Mathematical Sciences: Undergraduate Research Experience in Mathematics

数学本科研究经验将为本科生提供一个独特的机会，让他们参与动力系统，代数和统计学的研究。 在动力系统方面，学员将研究简单一维非线性映射和分段线性平面映射的稳定性、遍历性和混沌性。 在代数中，学生将研究由线性丢番图方程确定的幺半群。 在统计学方面，他们将研究使用范数l_1和l_infinity的回归模型以及遗传连锁的一些统计模型。 虽然所需的工具和技术是基本的性质和访问的学生，所涉及的问题是远远没有完全理解的积极研究人员在该领域。 因此，这项研究计划将是具有挑战性和令人兴奋的所有参与者。 通过计算机实验，学生将探索和建立有关的数学理论。 然后，如果可能的话，他们将被要求通过分析来证明这一点。

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.