Mathematical Sciences: Cornell's Summer REU Program in Mathematics

每年夏季（1997-2001），10名本科生将与3名教师导师一起进行与教师研究兴趣相关的研究项目，为期8周。这些项目将在学生的能力范围内仔细选择，并且有合理的机会使学生的工作对数学研究界感兴趣。预计一些结果将被合并到可发表的论文中，由学生单独或与教师共同完成，并且合作将在夏季期间之后继续进行。由于任何严肃的研究工作所涉及的时间短和固有的风险，学生将准备接受一个有利的结果，但不包括可发表的结果。将包括两种类型的研究项目：1)计算机探索项目，其中学生开始编写程序或使用现有软件来计算示例，并制定推测。在可能的情况下，学生也可以参与为他们所产生的实验结果寻找证明和传统数学解释的尝试；2)几何和组合学方面的项目，不需要广泛的背景知识就可以开始工作，聪明和洞察力是取得进展的关键。1997年夏季，教师导师将是R. Strichartz (P.I.)， K. Pilgrim和R. Ehrenborg。Strichartz将指导类型1的分形分析项目，Pilgrim将指导类型1的有理映射动力学项目，Ehrenborg将指导类型2的组合学项目。在未来的夏季，导师将包括私家侦探和另外两名从康奈尔大学教职员工和访客中选出的人。

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.