全学共通科目講義（１回生〜４回生対象）

 現代の数学と数理解析 ――　基礎概念とその諸科学への広がり

 授業のテーマと目的： 数学が発展してきた過程では、自然科学、 社会科学などの種々の学問分野で提起される問題を解決するために、 既存の数学の枠組みにとらわれない、 新しい数理科学的な方法や理論が導入されてきた。 また、逆に、そのような新しい流れが、 数学の核心的な理論へと発展した例も数知れず存在する。 このような数学と数理解析の展開の諸相について、第一線の研究者が、 自身の研究を踏まえた入門的・解説的な講義を行う。 数学・数理解析の研究の面白さ・深さを、 感性豊かな学生諸君に味わってもらうことを意図して講義し、 原則として予備知識は仮定しない。 第６回 日時： ２０１７年５月２６日（金） 　　　　　　１６：３０−１８：００ 場所： 数理解析研究所　４２０号室 講師： Helmke, Stefan 助教 題目： On Abel's Theorem 要約： Niels Henrik Abel was born in 1802 in Norway. In his very short life (until 1829) he made some major contributions to various fields of mathematics, including a proof of the impossibility to solve the quintic equation with radicals--a problem which puzzled mathematicians for more than two centuries. His most famous work however, is on a very broad generalization of the theory of elliptic integrals, which were studied since the early 18th century. These so-called abelian integrals had an enormous impact on the later developments of mathematics. In this lecture I will try to explain the contents and historical background of Abel's Theorem (on abelian integrals) in a hopefully elementary and coherent way. References： A quite comprehensive account on Abel's Theorem can be found in: Steven L. Kleiman, What is Abel's Theorem Anyway, in The Legacy of Niels Henrik Abel, Springer, 2002. The same volume contains many more interesting articles on the subject, including a short biography of Abel by Arild Stubhaug. The same author also published a full biography of Abel. Arild Stubhaug, Niels Henrik Abel and his times, translated from the Norwegian by Richard H. Daly, Springer, 2000. To see how the theory of abelian integrals fits into the general history of mathematics and how it was treated about a century ago, the following two references could prove helpful Morris Kline, Mathematical thought from ancient to modern times, Oxford University Press, 1972. Gilbert Ames Bliss, Algebraic functions, Dover Publications, 2004 (Originally published by the American Mathematical Society in 1933.) "http://www.kurims.kyoto-u.ac.jp/ja/special-02.html"