REU Site: The Mathematical and Theoretical Biology Institute

数学与理论生物学研究所(MTBI)是由亚利桑那州立大学(ASU)主办的为期八周的数学生物学本科生暑期研究体验项目。MTBI专注于动力系统(广义地解释为包括连续和离散的确定性和随机系统)和应用于生物学的建模。该计划的第一部分由MTBI教员上午的讲座组成，向学生介绍生物应用背景下的核心数学主题。典型的讲座主题包括非线性微分方程式和差分方程式的定性行为，包括平衡点的稳定性和分叉；概率和随机过程；从连续和离散的角度(时间和人口)的人口建模和流行病学；以及通过统计方法进行数据拟合，包括逆问题求解。下午，计算机实验室向学生介绍了用MatLab和Maple进行编程和计算；学生还经常接触到数学、R、XPP AUTO、LaTeX和其他有助于他们数学研究的软件。在MTBI的第二部分，学生们分组，确定一个感兴趣的研究主题。在MTBI教员的帮助下，他们将这个主题表述为一个数学问题，然后在MTBI教员的指导下，为项目的其余部分进行自己选择的项目。研究成果在一次座谈会上提交给亚利桑那州立大学社区，每个小组提交一份手稿。鼓励学生和教职员工在这一年继续他们的工作，并向专业期刊提交他们的研究论文。还鼓励学生在全年的全国性会议上展示他们的工作。MTBI从美国代表性较低的少数族裔、女性以及在本国机构中STEM和研究机会有限的个人中大量招聘。MTBI的教师在指导这类学生、帮助他们开发研究项目以及指导这些研究项目方面拥有丰富的经验。MTBI的总体目标是1)培养和培养那些在加强社区的同时对美国数学科学的文化和多样性产生影响的个人，以及2)在他们完成学士学位课程的过程中提高他们的成功率，以帮助在学术界或工业界工作的成功博士学者。MTBI的目标支持这些目标：招募主要但不完全针对个人；在数学科学方面提供密集和深入的研究经验；使学生熟悉数学生物学研究所必需的计算工具和软件；促进协作学习环境和所有参与者之间的牢固联系；为他们发展强大的支持网络；以及在完成MTBI经验后对学生进行至少六年的跟踪。凭借高质量的指导和研究，MTBI将继续在国家层面带来变化，并真正影响美国的劳动力。该网站由国防部与NSF REU计划共同资助。

The Mathematical and Theoretical Biology Institute (MTBI) is an eight-week multi-summer research experience for undergraduates in mathematical biology hosted by Arizona State University (ASU). MTBI focuses on dynamical systems (broadly interpreted to include continuous and discrete deterministic and stochastic systems) and modeling applied to biology. The first part of the program consists of morning lectures given by the MTBI faculty that introduce the students to core mathematical topics in the context of biological applications. Typical lecture topics include qualitative behavior of nonlinear differential and difference equations including stability and bifurcation of equilibria; probability and stochastic processes; population modeling and epidemiology from both a continuous and discrete perspective (both time and population); and data fitting through statistical methods including inverse problem solving. Afternoon computer laboratories introduce the students to programming and computation in MATLAB and Maple; students often are also exposed to Mathematica, R, XPP AUTO, LaTeX, and other software that will help with their mathematical research. During the second part of MTBI, the students divide into groups and identify a research topic of interest. With the help of the MTBI faculty, they formulate this topic into a mathematical question and then work on their self-selected projects for the remainder of the program under the direction of MTBI faculty. The research results are presented to the ASU community in a colloquium and each group submits a manuscript. Students and faculty are encouraged to continue their work during the year and submit their research papers to professional journals. Students are also encouraged to present their work at national conferences throughout the year. MTBI recruits heavily from U.S. underrepresented minorities, women, and those individuals with limited STEM and research opportunities in their home institutions. The MTBI faculty has extensive experience in mentoring these types of students, in helping them develop research projects, and in guiding these research projects. The overall goals of MTBI are 1) to develop and nurture individuals who will impact the culture and diversity of the U.S. mathematical sciences while strengthening their communities and 2) to increase their success rate as they journey through their baccalaureate programs to successful Ph.D. scholars working in academia or industry. MTBI's objectives support these goals: to recruit primarily but not exclusively targeted individuals; to provide an intensive and in-depth research experience in the mathematical sciences; to familiarize students with computational tools and software essential for research in mathematical biology; to foster a collaborative learning environment and strong bond among all participants; to develop a strong support network for them; and to track students for at least six years after completion of their MTBI experience. With quality mentoring and research, MTBI will continue to bring about change at the national level and truly impact the U.S. workforce.This site is co-funded by the Department of Defense in partnership with the NSF REU program.