REU Site: Purdue Research in Mathematics Experience (PRiME)

该奖项将为普渡大学提供为期三年的支持，为本科生提供为期八周的夏季住宿项目，以进行纯数学研究。该项目名为普渡大学数学经验研究（PRiME），每年夏天将招收8名本科生。该计划的主要目标是(1)为本科生提供代数几何，数论或概率论方面的研究经验，以产生值得在国家数学会议上发表或展示的新结果；(2)为本科生准备数学学士学位后学位。该项目还将致力于增加普渡大学和更广泛地区数学家的多样性。项目主管将高度重视从传统上在数学领域代表性不足的群体中招募参与者。此外，该计划的主管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，他们将与PRiME参与者讨论他们的专业旅程。PRiME项目将由Edray Goins教授（普渡大学）、jonathan Peterson教授（普渡大学）和Pamela Harris教授（美国军事学院）指导。三位联合主任还将得到两位研究生的协助，他们将帮助为本科生的研究提供额外的指导。每年夏天，该项目将选出八名学生参加普渡大学的PRiME项目。四名学生将参与代数几何/数论的研究，四名学生将参与随机漫步/随机过程的研究。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。在这个项目的过程中，学生们还将学习一些重要的技能，比如如何用数学排版语言LaTeX来写作，如何使用先进的符号计算软件包，比如Sage或Mathematica，以及如何为他们的结果准备一篇技术论文。在为期八周的课程结束时，学生们将对他们的发现进行总结。在项目完成后，学生将被鼓励在全国会议上展示他们的研究和/或提交他们的研究发表在数学期刊上。

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.