REU Site: The Mathematical and Theoretical Biology Institute

数学和理论生物学研究所（MTBI）是由亚利桑那州立大学（ASU）主办的数学生物学本科生为期八周的多夏季研究经验。MTBI侧重于动态系统（广泛解释为包括连续和离散确定性和随机系统）和应用于生物学的建模。该计划的第一部分包括由MTBI教师提供的上午讲座，向学生介绍生物学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和差分方程的定性行为，包括平衡态的稳定性和分岔；概率与随机过程；从连续和离散的角度（包括时间和人口）进行人口建模和流行病学；并通过统计方法进行数据拟合，包括反问题求解。下午的计算机实验室向学生介绍MATLAB和Maple的编程和计算；学生通常还会接触到Mathematica、R、XPP AUTO、LaTeX和其他有助于数学研究的软件。在MTBI的第二部分，学生分成小组并确定感兴趣的研究主题。在MTBI教师的帮助下，他们将这个主题制定为一个数学问题，然后在MTBI教师的指导下，为课程的剩余时间做他们自己选择的项目。研究结果将在研讨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。鼓励学生和教师在这一年中继续他们的工作，并向专业期刊提交他们的研究论文。学生们也被鼓励在全年的国家会议上展示他们的作品。MTBI主要从美国代表性不足的少数民族、女性和那些在本国机构中STEM和研究机会有限的个人中招募人才。MTBI教师在指导这些类型的学生，帮助他们开发研究项目和指导这些研究项目方面具有丰富的经验。MTBI的总体目标是1)发展和培养将影响美国数学科学文化和多样性的个人，同时加强他们的社区；2)提高他们的成功率，因为他们从学士学位课程到成功的博士学位，在学术界或工业界工作的学者。MTBI的目标支持以下目标：主要招募但不限于目标人员；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需的计算工具和软件；营造合作学习的环境，加强所有参与者之间的联系；为他们建立强大的支持网络；并在学生完成MTBI经验后对他们进行至少六年的跟踪。通过高质量的指导和研究，MTBI将继续在国家层面带来变革，并真正影响美国的劳动力。该站点由国防部与NSF REU项目合作资助。

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.