Showing papers in "Notices of the American Mathematical Society in 2004"

The bowl championship series: A mathematical review

Abstract: We discuss individual components of the college football Bowl Championship Series, compare with a simple algorithm defined by random walks on a biased graph, attempt to predict whether the proposed changes will truly lead to increased BCS bowl access for non-BCS schools, and conclude by arguing that the true problem with the BCS Standings lies not in the computer algorithms, but rather in misguided addition.

The international commission on mathematical instruction what? Why? for whom?

Abstract: Mathematics is an international—even universal— discipline, and this aspect finds institutional expression every four years in the International Congress of Mathematicians (ICM), where a world community of mathematicians assembles to report progress on shared problems and with a common technical language. But these things, which we now take for granted, were not always so. The “international movement” in mathematics took hold only at the end of the nineteenth century, the first congress being the 1897 ICM in Zürich. The body that now provides the international infrastructure for mathematics—for example, sponsoring the ICM’s—is the International Mathematical Union (IMU),1 an international nongovernmental and nonprofit scientific organization with the purpose of promoting international cooperation in mathematics. The members of the IMU are not individuals but countries, and the adhering (membership) entity in each member country is typically its Academy of Sciences or a professional organization of mathematicians. The IMU is known to mathematicians mainly indirectly through the publicly visible expressions of its work, like the ICM’s and the awarding of the Fields Medals. Our focus here is the International Commission on Mathematical Instruction (ICMI), the mathematics education counterpart to the IMU.

Armand Borel: 1923-2003

Abstract: 这篇结伴式文章多侧面展现了Armand Borel，他于2003年8月11日去世．8位作者记述他，依次是Serre，Chandrasekharan，Bombieri，Hirzebruch，Springer，Tits，Arthur，Prasad．Borel在代数和拓扑方面的研究足够好，使他在34岁时被聘为IAS(高等研究院)的数学教授．Serre综览他的数学全貌，而Hirzebruch侧重于拓扑方面以不同方式描述他的数学．Springer和Tits讨论Borel在代数群方面的工作，而Arthur评论算术群，以及Borel在这个领域的工作如何奠定自守形式现代理论的基石出．一位研究院的同事说道Borel强烈相信数学的统一性和书面记载的重要性．实现这些信念的方法包括各种角色：编辑、作者、教育家和会议组织者，本文作者中有几位详细描述了这些活动．Borel投入大量的努力到Bourbaki全集的撰稿中，Borel在1998年3月《通报》(Notices of the AMS)里文章“与Nicolas Bourbaki的25年，1949—1973”详细描写了他的经历．广泛认为Bourbaki关于Lie群和Lie代数这一章的写作Borel起了主要作用，这一章已经显出特别持久的价值．Borel是1962—79年间的Annals of Mathematics的编辑，1979—93年间Inventiones Mathematicae的编辑，以及其它杂志的编辑．1998-2000年间他悄悄地以无头衔的副主编方式为《通报》服务，在各种事务上向主编进言，尤其是纪念文章和《通报》与其它国家相应的杂志合作．Borel在策划关于A．Weil的各种文章以及纪念J．Leray和A．Lichnerowicz的文章，起了大而又默默无闻的作用．本文作者中几位描写到Borel著或编的一些书，这些书的列表中共有17本，除了他的文集：论文集【文集】，列在下面方框里．多数书是讨论班的结果，有时与他人合作有时没有．不管讨论班采取何种形式，人们都可相信Borel是每个人的导师．特别的注记是两次美国数学会暑期学校的会议录，1965年在Boulder[3]和1977年在Corvalli