「科学」のための共通言語 Common Language for the        Scienceシグマ (Σ) 記号とパイ (Π) 記号           mikawaya           垂水共之           t2@oka...
科学のための共通言語• 数  学  自然科学のための共通言語       「諸科学の共通言語としての数学の発掘と数理科学への展開」(研究代表者:高橋陽一郎)       http://www.iias.or.jp/research/projec...
シグマ記号• 平均のために                      小学校 5 年、 6 年の単元                              計算はできる     n                        ( H23 ...
なぜ シグマ( Σ )   n  ∑a  k =1         k   = a1 + a2 +  + an
なぜ シグマ( Σ )   n  ∑a  k =1         k   = a1 + a2 +  + an   n  A     k   =  k =1   n  A     k   =  k =1
なぜ シグマ( Σ )   n  ∑a  k =1         k   = a1 + a2 +  + an   n  A     k   = A1 ∪ A2 ∪  ∪ An  k =1   n  A     k   = A1 ∩ A...
なぜ シグマ( Σ )   n  ∑a  k =1         k   = a1 + a2 +  + an   n  A     k   = A1 ∪ A2 ∪  ∪ An  k =1   n  A     k   = A1 ∩ A...
なぜ シグマ( Σ ) n∑ak =1       k   = a1 + a2 +  + an nA     k   = A1 ∪ A2 ∪  ∪ Ank =1 nA     k   = A1 ∩ A2 ∩  ∩ Ank =1 n∏a...
なぜ シグマ( Σ )   n  ∑a  k =1         k   = a1 + a2 +  + an   n  A     k   = A1 ∪ A2 ∪  ∪ An  k =1   n  A     k   = A1 ∩ A...
なぜ シグマ( Σ ) n∑ak =1       k   = a1 + a2 +  + an          ∑   Sum n∏a             = a1 ? a2 ? ? an       ∏k =1 n       k ...
なぜ シグマ( Σ )   n  ∑a  k =1         k   = a1 + a2 +  + an   n  A     k   = A1 ∪ A2 ∪  ∪ An  k =1   n  A     k   = A1 ∩ A...
なぜ シグマ( Σ )   n  ∑a  k =1         k   = a1 + a2 +  + an   n  A     k   = A1 ∪ A2 ∪  ∪ An  k =1   n  A     k   = A1 ∩ A...
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科学のための共通言語

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科学のための共通言語

  1. 1. 「科学」のための共通言語 Common Language for the Scienceシグマ (Σ) 記号とパイ (Π) 記号 mikawaya 垂水共之 t2@okayama-u.ac.jp
  2. 2. 科学のための共通言語• 数  学  自然科学のための共通言語 「諸科学の共通言語としての数学の発掘と数理科学への展開」(研究代表者:高橋陽一郎) http://www.iias.or.jp/research/project/2011_03.htmlとすれば• 統計学  科学(自然、社会、人文)の ための        共通言語
  3. 3. シグマ記号• 平均のために 小学校 5 年、 6 年の単元 計算はできる n ( H23 統計検定試験 2 級、正解率 96% ) ∑x i =1 i = x + x2 +  + xn• 拒絶反応! n n(n + 1) ∑k = 2 k =1 n n(n + 1)(2n + 1) ∑k = k =1 2 6 2 n  n(n + 1)  ∑k =  2  k =1 3  
  4. 4. なぜ シグマ( Σ ) n ∑a k =1 k = a1 + a2 +  + an
  5. 5. なぜ シグマ( Σ ) n ∑a k =1 k = a1 + a2 +  + an n A k = k =1 n A k = k =1
  6. 6. なぜ シグマ( Σ ) n ∑a k =1 k = a1 + a2 +  + an n A k = A1 ∪ A2 ∪  ∪ An k =1 n A k = A1 ∩ A2 ∩  ∩ An k =1
  7. 7. なぜ シグマ( Σ ) n ∑a k =1 k = a1 + a2 +  + an n A k = A1 ∪ A2 ∪  ∪ An k =1 n A k = A1 ∩ A2 ∩  ∩ An k =1 n ∏a k =1 k =
  8. 8. なぜ シグマ( Σ ) n∑ak =1 k = a1 + a2 +  + an nA k = A1 ∪ A2 ∪  ∪ Ank =1 nA k = A1 ∩ A2 ∩  ∩ Ank =1 n∏ak =1 k = a1 ? a2 ? ? an
  9. 9. なぜ シグマ( Σ ) n ∑a k =1 k = a1 + a2 +  + an n A k = A1 ∪ A2 ∪  ∪ An k =1 n A k = A1 ∩ A2 ∩  ∩ An k =1 n ∏a k =1 k = a1 ? a2 ? ? an
  10. 10. なぜ シグマ( Σ ) n∑ak =1 k = a1 + a2 +  + an ∑ Sum n∏a = a1 ? a2 ? ? an ∏k =1 n k ProductA k = A1 ∪ A2 ∪  ∪ Annk =1∏Aa ==Aa∩×A ∩∩a n a × × k 1 2 n1k=k =1 k  A 1 2 n
  11. 11. なぜ シグマ( Σ ) n ∑a k =1 k = a1 + a2 +  + an n A k = A1 ∪ A2 ∪  ∪ An k =1 n A k = A1 ∩ A2 ∩  ∩ An k =1 n ∏a k =1 k = a1 ? a2 ? ? an
  12. 12. なぜ シグマ( Σ ) n ∑a k =1 k = a1 + a2 +  + an n A k = A1 ∪ A2 ∪  ∪ An k =1 n A k = A1 ∩ A2 ∩  ∩ An k =1 n ∏a k =1 k = a1 × a2 ×  × an
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