REU SITE: Exploration and Professional Excellence in the Mathematical Sciences

一个目标推动着我们在乌尔辛斯学院所做的一切--以一种我们的学生从未想过的方式改变生活和促进成长。为了实现我们的REU学者的这一目标，Ursinus REU网站有三个关键组成部分：i)重要的和可访问的数学和计算机科学研究问题，ii)个人发展计划(IdP)，以及iii)我们服务于代表性不足的学生的承诺。参与者将是三个研究小组之一的成员，每个小组由三名成员组成，每个小组由一名资深教员领导。每个团队都致力于一个原创的研究项目，选择这个项目既是因为它的重要性，也是因为它对本科生来说很容易理解。一些项目持续两年，而另一些项目则在一年内完成，以允许更多不同的主题，并让REU学者接触到新的教员。除了项目外，我们还致力于培养学生的数学成熟度和专业性。我们将通过IdP跟踪学生的进步。这项计划在为期八周的REU中评估了在数学科学领域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将帮助学生在自己的薄弱领域有所提高，并挑战学生进一步发展自己的优势。IDP设定了可衡量的目标，并在校园为期八周的项目之前、期间和之后监测进展。最后，我们承诺在REU项目中纳入和给予代表人数不足的学生机会。PI团队将向该地区当地的学校招聘广告，如费城社区学院，那里有大量未被充分代表的学生。我们还将通过专业组织，如NAM和数学联盟进行广告宣传。所有高级人员都有与代表性不足的学生合作和辅导的历史，他们希望在REU期间继续这样做。REU的研究项目涵盖了反映高级人员专业知识的各种主题。REU将以离散莫尔斯理论和计算拓扑学项目为特色，应用于音乐分析、视频分析和计算机图形学。我们的代数项目探索了划分恒等式、温和的填充函数和彩虹染色。另一组项目涉及机器学习，重点是增量语言处理。学习线性代数的学生有机会学习任何地方的满射函数。除了他们的核心研究项目，学生们还将通过每周一次的研讨会接受数学写作和演讲技巧的培训，旨在培养这些基本的沟通技能。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。

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.