Moduli of Generalized Spin Curves, Class Size and Calculus Learning

这是职业生涯项目授予泰勒·贾维斯教授的奖项。这个产品兼具教育和研究两部分。本研究将研究高自旋曲线的模空间以及由此产生的模空间的不同紧化。他特别希望研究退化曲线上线束和矢量束的模量。在教育方面，他有两个计划。第一个是严格研究班级规模对学生微积分入门课程的影响，第二个是为初中学生开发一门新的抽象代数课程。这个项目的数学研究属于算术几何的一般领域，这一学科融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。教育部分属于科学课程改革的广泛领域，如果国家要满足对受过科学训练的成年人的需求，这是至关重要的。

Jarvis 9501617 This is an award made under the CAREER program to Professor Tyler Jarvis. This product has both an educational component and a research component. The research will be to study the moduli space of higher spin curves and of different compactifications of the resulting moduli space. In particular he hopes to study the moduli of line and vector bundles on degenerating curves. In education he has two projects. The first is a rigorous study of the effect of class size on students in introductory calculus and the second is to develop a new abstract algebra course for junior level students. The mathematical research in this project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks. The educational component falls into the broad area of science curriculum reform which is vital if the nation is to meet its need for scientifically trained adults.