REU Site: Research Challenges of Computational and Experimental Mathematics

该奖项提供了支持REU网站“计算和实验数学的研究挑战”在摩拉维亚学院。作为摩拉维亚学院，穆伦贝格学院和雪松佳洁士学院之间的合作，该计划将集中在与实验数学及其在刺激新的研究中的作用相关的研究项目。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，工业界和政府之间的合作伙伴关系。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。该计划将为这些学生提供必要的工具来理解（以及关闭）猜想，统计显著结果和正式证明之间的差距。研究人员和他的同事将通过强调计算机在发展数论，算法和枚举组合学，组合数论，图论，博弈论和许多其他数学领域的知识方面所发挥的重要作用来培养这种能力。更强大的计算设备的预测为未来的数学家提供了有趣的挑战，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融入纯数学方法的日益重要性，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Ghandhan问题，Beatty序列对，加泰罗尼亚三角形中唯一出现的完美幂，以及从推广现有序列中产生的问题。导师有经验的访问，研究，并在实验数学开放的问题作出贡献。该计划的目标是宣传实验数学在学生和早期职业研究人员的干部中日益重要，以帮助建立它作为他们的研究武器库中的工具;鼓励参与者继续他们的教育进入研究生院并追求研究事业;并为培训20人做出贡献-该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.