REU Site: Differential/Difference Equation Models and Number Theory

查塔努加田纳西大学REU站点主要集中在微分和差分方程，生物学数学建模，数论和概率论。研究重点集中在六个方面：(1)具有Allee效应的人口模型；（ii）有时滞的数学模型；（iii）电报方程；（iv）离散周期边值问题；(v)黎曼ζ函数；（vi）随机调和多项式。这包括对尼科尔森的苍蝇模型、动物红细胞存活的Lasota-Wazewska模型和血细胞生成的Mackey-Glass模型等著名模型的研究。此外，将探讨随机调和多项式和黎曼ζ函数的性质，如部分和和零的分布。每个主题都适合初级/高级本科生；但每个主题也会自然地引出许多实质性和有趣的数学问题。导师将介绍主题并提供必要的背景知识，但其目标是将重点转移到学生身上，学生将根据自己的兴趣和能力提出和调查问题。上述项目将涉及8至10名本科生，在4名应用数学家和纯数学专家的指导下，在2013年至2015年连续三个夏季，每人8周的积极研究时间。这个REU网站的主要重点是数学培训，积极参与研究和指导。它的目标是为本科生提供有意义的数学研究经验，向他们展示做研究的乐趣，并鼓励他们追求数学科学的高级学位和/或职业。会议报告和研究成果的出版将被大力鼓励。这个REU网站将极大地促进本科学生对数学研究的兴奋和发展。此外，它将补充目前维持和加强我国在数学科学及其应用的科学研究方面的领导地位的努力。该项目由数学科学部和刺激竞争性研究实验项目办公室（EPSCoR）共同资助。

The University of Tennessee at Chattanooga REU Site has major areas of concentration in differential and difference equations, mathematical modeling in biology, number theory, and probability. The research focus is on six main topics: (i) population models with Allee effects; (ii) mathematical models with time delays; (iii) telegraph equations; (iv) discrete periodic boundary value problems; (v) the Riemann zeta-function; and (vi) random harmonic polynomials. This includes the study of such well-known models as Nicholson's blowflies model, the Lasota-Wazewska model of survival of red blood cells in animals, and the Mackey-Glass model of blood cell production. In addition, properties of random harmonic polynomials and the Riemann zeta-function, such as partial sums and distribution of zeros, will be explored. Each of these topics is accessible to junior/senior level undergraduates; but each topic also leads naturally to many substantial and interesting mathematical issues. The mentors will introduce the topics and provide the necessary background but with the goal of shifting the focus to the students who will pose and investigate questions according to their own interests and abilities.The projects described above will involve a total of 8 to 10 undergraduate students in active research for eight weeks each for three consecutive summers from 2013 to 2015 under the supervision of 4 applied and pure mathematicians who are dedicated researchers and mentors. The primary focus of this REU Site is in mathematical training, active participation in research, and mentoring. Its objectives are to provide undergraduate students with meaningful research experience in mathematics, to show them the joy of doing research, and to encourage them to pursue advanced degrees and/or careers in the mathematical sciences. Conference presentations and publication of research findings will be strongly encouraged. This REU Site will greatly contribute to the excitement and development of mathematical research among undergraduate students. Moreover, it will supplement current efforts in sustaining and strengthening our nation's leadership in scientific research in the mathematical sciences and their applications. This project is jointly funded by the Division of Mathematical Sciences and the Office of the Experimental Program to Stimulate Competitive Research (EPSCoR).