REU Site: Research Challenges of Computational and Experimental Mathematics

REU 网站：计算和实验数学的研究挑战

• 批准号: 1852378
• 负责人: Nathan Shank
• 金额: $ 32.18万
• 依托单位: Moravian University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-04-01 至 2023-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1852378&HistoricalAwards=false
• 关键词: REU; Site; Research; Challenges; Computational

This award provides support for the REU Site "Research Challenges of Computational and Experimental Mathematics" at Moravian College. As a collaboration between Moravian College, Muhlenberg College, and Cedar Crest College, this program will concentrate on research projects associated with experimental mathematics and its role in stimulating new research. Experimental mathematics uses computer-assisted techniques to investigate mathematical patterns and properties. Experimental mathematics is impacting research in scientific and engineering fields beyond the mathematical sciences, giving it the potential to increase partnerships between academia, industry, and government. As society's reliance on data and data driven results has increased, so has the need for a workforce capable of analyzing and interpreting that data. This program will equip those students with the necessary tools to understand (as well as close) the gaps between conjecture, a statistically significant result, and a formal proof. The investigator and his colleagues will nurture this capacity by highlighting the important role computers have played in developing conjectures in areas that include number theory, algorithmic and enumerative combinatorics, combinatorial number theory, graph theory, game theory, and many other mathematical fields, as well as tools necessary for identifying such conjectures.Projections of more powerful computational devices present the future mathematician with interesting challenges, including experimentation by developing computational algorithms and meta-algorithms through the use of computers. The intellectual focus of this research concentrates on the increasing importance of integrating computer technology into pure mathematics methodology, as well as its contribution to other fields, such as algorithmic applications in computer science, biology, and medicine. Mentors are drawn from the Lehigh Valley Association of Independent Colleges (LVAIC) and neighboring institutions. Research projects include experimental mathematics topics such as the Ghandhan problem, Beatty Pair of sequences, perfect powers that appear uniquely in the Catalan triangle, and problems emanating from generalizing existing sequences in the Online Encyclopedia of Integer Sequences. The mentors have experience accessing, researching, and contributing to open problems in experimental mathematics. The program goals are to publicize the growing importance of experimental mathematics among a cadre of students and early-career researchers to help establish it as a tool in their research arsenal; encourage participants to continue their education into graduate school and pursue careers in research; and contribute toward the training of the twenty-first century workforce.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项为莫拉维亚学院的REU网站“计算和实验数学的研究挑战”提供支持。作为摩拉维亚学院、Muhlenberg学院和Cedar Crest学院之间的合作，该项目将专注于与实验数学相关的研究项目及其在刺激新研究方面的作用。实验数学使用计算机辅助技术来研究数学模式和性质。实验数学正在影响数学科学以外的科学和工程领域的研究，使其有可能增加学术界、产业界和政府之间的伙伴关系。随着社会对数据和数据驱动的结果的依赖增加，对能够分析和解释这些数据的劳动力的需求也在增加。本课程将为这些学生提供必要的工具来理解(以及弥合)猜想、具有统计学意义的结果和正式证明之间的差距。研究人员和他的同事们将通过强调计算机在发展猜想方面发挥的重要作用来培养这种能力，这些领域包括数论、算法和计数组合学、组合数论、图论、博弈论和许多其他数学领域，以及识别这些猜想所需的工具。更强大的计算设备的投射向未来的数学家提出了有趣的挑战，包括通过使用计算机开发计算算法和元算法的实验。这项研究的智力焦点集中在将计算机技术整合到纯数学方法论中的日益重要的意义上，以及它对其他领域的贡献，如计算机科学、生物学和医学中的算法应用。导师来自利哈伊谷独立学院协会(LVAIC)和邻近的机构。研究项目包括实验数学主题，如甘德汉问题、Beatty序列对、在加泰罗尼亚三角中唯一出现的完全幂，以及在线整数序列百科全书中推广现有序列所产生的问题。导师有接触、研究和解决实验数学开放问题的经验。该计划的目标是在一批学生和职业生涯早期的研究人员中宣传实验数学日益增长的重要性，以帮助将其建立为他们研究武器库中的工具；鼓励参与者继续他们的教育到研究生院并从事研究事业；并为21世纪劳动力的培训做出贡献。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

On binomial coefficients associated with Sierpiński and Riesel numbers

关于与 SierpiÅski 和 Riesel 数相关的二项式系数

• 发表时间: 2021
• 期刊: Integers
• 作者: Armbruster, Ashley;Barger, Grace;Bykova, Sofya;Dvorachek, Tyler;Eckard, Emily;Harrington, Joshua;Sun, Yewen;Wong, Tony W.
• 通讯作者: Wong, Tony W.

Sum index and difference index of graphs

图的和指数与差指数

• DOI: 10.1016/j.dam.2022.10.020
• 发表时间: 2023
• 期刊: Discrete Applied Mathematics
• 影响因子: 1.1
• 作者: Harrington, Joshua;Henninger-Voss, Eugene;Karhadkar, Kedar;Robinson, Emily;Wong, Tony W.H.
• 通讯作者: Wong, Tony W.H.

On the properties of fibotomic polynomials

关于斐博多项式的性质

• DOI: 10.1016/j.aam.2022.102344
• 发表时间: 2022
• 期刊: Advances in Applied Mathematics
• 影响因子: 1.1
• 作者: Byer, Cameron;Dvorachek, Tyler;Eckard, Emily;Harrington, Joshua;Wise, Lindsey;Wong, Tony W.H.
• 通讯作者: Wong, Tony W.H.

Covering systems with odd moduli

覆盖具有奇模数的系统

• DOI: 10.1016/j.disc.2022.112936
• 发表时间: 2022
• 期刊: Discrete Mathematics
• 影响因子: 0.8
• 作者: Harrington, Joshua;Sun, Yewen;Wong, Tony W.H.
• 通讯作者: Wong, Tony W.H.

Nimber Sequences of Node-Kayles Games

Node-Kayles 博弈的 Nimber 序列

• 发表时间: 2020
• 期刊: Journal of integer sequences
• 影响因子: 0.5
• 作者: Brown, S.;Daugherty, S.;Fiorini, E.;Maldonado, B.;Manzano-Ruiz, D.;Rainville, S.;Waechter, R.;Wong, T.
• 通讯作者: Wong, T.