IMU-05 Calculus

Transcript

1. pineapple.cc ௕࡚େֶ৘ใσʔλՊֶ෦ େֶ਺ֶೖ໳
    Introduction to University Mathematics
2. pineapple.cc ߨٛͷਐΊํʢୈճʙୈճʣ Agenda (Day 2 to Day 8) w େֶ਺ֶ΁ͷೖ໳
   Introduction to University Mathematics ⭐⭐
   w ਺ֶΛ޷͖ʹͳΔ࿩
   Stories about math that makes you fun ⭐
   w ܭࢉػՊֶʢ৘ใՊֶʣ΁ͷڮ౉͠
   A bridge to computer science ⭐⭐⭐
3. pineapple.cc ධՁ Credits w ग़੮
   Attendance
   w ΫΠζͱϛχϨϙʔτ
   Quiz and mini report
   w Ϩϙʔτʢ೚ҙʣ
   Report (optional)
4. pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺
5. pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ϒʔϧ୅਺
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6. pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ϒʔϧ୅਺
   w ˔
   BOE
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7. pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ϒʔϧ୅਺
   w OPU
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   w OPU
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   w OPU
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   BOE
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   w OPU
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8. pineapple.cc ܈ɾ؀ɾମ
   group, ring, field
9. pineapple.cc ܈ͱ൒܈ Group and Semigroup w ดੑ
   
   w ݁߹ੑ
   
   w தཱݩͷଘࡏ
   
   w ٯݩͷଘࡏʢ܈ͷΈʣ
   {੔਺} + {੔਺} = {੔਺} (A + B) + C = A + (B + C) 0 + A = A + 0 = A (−A) + A = A + (−A) = 0
10. pineapple.cc ؀ Ring w ดੑʢՃ๏ͱ৐๏ʣ
    
    w ݁߹ੑʢՃ๏ͱ৐๏ʣ
    
    w தཱݩͷଘࡏʢՃ๏ͱ৐๏ʣ
    w ٯݩͷଘࡏʢՃ๏ʣ
    
    w Մ׵ੑʢՃ๏ʣ
    
    w ෼഑ੑ
    {੔਺} + {੔਺} = {੔਺}, {੔਺} × {੔਺} = {੔਺} (A + B) + C = A + (B + C), (A × B) × C = A × (B × C) 0 + A = A + 0 = A, 1 × A = A × 1 = A (−A) + A = A + (−A) = 0, 1 A × A = A × 1 A = 1 (A ≠ 0) A + B = B + A A × (B + C) = A × B + A × C
11. pineapple.cc ମʢՄ׵ମʣ Field w ดੑʢՃ๏ͱ৐๏ʣ
    w ݁߹ੑʢՃ๏ͱ৐๏ʣ
    w தཱݩͷଘࡏʢՃ๏ͱ৐๏ʣ
    w ٯݩͷଘࡏʢՃ๏ͱ৐๏ɼͨͩ͠Ճ๏தཱݩΛআ͘ʣ
    w Մ׵ੑʢՃ๏ͱ৐๏ʣ
    w ෼഑ੑ
12. pineapple.cc ϒʔϧ୅਺ͱਐ๏ͷ੔਺୅਺ Boolean Algebra and Integral Algebra of Binary System w ࿦ཧ୅਺ͱϒʔϧ୅਺
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    w ܭࢉػՊֶͰ͸ਐ๏ͷ੔਺୅਺Λࢉज़ʢBSJUINFUJDʣૢ࡞ɼϒʔϧ୅਺Λ ࿦ཧʢMPHJDBMʣૢ࡞ͱݺͿ ¯ A ≜ OPU A A ∩ B ≜ A BOE B A ∪ B ≜ A PS B
14. pineapple.cc A B A B
15. pineapple.cc ༗໊ͳؔ਺
    some popular functions
26. pineapple.cc ؔ਺ʢଓ͖ʣ
43. pineapple.cc ඍ෼
58. pineapple.cc
59. pineapple.cc ܭࢉػՊֶͱܕͷ࿩
60. pineapple.cc ਺ֶʹ͓͚Δܕ Types in Mathematics w ࣗવ਺ʢج਺ʣ
    w ੔਺
    w ༗ཧ਺
    w ࣮਺
    w ෳૉ਺
    w ௒ෳૉ਺
    w ߦྻ
    w εΧϥʔͱϕΫτϧ ʲϊʔτ1ʳ εΧϥʔͱϕΫτϧ͸ʮม׵ੑʯʹΑͬͯ ఆٛ͞ΕΔ͜ͱʹ஫ҙ͠Α͏ ʲϊʔτ2ʳ ܭࢉػՊֶͰ͸εΧϥʔͱϕΫτϧ͸ผͷҙຯͰ΋ ༻͍ΒΕΔ͜ͱʹ஫ҙ͠Α͏
61. pineapple.cc ෺ཧֶʹ͓͚Δܕʢجຊ୯Ґʣ Types in Physics w ࣌ؒ
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62. pineapple.cc ଎౓ º ࣌ؒ  ڑ཭
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64. pineapple.cc ࣌ؒ º ࣌ؒ 
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66. pineapple.cc ϓϩάϥϛϯάʹ͓͚Δܕ Types in Computer Science w ੔਺ܥ
    w ੔਺ int
    w ࿦ཧ bool
    w ྻڍ enum
    w จࣈʢΫϥγΧϧʣ char
    w ϙΠϯλ
    w ුಈখ਺఺ܥ
    w *&&&୯ਫ਼౓ුಈখ਺఺ fl oat
    w *&&&ഒਫ਼౓ුಈখ਺఺ double
    w ഑ྻܥ
    w ഑ྻ array/vector
    w จࣈྻ string
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    w ߏ଄ମ struct
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    w ؔ਺ʢ㱠ؔ਺ϙΠϯλʣ
    
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67. pineapple.cc @kanaya