REU Site: Research, Education and Training in Computational Mathematics and Nonlinear Dynamics of Bio-Inspired and Engineering Systems

乔治梅森大学数学科学系将于2012年6月4日至8月3日和2013年6月3日至8月2日举办一个为期两年的多学科REU项目，研究生物、生物启发和工程系统的计算数学和非线性动力学。这个为期九周的暑期项目每年将让12名高素质的本科生和两名K-12教师接触数学、解决问题、可视化技术以及生物启发和工程系统应用方面的高级主题。这个暑期研究项目将为参与者提供一个独特的经验，让他们了解如何应用数学来理解生物、生物启发和工程系统的定性和定量行为。拟议的项目将涉及三个子项目，在一个共同的主题下，这将有助于理解生物，生物启发和工程系统的定量行为。这些包括(a)生物、生物启发问题的建模和分析(b)材料数学和(c)利用技术的数学教育。所有这些都将在计算数学和非线性动力学的保护伞下协同联系在一起。选择的问题范围从动脉瘤力学到微型飞行器的建模，光伏纳米器件的设计，多孔衬底和材料工程应用的相图计算，以及高效教育工具的设计。通过这些研究问题，我们希望鼓励学生和教师在发现中学习，并增强他们对数学在工程、科学和医学中的多学科作用的理解。教师将能够利用他们的解决问题的能力和研究经验，在他们的高中数学课堂上进行开放式的探索和发展相关的课程研究。两名研究生将作为研究生导师参与该项目。该项目将有助于培养研究生的智力成长和发展，并为他们提供宝贵的指导经验。每个为期九周的暑期课程还将包括以下活动：主题系列讲座；研究生辅导俱乐部；客人座谈会;学生研讨会;计算实验室以及科学和社会之旅。REU网站将涉及7名合格的教师，他们在研究和教学成就方面表现出色，指导了研究生和本科生的研究，并参与了K-12的外展活动。这个多学科研究项目将极大地提高人们对数学和计算方法在理解生物、生物启发和工程系统方面日益增长的效用的认识。它将有助于本科生和K-12教师的科学发展，并将培养研究生的智力成长和发展，为他们提供宝贵的指导经验。该项目将整合和补充GMU现有的成功指导项目，与当地K-12高中的合作伙伴关系，并与其他机构建立新的合作关系。这种共生关系将为目标学生提供更好的学习和研究机会，为他们在数学和工程领域的成功做好准备，这将帮助他们从大学到研究生院。REU计划将为4名K-12教师提供独特而宝贵的解决问题和开放式探索的经验，他们将在高中数学课堂上使用这些经验。该项目还将极大地鼓励女性和未被充分代表的少数族裔从事数学、计算和生物科学之间的多学科职业。

The Department of Mathematical Sciences at George Mason University will host a two-year multidisciplinary REU program in computational mathematics and nonlinear dynamics of biological, bio-inspired and engineering systems from June 4 - Aug 3, 2012 and June 3 - Aug 2, 2013. This nine-week summer program will expose twelve highly qualified undergraduate students and two K-12 teachers each year, to advanced topics in mathematics, problem-solving, visualization techniques and applications to bio-inspired and engineering systems. This summer research program will provide the participants with a unique experience of how mathematics can be applied to understand the qualitative and quantitative behavior of biological, bio-inspired and engineering systems. The proposed program will involve three subprograms under a common broad theme that will help understand the quantitative behavior of biological, bio-inspired and engineering systems. These include (a) Modeling and analysis of biological, bio-inspired problems (b) Mathematics of materials and (c) Mathematics Education using Technology. All of them will be synergistically linked together under the umbrella of computational mathematics and nonlinear dynamics. Selected problems range from Aneurysm mechanics to Modeling of Micro Air Vehicles, Design of photovoltaic nanodevices, Porous substrates and Phase diagram calculation for materials engineering applications, as well as the design of efficient educational tools. Through these research problems, we hope to encourage students and teachers to learn by discovery and enhance their understanding of the multidisciplinary role of mathematics in engineering, science and medicine. The teachers will be able to use their problem-solving skills and research experience from the program to do open-ended exploration and develop related lesson studies in their high-school mathematics classrooms. Two graduate students will be involved in this program as graduate mentors for the participants. The program will help nurture the intellectual growth and development of graduate students and also provide them with a valuable experience of mentoring. Each nine-week summer program will also include the following activities: lecture series on topics; graduate mentoring club; guest colloquia; student seminars; computational laboratory as well as scientific and social tours. The REU site will involve seven qualified faculty who have excelled in their research and teaching accomplishments, have guided graduate and undergraduate research, and have been involved in K-12 outreach activities. The multi-disciplinary research program will greatly enhance the awareness of the ever-increasing utility of mathematical and computational approaches in understanding biological, bio-inspired and engineering systems. It will contribute to the scientific development of undergraduate students and K-12 teachers and will nurture the intellectual growth and development of graduate students providing them with a valuable experience of mentoring. This program will integrate and complement the existing successful mentoring programs at GMU, partnerships with local K-12 high schools and also establish new collaborations with other institutions. This symbiotic relationship will provide enhanced learning and research opportunities for targeted students to prepare for success in the mathematical and engineering fields that will assist them from college to graduate school. The REU program will provide a unique and invaluable experience to four K-12 teachers in problem-solving and open-ended exploration that they will use in their high-school mathematics classrooms. This program will also greatly encourage women and underrepresented minorities to pursue multidisciplinary careers that bridge mathematical, computational and biological sciences.