Friday Special Lecture for High School and University Students
Held on 2020

Friday Special Lecture for High School and University Students

The spread of group theory in mathematics -- Starting with the Fourier expansion --
Yoshitaka Kida


00:00 タイトル
00:21 司会より金曜講座の概要と本日の講師紹介
03:46 講義の導入/フーリエ展開三角関数をきっかけに
07:31 講義の概要 Ⅰ.三角関数とフーリエ級数展開 Ⅱ. 群とその研究 Ⅲ. 私について"
08:21 Ⅰ. 三角関数(定規による角度の表現法)
14:23 三角関数は万物を描写する
17:56 f(x) のフーリエ級数展開とその導入について
21:02 フーリエ級数展開とは
27:22 フーリエ級数展開について結論
29:36 先の結論への説明。なぜ微分方程式がとけるのか
41:19 Ⅱ.群= 和(もしくは積)を持つもの
44:58 群の上の関数のフーリエ展開
47:59 群に対するフーリエ展開の研究の歴史
54:38 ハウスドルフのパラドックス(ワイルドさの象徴)と従順性について
1:03:41 Ⅲ.私について(数学を中心に)
1:10:46 Max Planck研究所(ボン)について
1:14:11 数学の研究のよいところ
1:17:46 エンドタイトル
In mathematics, a group is a set that has something called multiplication. The set of numbers is an example. Because groups can have anything that should be called multiplication, they appear in many situations. In fact, groups are one of the essential concepts for understanding various mathematics. Fourier expansion, on the other hand, is a method of representing a function on a number line by superimposing trigonometric functions of different periods, and is an interesting topic both mathematically and practically. In this lecture, I will introduce some aspects of the study of group theory, starting with the relationship between groups and Fourier expansions.

- This lecture was conducted only in Japanese.

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the University of Tokyo Graduate School of Mathematical Science / Professor

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