Mathematical Sciences: Undergraduate Research Experience in Mathematics

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Undergraduate Research Experience in Mathematics will provide a unique opportunity for undergraduate students to get involved in research in dynamical systems, Algebra, and statistics. In dynamical systems, participants will investigate stability, ergodicity and chaos of simple one dimensional nonlinear maps as well as piecewise linear planar maps. In Algebra, students will investigate monoids determined by Linear Diophantine equations. In statistics, they will study regression models using the norms l_1 and l_infinity and some statistical models for genetic linkage. Although the tools and techniques needed are of elementary nature and accessible to the students, the problems involved are far from being completely understood by active researchers in the field. Hence this research program will be challenging and exciting to all the participants. Through computer experimentation, students will explore and make conjectures about the mathematical theory. Then they will be asked to prove it analytically if possible.