????(??) Leopold Kronecker(1823~1891) - PowerPoint PPT Presentation

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????(??) Leopold Kronecker(1823~1891)

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Title: ????(??) Leopold Kronecker(1823~1891)


1
????(??)Leopold Kronecker(18231891)
God made the natural numbers, all else is the
work of man.
2
????The Crisis in Mathematics
? 8 ?
3
???????
  • ??????
  • ?????
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  • ???????
  • ????!

4
??????
  • ????? ?????????????????

Everything is a number
????
?????Pythagoras (ca 560ca 480 BC)
5
????
6
(No Transcript)
7
????Hippasus(???470???)
8
??? ????
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9
????
  • ?? Zeno
  • ?495 BC 430 BC

10
??? ????
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  • ????(??????)

CD 2AB
CD AB ?
11
??????
  • ???
  • Exhaustion
  • ??????????
  • ????
  • ?5?

????Eudoxus (409356 BC)
12
  • ?????(??????????????????)

?a?b c?d????????????????????m?n,????
? ma gt nb,? mc gt nd ? ma nb,? mc nd ? ma lt
nb,? mc lt nd
??
13
?????Aristotle (384-322 BC)
  • ???
  • ?(???)
  • ???
  • ?(????????)
  • ???

14
????Euclid (ca. 325-ca. 270BC)
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15
  • ????
  • 1482?
  • ???

16
??????? ?????
  • ??????????,??????????,???????
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17
???????
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18
??????
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19
???? ????
20
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21
(No Transcript)
22
??? ????????,???????,???????????????!
23
????
  • ????? ???????
  • ??????
  • ????? ?????

24
????
25
????(??)J.-le-R. dAlembert (17171783)
  • ??????
  • ???????
  • ???????
  • ??????
  • ??(??, Michel Rolle, 16521719)
  • ???????????????

?????
26
????
  • ????(??, S. F. Lacroix, 17651843)
  • ????? ??????????????,???????!

27
??,???????,????????????????????,??????,???
??,??????????????
???(??) Alexis-Claide Clairaut(17131765)
28
?????(??)James Sylvester (18141897)
29
???(??)Jakob Jacobi (18041851)
  • ??(1812?) ????????
  • ?????????????

30
??(??)Augustin Cauchy (17891857)
  • ???????????????????,???????????????

31
??????(??) Karl Weierstrass (18151897)
  • ?? ???????
  • ??????????
  • ???????
  • e-d??
  • ????????
  • ????????

32
??(??)Karl F. Gauss (1777-1855)
  • ?????????????

33
????!
  • ???????
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  • ????

34
??????????(?????????)?,?????????????,????????
??????????????????????????,?????????????,???????
???,??????????,???????????????
????(??,Michael Stifel,14861867)
35
?????
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  • ??????? ?????

36
???????
  • ? ?(?????)????
  • ???(?????)?? ?
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37
???????
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38
???
  • ???
  • ?????????????
  • ???(??, A.-M. Legendre, 17521833)
  • p???????

39
???
???
????
  • ???
  • ?????
  • ?????
  • ??(??,Leonhard Euler, 17071783)
  • ??? ????????

40
???(??) Joseph Liouville (18091882)
  • 1844?
  • ??????

41
1873? e????
42
??? ???????(1872)
  • ??? ????????(1883)

43
  • ?? ??????(??)??(a1 , a2 ,, an,)

an? a
  • ?? ???????????
  • ??? ???(????)
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44
  • ?? ????????

a
??a ??(A1, A2)
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45
???-???? ?????????????????????
????
46
The End
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