REU site: Complexity Across Disciplines (CAD)

这笔赠款资助了博伊西州立大学数学系主办的REU网站“跨学科复杂性”。这个网站寻求培养一批年轻的研究人员，他们的工作和视野超越了STEM学科之间的现有界限。每个研究导师将邀请一个国家招募的本科生团队参与一个研究项目，该项目具有很强的跨学科范围，并基于有限的数学结构。这些项目的数学基础包括代数结构、组合结构和博弈论。十名REU研究人员中的每一位都将深入研究当代研究问题，并将其应用于密码学、生物学和其他几个研究领域。这些项目与数学中的重要公开问题有着深刻的联系，并可能导致对当前商业使用的密码系统的安全性具有重要意义的发现。从博弈论的观点来检查某些基因组重排过程的想法对该领域来说是新的，作为一种数学探索具有内在的价值，并有可能澄清在自然重排过程中观察到的现象。对分裂系统的研究可以为医疗、化学和电气测试以及纠错的数学工具提供新的见解。通过对生命基本过程的科学理解取得重大进展，通过互联网的发明，历史上最大的信息处理变革，以及我们日常生活中所有基本任务的自动化，计算和复杂性的性质已经从学术扩展到实践领域。人们需要了解计算的基本限制，从而了解生活、日常生活和信息处理的基本过程。在这个网站上展示的研究项目最终涉及到计算的限制问题。提供这些项目的动机源于对高效搜索或排序算法以及高效信息安全工具的追求。REU项目及其项目的研究方向由经验丰富的导师指导，其中包括一名早期职业调查员、一名女性研究员和一名资深科学家。通过招生过程，该项目为来自全国各地此类机会有限的机构的学生带来了本科生的研究经验。通过REU网站与NASA资助的爱达荷州科学和航空航天学者的合作，让REU的学生参与针对K-12学生的智力拓展活动，来自机会有限的农村社区的学生可以一对一地接触到来自全国各地积极进取的STEM学生。这一外展活动有可能改变K-12学生对自己在STEM领域职业生涯的看法。该网站与博伊西州立大学的其他几个夏季本科生研究项目合作，提供了一系列丰富的专业和跨学科发展活动。

This grant funds the REU site "Complexity Across Disciplines" at Boise State University, hosted in the Department of Mathematics. This site seeks to produce cohorts of young researchers whose work and vision transcend current boundaries between STEM disciplines. The research mentors will each engage a team of nationally recruited undergraduate students in a research project with strong interdisciplinary scope and based on finitary mathematical structures. The mathematical foundations for these projects include algebraic structures, combinatorial structures and game theory. Each of the cohorts of ten REU researchers will be thoroughly engaged in contemporary research problems with applications to cryptology, biology and several other fields of inquiry. The projects have deep connections with important open problems in mathematics, and could lead to discoveries of importance to the security of currently commercially used cryptosystems. The idea to examine certain genomic rearrangement processes from a game-theoretic point of view is new to the field, has inherent value as a mathematical exploration, and has the potential to clarify observed phenomena in natural rearrangement processes. The study of splitting systems could give new insights into mathematical tools for medical, chemical and electrical testing as well as error correction.The nature of computing and complexity has expanded from the academic to the practical arena through great strides in scientific understanding of basic processes of life, the biggest transformation in information processing in history through invention of the internet, and automation of all basic tasks in our daily lives. The need to understand fundamental limitations on computing, thus on basic processes of life, daily living and information processing, has never been greater. The research projects featured at this site ultimately relate to the question of limitations on computing. The motivations for the offered projects arise from the quest for efficient search or sorting algorithms and for efficient information security tools. The research direction of this REU program and its projects are guided by experienced mentors that include an early career investigator, a female researcher and a senior scientist. Through its recruitment process this program brings undergraduate research experiences to students from institutions across the nation where such opportunities are limited. By involving the REU students in intellectual outreach activities targeting K-12 students through the REU site's partnership with the NASA funded Idaho Science and Aerospace Scholars, students from rural communities with limited opportunities have one-on-one exposure to highly motivated STEM students from across the nation. This outreach activity has the potential to transform the vision of the K-12 students about their own careers in a STEM field. The site offers, in collaboration with several other summer undergraduate research programs at Boise State University, a rich array of professional and interdisciplinary development events.