REU Site: Differential/Difference Equation Models and Number Theory

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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).