EMSW21-MCTP: The Summer Mathematics Institute at Cornell

【摘要】马克里希纳总体而言，美国女性和少数族裔（非裔美国人、拉美裔美国人和印第安人）完成数学科学博士学位的人数很少，在顶级项目完成学位的人数就更少了。我们的提议，康奈尔大学夏季数学学院（SMI），是针对代表性不足的群体，但将向所有有才华的学生开放，他们在本科院校没有机会获得全面的高等数学课程。每年我们都会为12-14名学生开设一个为期8周的暑期项目。学生们将学习严格的代数或实分析课程，这些课程每年交替进行，允许一些学生参加两次课程。我们预计大多数的第一次参与者将在他们的大三和大四之间，尽管我们也会考虑完成已经在当年的主题课程的大二学生。学生还将参与一个研究项目，以3-5人为一组。虽然有些学生可能会做原创研究，但我们认为，在大多数情况下，学生将参与重新发现已经发表的结果的过程。为了在一流的研究型博士课程中脱颖而出，研究生必须从本科数学问题解决过渡到研究生课程所要求的抽象推理，并学会交流数学思想。如果不能实现这种转变，就会阻碍学生在课堂和研讨会上的表现，并严重阻碍他们在研究生学习中取得成功。在真正的分析和代数的核心科目彻底的基础是必不可少的纯粹和应用数学家。准备不足严重阻碍进入和完成研究生学业。这种情况在少数民族学生中尤为突出，他们中的许多人在从资源有限的大学毕业后开始研究生学习，教授高等数学课程。事实上，我们看到康奈尔大学的学生在我们的纯课程和应用课程中都遇到了这种困难。SMI将通过拓宽他们的数学知识，加强他们对基本概念的理解，提高他们的沟通技巧，并提供数学研究经验和学习在具有挑战性的博士课程中的期望，帮助这些学生过渡到研究生院并在研究生院取得成功。参加SMI既可以提高学生获得顶级研究生课程录取的机会，也可以提高他们在研究生院注册成功的机会。由于我们预计每个班可能有3-5名学生将参加SMI的两个夏天，我们预计在五年内我们将培训大约55名学生。最终，SMI将有助于扩大美国数学界的人才库。

AbstractRamakrishnaThere is a dearth of American women and underrepresented minorities (African-American, Latino-American and Native American) completing doctorates in the mathematical sciences overall, and even fewer completing their degrees at top tier programs. Our proposal, the Summer Mathematics Institute at Cornell (SMI), is aimed at underrepresented groups, but will be open to all talented students who do not have access to a full range of advanced mathematics courses at their undergraduate institutions. Each year we will run an eight-week summer program for 12-14 students. Students will take a rigorous course in algebra or real analysis, with the subjects alternating yearly to allow the possibility for some students to attend the program twice. We expect that most of the first time participants will be in between their junior and senior years, although we will also consider finishing sophomores who have already had a course in that year's topic. Students will also participate in a research project, working in groups of 3-5. While some students may do original research, we imagine that in most cases students will be engaged in the process of rediscovering results that have already been published.To excel in a top tier research oriented doctoral program graduate students must negotiate the transition from undergraduate mathematics problem solving to engaging in the abstract reasoning required in graduate course work and learn to communicate mathematical ideas. Failure to make this transition inhibits performance in both course and seminar work and is a serious obstacle to success in graduate studies. A thorough grounding in the core subjects of real analysis and algebra is essential for pure and applied mathematicians. Inadequate preparation significantly hinders entering and completing graduate school. This situation is particularly salient in the case of minority students, many of whom begin graduate study after coming from colleges with limited resources to teach advanced math courses. Indeed, we have seen students at Cornell experience this difficulty in both our pure and applied programs. SMI will facilitate these students' transition to and success in graduate school by broadening their knowledge of mathematics, strengthening their understanding of basic concepts, enhancing their communications skills, and providing an experience of mathematical research and learning what to expect in a challenging doctoral program. SMI participation will both improve students' chances of gaining admission at a top tier graduate program and their chances of success upon enrolling in graduate school. As we anticipate that perhaps 3-5 students in each class will attend SMI for two summers, we expect that over _ve years we will train approximately 55 students. Ultimately, SMI will help widen the talent pool from which American mathematics will draw.