REU Site: Differential/Difference Equation Models and Number Theory

田纳西大学查塔努加分校的主要研究方向是微分方程式、生物数学模型、数论和概率论。主要集中在六个主题上：(I)具有Allee效应的种群模型；(Ii)具有时滞的数学模型；(Iii)电报方程；(Iv)离散周期边值问题；(V)Riemann Zeta函数；(Vi)随机调和多项式。这包括对著名模型的研究，如尼科尔森的苍蝇模型，动物体内红细胞存活的Lasota-Wazewska模型，以及血细胞产生的Mackey-Glass模型。此外，还将探讨随机调和多项式和Riemann Zeta函数的性质，如部分和和、零点分布等。这些主题中的每一个都是初级/高级本科生可以接触到的；但每个主题自然也会引出许多实质性的和有趣的数学问题。导师将介绍主题并提供必要的背景，但目标是将重点转移到根据自己的兴趣和能力提出和调查问题的学生身上。上述项目将包括8至10名本科生，从2013年到2015年连续三个暑期，在4名应用和纯数学家的指导下进行为期8周的积极研究，他们都是敬业的研究人员和导师。这个REU网站的主要焦点是数学培训、积极参与研究和指导。其目的是为本科生提供有意义的数学研究经验，向他们展示从事研究的喜悦，并鼓励他们在数学科学领域攻读更高的学位和/或职业。将大力鼓励会议报告和研究成果的出版。这个REU网站将极大地促进本科生对数学研究的兴奋和发展。此外，它还将补充目前在维持和加强我国在数学科学及其应用方面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激励竞争性研究实验计划办公室(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).