REU Site: Purdue Research in Mathematics Experience (PRiME)

该奖项将为普渡大学提供三年的支持，为本科生提供为期八周的暑期住宿项目，以进行纯数学研究。该项目名为普渡大学数学体验研究（PRiME），每年夏天将接待八名本科生。该项目的主要目标是（1）为本科生提供代数几何、数论或概率方面的研究经验，旨在产生值得在全国数学会议上发表或展示的新成果，以及（2）为本科生获得数学学士学位做好准备。该计划还将致力于增加普渡大学乃至更广泛地区数学家的多样性。项目负责人将高度重视从传统上数学领域代表性不足的群体中招募参与者。此外，该项目的负责人将邀请来自代表性不足群体的数学家在夏季 REU 研讨会系列中发言，他们将在其中与 PRiME 参与者讨论他们的职业旅程。 PRiME 项目将由 Edray Goins 教授（普渡大学）、Jonathon Peterson（普渡大学）和 Pamela Harris（美国军事学院）教授指导。三位联合主任还将得到两名研究生的协助，他们将帮助为本科生的研究提供额外的指导。每年夏天，该项目都会选择八名学生参加普渡大学的 PRiME 项目。其中四名学生将参与代数几何/数论研究，四名学生将参与随机游走/随机过程研究。为了让学生为研究做好准备，将有为期两周的短期课程，主题包括抽象代数、复分析、微分几何、图论、数论、马尔可夫链和随机过程。在课程期间，学生还将学习重要技能，例如如何使用数学排版语言 LaTeX 进行写作、如何使用 Sage 或 Mathematica 等高级符号计算包，以及如何根据其结果准备技术论文。在八周的课程结束时，学生将总结他们的发现。该计划完成后，将鼓励学生在全国会议上展示他们的研究和/或提交他们的研究以在数学期刊上发表。

This award will provide three years of support for Purdue University to offer an eight week summer residential program for undergraduate students to conduct research in pure mathematics. The program, entitled Purdue Research in Mathematics Experience (PRiME) will host eight undergraduates each summer. The main goals of the program are (1) to provide undergraduate students with a research experience in algebraic geometry, number theory, or probability with the aim of producing new results worthy of publication or presentation at a national mathematics meeting, and (2) to prepare undergraduates for a post-baccalaureate degree in mathematics. The program will also work to increase the diversity of mathematicians both at Purdue University and more broadly. The program directors will place a high importance on recruiting participants from groups traditionally underrepresented in mathematics. Additionally, the directors of the program will invite mathematicians from underrepresented groups speak in a Summer REU Colloquium series in which they will discuss with the PRiME participants their professional journey. The PRiME program will be directed by Professors Edray Goins (Purdue University), Jonathon Peterson (Purdue University) and Pamela Harris (United States Military Academy). The three co-directors will also be assisted by two graduate students who will help provide additional guidance in the undergraduate students research. Each summer the program will select eight students to participate in the PRiME program at Purdue. Four of the students will participate in research in algebraic geometry/number theory, and four students will participate in research on random walks/stochastic processes. To prepare students for research there will be a two week period with short courses on topics such as Abstract Algebra, Complex Analysis, Differential Geometry, Graph Theory, Number Theory, Markov Chains, and Stochastic Processes. During the course of the program, students will also be taught important skills such as how to write with the mathematical typsetting language LaTeX, how to use advanced symbolic computing packages such as Sage or Mathematica, and how to prepare a technical paper of their results. At the conclusion of the eight week program, students will present a summary of their findings. Following the completion of the program, students will be encouraged to present their research at a national conference and/or submit their research for publication in a mathematics journal.