REU Site: HWS-REU: Discovering Mathematics in New York State

每年夏天，霍巴特和威廉史密斯学院（HWS）的本科生研究经验项目将为10名本科生提供数学研究的实践介绍。该项目将向全国各地的学生开放，特别注重从纽约州的公立学院和大学招收不同类型的学生。在为期九周的项目中，参与者将获得作为研究人员的独立性，并培养向更广泛的科学界和公众展示他们的成果的技能。学生将组成小型研究小组，在HWS专家的指导下，对各种数学领域的主题进行研究。此外，研讨会系列和参观附近的研究生课程将帮助参与者做出明智的决定，追求职业生涯作为一个数学家。在整个项目中建立的师生关系将通过教师的正式签到来帮助学生的职业发展，至少在REU之后延长两年。研究项目将探索图论、代数或数学生物学的主题。在图论中，主题将包括覆盖良好的图的某些子类的分类以及与优美树标记猜想相关的树标记问题。在代数中，单项式理想将通过它们与组合结构（如图及其子图）的联系来探索。在数学生物学中，参与者可以开发新的算法，从遗传数据中重建系统发育树，使用微分方程模型来探索病毒感染和对抗它们的免疫反应的动态相互作用，或者开发和分析大脑内神经连接网络的计算模型。

Each summer, the Research Experience for Undergraduates program at Hobart and William Smith Colleges (HWS) will provide ten undergraduates a hands-on introduction to mathematics research. The program will be open to students from across the nation, with a particular focus on recruiting a diverse pool of students from public colleges and universities in New York State. Over the course of the nine-week program, participants will gain independence as researchers and develop the skills to present their results to the broader scientific community and the public. Small research teams of students will be formed to pursue research on topics from a wide variety of mathematical fields under the guidance of HWS faculty members expert in these areas. Additionally, a colloquium series and visits to nearby graduate programs will help participants make informed decisions about pursuing a career as a mathematician. The faculty-student relationships built throughout the program will be extended at least two years beyond the REU through formal check-ins by faculty to assist students in career development. Research projects will explore topics in graph theory, algebra or mathematical biology. In graph theory, topics will include the classification of certain subclasses of well-covered graphs and tree labeling problems related to the graceful tree labeling conjecture. In algebra, monomial ideals will be explored through their connection to combinatorial structures such as graphs and their subgraphs. In mathematical biology, participants may work to develop novel algorithms for reconstructing phylogenetic trees from genetic data, use differential equation models to explore the dynamic interaction of viral infections and the immune responses that combat them, or develop and analyze computational models of networks of neural connections within the brain.