Mathematical Sciences: Undergraduate Research Experience in Mathematics

本科数学研究经验将为本科生提供参与动力系统、代数和统计学研究的独特机会。在动力系统中，参与者将研究简单的一维非线性映射以及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决定的一元群。在统计学方面，他们将研究使用l_1和l_infinity规范的回归模型和一些遗传连锁的统计模型。尽管所需要的工具和技术是基本性质的，学生可以获得，但所涉及的问题远未被该领域的活跃研究人员完全理解。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，学生将对数学理论进行探索和推测。然后，如果可能的话，他们会被要求用分析的方法证明它。

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.