Workshop on Emerging Mathematical Foundations for Design; Washington, DC; Summer 2020

本研讨会旨在扩大数学工具的范围，以解决复杂的工程设计问题。具体来说，该研讨会有助于探索和弥合三个领域之间的语言和概念障碍-工程设计，数学和计算机科学-通过使用旨在发现数学和计算机科学的新增长领域的有针对性的合作和写作练习，可以适应和应用于解决现实世界的工程问题。该研讨会还旨在通过加强学生的教育成果，并为美国学术和工业劳动力提供一条途径，在未来几十年内发展和开发这些新的数学工具，来培养这些交叉领域的新一代研究生。本次研讨会推进了NSF的使命，即通过将先进的数学工具以更快的速度过渡到工程研究和实践中来促进科学的进步。 这个为期多天的研讨会将汇集三组人：（1）工程/系统设计研究人员，（2）数学家，统计学家和计算机科学家，以及（3）来自这些领域的研究生。会议的目的是进行一系列的“翻译”练习，其中数学家，统计学家和计算机科学家具有工程设计和系统工程（EDSE）研究人员通常不存在或使用的学科领域的知识，与EDSE研究人员成对和小组合作，以“翻译”未开发的数学领域的关键思想或结果-特别是，从表征理论的不同领域-到EDSE研究人员可以在EDSE问题的背景下解释的语言。这些练习包括从科学传播技术改编的有针对性的写作练习，以及来自代表性和不同工程学科的研究生的介绍性讲座和解决问题的练习。研讨会的主要目标是激发数学和计算科学未探索领域之间的新兴趣和联系，以便（1）EDSE研究社区在这些新的科学领域有具体，易于理解的立足点;（2）数学家，统计学家和计算科学家看到他们的工作在更广泛的EDSE兴趣问题中的具体应用;和（3）研讨会促进了CMMI和DMS和CISE董事会之间的融合研究，扩大了对工程设计问题感兴趣的人员库，以及这些研究人员解决这些紧迫问题的可用数学工具。研讨会的具体成果包括一系列白皮书，介绍了EDSE数学领域的关键思想，和数学和计算机科学观众与工程师在人类设计产品或系统时发生的当前问题的例子，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的评估被认为值得支持。影响审查标准。

This workshop aims to expand the scope of mathematical tools available to solve complex engineering design problems. Specifically, the workshop helps explore and bridge language and conceptual barriers between three fields--Engineering Design, Mathematics, and Computer Science--through the use of targeting collaboration and writing exercises designed to uncover new growing areas of mathematics and computer science can be adapted and applied to solved real-world engineering problems. The workshop also seeks to train a new generation of graduate students in these intersecting areas by strengthening educational outcomes for students and providing a pathway for the US academic and industrial workforce to grow and develop these new mathematical tools over future decades. This workshop advances NSF's mission to promote the progress of science by transitioning advanced mathematical tools into engineering research and practice at an accelerated rate compared to what would be possible without the workshop. This multi-day workshop will bring together three groups of people: (1) Engineering/System Design Researchers, (2) Mathematicians, Statisticians, and Computer Scientists, and (3) graduate students from across those areas. The meeting's purpose is to perform a series of "translation" exercises wherein Mathematicians, Statisticians, and Computer Scientists with knowledge of subject areas not typically present in or used by Engineering Design and Systems Engineering (EDSE) researchers, work in pairs and small groups with EDSE researchers to "translate" key ideas or results from under-explored areas of mathematics--specifically, from different areas of Representation Theory--to a language that EDSE researchers can interpret in the context of EDSE problems. These exercises include both targeted writing exercises adapted from science communication techniques as well as introductory lectures and example problem-solving exercises by graduate students from representative and diverse engineering disciplines. The key goal of the workshop is to spark new interest and connections between unexplored areas of Mathematics and Computational Science such that (1) the EDSE research community has concrete, easy-to-understand footholds into those new scientific areas; (2) Mathematicians, Statisticians, and Computational Scientists see concrete applications of their work in problems of broader EDSE interest; and (3) the workshop promotes convergence research between the CMMI and DMS and CISE directorates, expanding the pool of people interested in Engineering Design problems and the available mathematical tools those researchers have to address those pressing problems. The concrete deliverables from the workshop include a set of white-papers that introduce the key ideas from one area of mathematics to EDSE, and Mathematics and Computer Science audiences with examples of current problems that occur when engineers design products or systems at the Human-Technology Frontier.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.