Vertical Integration of Research and Education in the Mathematical Sciences

摘要：世界正变得越来越数学化。例如，近几十年来，我们已经看到复杂的数学工具在金融和生物学科中的扩散，更不用说相对较新的计算机科学学科了，它有自己独特的数学问题。这些学科，以及其他具有跨学科性质的学科，最好通过分析、计算和统计方法的结合来研究，数学科学家与所研究的特定科学的科学家一起工作。我们将通过跨学科和垂直整合的工作组为学生和研究人员创造学习这些学科的机会。莱斯大学数学系、统计学系和计算与应用数学系将围绕四五个跨学科研究课题联合组织新的课程、研讨会和实验室。这些活动旨在将纯数学、数值方法、统计科学和所研究的特定科学的知识遗产，以及教师、博士后、研究生和本科生的教育阶层编织在一起。这些主题中也会有一些问题，这些问题可以作为该领域基本科学问题的介绍。学生和教师将以小组形式（称为PFUG’s——博士后、教员、本科生、研究生），在跨学科团队的指导下探索这些问题。对于我们的学生，我们将创造一个令人兴奋的数学科学研究经验的机会，在与其他科学或工程学科的互动中，其他学生，博士后和教师将分享他们的魅力，他们将作为导师。我们的研究人员将被介绍并参与他们研究领域之外的主题，他们也可能在这些领域做出重大贡献。通过这个VIGRE项目，我们将在我们目前的优势和兴趣的基础上重塑莱斯大学的数学科学课程，以便为学生和教师创造新的机会，拓宽和深化他们对数学在我们日益增长的对世界的理解中发挥核心作用的理解。

Rice University VIGRE Abstract:The world is becoming more mathematical. For example, in recent decades we have seen the diffusion of sophisticated tools of mathematics into the subjects of finance and biology, to say nothing of the relatively new subject of computer science, with its own distinctive mathematical issues. These subjects, and others of an interdisciplinary nature, are best studied by a combination of analytical, computational and statistical methods, with the mathematical scientists working alongside those from the particular science under study. We will create opportunities for students and researchers to learn these subjects by working in interdisciplinary and vertically integrated working groups. The Rice University Departments of Mathematics, Statistics, and Computational and Applied Mathematics will jointly organize new courses, seminars and laboratories focussed around four or five interdisciplinary research topics. These activities are designed to weave together the intellectual heritages of pure mathematics, numerical methods, statistical science, and the particular science under study, and the educational strata of faculty, post-docs, graduate students and undergraduates. These topics will also have in them questions which serve as introductions to the fundamental scientific issues of the field. Working in small groups (called PFUG's - Post-doc, Faculty, Undergraduate, Graduate student), students and faculty will explore these questions in heavily mentored, interdisciplinary teams. For our students we will create the opportunity for an exciting research experience in the mathematical sciences, in interaction with another scientific or engineering discipline, and other students, post-docs and faculty who share their fascination who will serve as mentors. Our researchers will be introduced and become involved in topics outside of their research areas in which they also might make substantial contributions. With this VIGRE project, we will reshape the mathematical sciences curriculum at Rice, building on our current strengths and interests, in order to create new opportunities for students and faculty to broaden and deepen their understanding of the ways in which mathematics plays a central role in our growing understanding of the world.