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, 荣誉学生, 数学方面的荣誉项目. The capstone project is an opportunity for the student to deeply explore a mathematical topic under the guidance of a 教师 member and share their insights with others.

高级综合项目

为高级综合项目, 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, 就这个主题写一篇论文, 并以此论文为基础给学生做了一次演讲, 教师, 和客人. 

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.

荣誉项目

The Honors Project is a year-long endeavor in which an honors student works intensively on the definition and solution of a scholarly problem, 或者是关于创造性工作的发展. 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 教师, students 和客人.

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 荣誉计划网站.

2021–2022

• 泰迪:主教 棒球中的数据分析.”
  博士导师:. 迈克尔Klucznik.

  泰迪是邦尼棒球队的接球手, 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.

• 艾丽卡低: “Elliptic Curve Cryptography: An Efficient Cryptosystem and Its Applications.(荣誉项目)
  博士导师:. 克里斯。希尔.

  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...

• 本MacConnell: 非交换代数的对称性.”
  博士导师:. 克里斯汀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, 很好地结合了他的数学和物理双专业.

• 吉莉安·麦克尼尔: 数独拉丁方格的正交性.”
  博士导师:. 莫林·考克斯

  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

• 艾莉森Garlock: 通过群论理解魔方.”
  博士导师:. 克里斯汀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, 对某个导师来说是无价的.)

• 莎拉通力: 振荡与连续性.”
  博士导师:. 莫林·考克斯.

  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.

• 汉娜Schifley: “纽约州的冠状病毒.”
  博士导师:. 莫林·考克斯.

  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

• 伊桑McKeone: “What do turtles, the cube root of 2, and paper folding all have in common? 贝洛赫褶皱.”
  博士导师:. 克里斯汀Uhl.

  伊森的项目集中在玛格丽塔P. Beloch在1936年发现了折纸, 这是, 通过折纸建筑, 可以用来解一般的三次方程吗. He applied the method to show how paper-folding can be used to solve the classic problem of doubling the cube, a problem 这是 impossible to solve using traditional straightedge-and-compass constructions.

• 斯宾塞哑剧演员的表演: 密码学和RSA算法.”
  博士导师:. 克里斯。希尔.

  Spencer's project explored the RSA (Rivest-Shamir-Adleman) public key cryptosystem. 在简要概述了密码学的历史之后, 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总结了RSA的一些漏洞.