全学共通科目講義(1回生~4回生対象)
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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 |
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日時: | 2014年6月13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 Solutions of Polynomial Equations |
要約: |
In the early 16th century, the Italian mathematicians
Scipione del Ferro and Niccolò Tartaglia independently
found a formula, expressing the roots of a polynomial equation of
degree three in terms of radicals, now called Cardano's Formula.
Shortly after that, the equation of degree four was solved in
a similar way by Lodovico Ferrari. This started a 200 years
hunt for a solution of the equation of degree five. In the
18th century, Leonard Euler found a new way to solve the
equation of degree four and he thought, he could solve the
equation of degree five then too, but failed. This led
Joseph Louis Lagrange, in a famous paper, to analyze the
reasons, why all of the methods, which were successful in solving
polynomial equations of degree four and lower, failed for
degrees five and higher. While he himself did not attempt to
show that such a solution cannot exist, his work eventually
inspired Paolo Ruffini, Niels Henrik Abel and Évariste Galois
to prove exactly this. Besides this slightly disappointing
result, Lagrange's paper was enormously important for the future
developments in algebra. In this lecture, we will learn
about Lagrange's beautiful ideas, how to solve polynomial
equations.
References:
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"http://www.kurims.kyoto-u.ac.jp/ja/special-02.html" |