.”
  Mentor: Dr. Christine Uhl.

  Ethan's project focused on Margharita P. Beloch's discovery in 1936 that origami, that is, paper-folding constructions, can be used to solve general cubic equations. He applied the method to show how paper-folding can be used to solve the classic problem of doubling the cube, a problem that is impossible to solve using traditional straightedge-and-compass constructions.

• Spencer Mummery: “Cryptography and the RSA Algorithm.”
  Mentor: Dr. Chris Hill.

  Spencer's project explored the RSA (Rivest-Shamir-Adleman) public key cryptosystem. After a brief overview of the history of cryptography, Spencer provided the required background on modular arithmetic and discussed some key results on primality and factoring. He then proved that the RSA decryption algorithm works and provided an example. Spencer concluded with some of the vulnerabilities of RSA.