Mathematical Sciences: Cornell's Summer REU Program in Mathematics

每年夏天(1997-2001)，10名本科生将在为期8周的时间里，与3名教师导师一起研究与教师研究兴趣相关的研究项目。这些项目将经过仔细的选择，以使它们在学生的能力范围内，并有合理的机会使学生的工作对数学研究社区感兴趣。预计一些结果将被纳入到可发表的论文中，要么由学生单独完成，要么与教职员工共同完成，合作将持续到暑期之后。由于时间很短，而且任何严肃的研究工作都存在固有的风险，学生们将准备接受不包括可发表结果的有利结果。将包括两类研究项目：1)计算机探索项目，即学生从编写程序或使用现有软件计算实例开始，并提出猜想。在他们有能力的范围内，学生也可以尝试为他们产生的实验结果找到证据和常规的数学解释；2)几何和组合数学的项目，这些项目不需要广泛的背景知识就可以开始工作，对这些项目来说，聪明和洞察力是进步的关键。1997年夏天，教员导师将是R.Strichartz(P.I.)、K.Pilgrim和R.Ehrenborg。Strichartz将指导类型1)关于分形学分析的项目，Pilgrim将指导类型1)关于有理映射动力学的项目，而Ehrenborg将指导类型2)关于组合学的项目。在未来的暑假，导师将包括P.I.和从康奈尔大学教职员工和来访者中挑选的另外两人。

Each summer (1997-2001) for 8 weeks, 10 undergraduate students will work with 3 faculty mentors on research projects related to the faculty members' research interests. These projects will be chosen carefully so that they are within the students' ability and there is reasonable chance that the students' work will be of interest to the mathematical research community. It is expected that some of the results will be incorporated into publishable papers, either by the students alone or jointly with the faculty member, and that the collaboration will continue beyond the summer period. Because of the short period of time and the inherent risks involved in any serious research effort, the students will be prepared to accept a favorable outcome that does not include publishable results. The two types of research projects that will be included are: 1) Computer exploration projects, in which the students begin by writing programs or using existing software to work out examples, and formulate conjectures. To the extent that they are able, the students may also participate in attempts to find proofs and conventional mathematical explanations for the experimental results they have generated; 2) Projects in geometry and combinatorics, that do not require extensive background knowledge to begin working on, and for which cleverness and insight are the keys to progress. For the summer of 1997, the faculty mentors will be R. Strichartz (P.I.), K. Pilgrim and R. Ehrenborg. Strichartz will direct projects of type 1) on analysis on fractals, Pilgrim will direct projects of type 1) on dynamics of rational maps, and Ehrenborg will direct projects of type 2) on combinatorics. For future summers, the mentors will include the P.I. and 2 others chosen among Cornell faculty and visitors.