REU SITE: Exploration and Professional Excellence in the Mathematical Sciences

一个目标驱动我们在Ursinus College所做的一切-以我们的学生从未想过的方式改变生活和促进成长。 为了为我们的REU学者实现这一目标，Ursinus REU网站具有三个关键组成部分：i）重要且易于理解的数学和计算机科学研究问题，ii）个人发展计划（IDP），以及iii）我们致力于为代表性不足的学生提供服务。参与者将是三个研究小组之一的成员，每个研究小组由三名成员组成，每个研究小组由一名高级教师领导。 每个团队都有一个原创的研究项目，选择它的重要性和它对本科生的可访问性。 有些项目持续两年，而另一些则在一年内完成，以允许更多样化的主题，并使REU学者接触新的教师。除了项目工作，我们有意培养学生在数学成熟度和专业性方面的成长。 我们将通过IDP跟踪学生的进步。该计划在为期八周的REU中评估了在数学科学职业生涯中取得成功所需的硬技能和软技能。从“团队合作能力”到“数学知识”，IDP将帮助学生提高他们的薄弱领域，并挑战学生进一步发展他们的优势。IDP设定可衡量的目标，并在为期八周的校园计划之前，期间和之后监测进展。 最后，我们承诺在REU计划，包括并给予机会，代表性不足的学生。PI团队将向该地区当地的学校（例如费城社区学院）做广告并进行招聘，这些学校的学生人数众多，代表性不足。 我们还将通过专业组织，如NAM和数学联盟做广告。所有高级人员都有与代表性不足的学生合作和指导的历史，他们希望在REU期间继续这样做。REU研究项目涵盖反映高级人员专业知识的各种主题。该REU将在两个离散莫尔斯理论和计算拓扑与音乐分析，视频分析和计算机图形应用的拓扑项目。我们的代数项目探索分区身份，驯服填充功能，和彩虹着色。另一组项目涉及机器学习，重点是增量语言处理。线性代数的学生有机会学习到处满射函数。除了他们的核心研究项目，学生将通过一系列旨在培养这些基本沟通技巧的每周研讨会，在数学写作和演示技巧方面进行培训。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

One goal drives everything we do at Ursinus College--to change lives and foster growth in a way that our students never thought possible. To accomplish this goal for our REU scholars, the Ursinus REU site features three key components: i) important and accessible math and computer science research problems, ii) an Individual Development Plan (IDP), and iii) our commitment to serving underrepresented students. Participants will be a member of one of three research teams each consisting of three members and each led by a senior faculty. Each team works on an original research project, chosen both for its importance and for its accessibility to undergraduate students. Some projects continue for two years, while others are done in a single year to allow for more diverse topics and to expose REU scholars to new faculty. In addition to working on projects, we are intentional about fostering students' growth in their mathematical maturity and in their professionalism. We will track student progress though the IDP. This plan assesses over the eight-week REU both the hard and soft skills needed for success in careers in the mathematical sciences. From "ability to work in a team" to "mathematical knowledge," the IDP will help students to improve in their weak areas and challenge students to develop their strengths further. The IDP sets measurable goals and monitors progress before, during, and after the eight-week program on campus. Finally, we commit in the REU program to including and giving opportunities to underrepresented students. The PI team will advertise to and recruit from schools local to the area, such as Community College of Philadelphia, with large populations of underrepresented students. We will also advertise through professional organizations, such as NAM and Math Alliance. All Senior Personnel have a history of working with and mentoring underrepresented students, and they desire to continue to do so during the REU.The REU research projects cover a diverse range of topics reflecting the expertise of the Senior Personnel. The REU will feature topology projects in both discrete Morse theory and computational topology with applications to music analysis, video analysis, and computer graphics. Our algebra projects explore partition identities, tame filling functions, and rainbow colorings. Another set of projects involves machine learning, with a focus on incremental language processing. Students of linear algebra have the opportunity to study everywhere surjective functions. In addition to their core research projects, students will be trained in mathematical writing and in presentation techniques through a series of weekly workshops designed to foster these essential communication skills.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.