Jak na mě vyskočila matematika

Potřebuje programátor vysokoškolskou matematiku? Když jsem nastupoval do Jutu jako návrhář a implementátor programovacího jazyka, myslel jsem si, že ji využiji zhruba stejně jako ve své předchozí práci – vůbec. Rychle se ale ukázalo, že jsem se mýlil. Matematika na mě vyskočila hned na několika místech a já si rychle osvěžoval pojmy jako neutrální prvek, afinní prostor nebo dimenzionální analýza. V přednášce bych rád ukázal, kde všude jsem na matematiku při své práci nečekaně narazil a co všechno bych udělal špatně, kdybych jí nerozuměl.

Přednášku je možno chápat jako malý příspěvek do diskuze na témata „Potřebují programátoři vysokou školu?“ a „Kolik matematiky a další teorie by se na programátorských VŠ mělo učit?“

Předneseno na pražském Ruby srazu.

Detaily:
http://srazy.info/prvni-streda-ruby-on-rails/5420
https://www.facebook.com/events/1618055091803470/

Transcript

1. Jak na mě vyskočila
   MATEMATIKA
   David Majda
   Praha, 6.5.2015
   

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2. INTRO
   

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6. {
   time: "2015-05-03T09:29:15.000Z"
   space: "default",
   source_type: "metric",
   name: "response_time",
   value: 134.675
   }
   

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7. read … | (
   batch :5 seconds: | reduce max('value') by host | @timechart;
   keep time, value | @logger
   )
   

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8. read … | (
   batch :5 seconds: | reduce max('value') by host | @timechart;
   keep time, value | @logger
   )
   read
   @timechart
   batch reduce
   keep @logger
   

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9. DEMO
   

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10. LOGIKA
    ALGEBRA I
    ALGEBRA II
    ALGEBRA III
    ANALÝZA
    TEORIE RELATIVITY
    

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11. LOGIKA
    

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12. read status = 500
    

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13. read status = 500
    or (status = 404 and url !~ …)
    

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14. read status = 500
    or (status = 404 and url !~ …)
    

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15. Konjunktivní normální
    forma
    

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16. (a
    1,1
    ∨ … ∨ a
    1,m(1)
    )
    ∧
    …
    ∧
    (a
    n,1
    ∨ … ∨ a
    n,m(n)
    )
    

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17. read status = 500
    or (status = 404 and url !~ …)
    

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18. read (status = 500 or status = 404)
    and (status = 500 or url !~ …)
    

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19. read (status = 500 or status = 404)
    and (status = 500 or url !~ …)
    

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20. ALGEBRA I
    

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21. read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    

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22. { c: 3, s: 6, m: 3 }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    { x: 1 }
    { x: 2 }
    { x: 3 }
    

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23. { c: 2, s: 3, m: 2 }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    { x: 1 }
    { x: 2 }
    

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24. { c: 1, s: 1, m: 1 }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    { x: 1 }
    

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25. { c: ?, s: ?, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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26. { c: 0, s: ?, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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27. { c: 0, s: ?, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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28. { c: 0, s: 0, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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29. { c: 0, s: 0, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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30. { c: 0, s: 0, m: undefined }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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31. { c: 0, s: 0, m: undefined }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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32. Neutrální prvek
    

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33. e: ∀a(e ⊕ a = a ⊕ e = a)
    

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37. { c: 0, s: 0, m: -Infinity }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nic)
    

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38. ALGEBRA II
    

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39. read … value > 0.95
    | reduce c = count()
    

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40. Elasticsearch
    Cassandra
    read … value > 0.95
    | reduce c = count()
    

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41. Elasticsearch
    Cassandra
    read … value > 0.95
    | reduce c = count()
    

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42. Asociativita
    

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43. (a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)
    

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44. count
    count_unique
    sum
    avg
    min
    max
    first
    last
    pluck
    percentile
    sigma
    

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45. count
    count_unique
    sum
    avg
    min
    max
    first
    last
    pluck
    percentile
    sigma
    

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48. Monoid
    

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49. Množina S, operace ⊕ : S ⨉ S → S
    ⊕ je asociativní na prvcích S
    V S existuje neutrální prvek vůči ⊕
    

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50. ALGEBRA III
    

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51. read time < :2015-04-01:
    

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52. Moment
    Duration
    :2015-04-01T20:05:27.034:
    :now:
    :3 weeks and 1 day ago:
    :20:05:27.034:
    :3s:
    :1 hour and 23 minutes:
    

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53. read time < :2015-04-01: - :1 day:
    

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54. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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55. Afinní prostor
    

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61. m
    1
    m
    2
    m
    2
    t
    d
    1
    d
    2
    

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62. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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63. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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64. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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65. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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66. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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67. Dimenzionální analýza
    

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68. v = s / t
    η = P
    výst
    / P
    vst
    

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69. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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70. N * D → D
    D * N → D
    N / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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71. N * D → D
    D * N → D
    D / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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72. View Slide

73. N * D → D
    D * N → D
    D / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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74. N * D → D
    D * N → D
    D / D → N
    D / N → D
    D % N → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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75. N * D → D
    D * N → D
    D / D → N
    D / N → D
    D % D → D
    M + D → M
    D + M → M
    D + D → D
    M - M → D
    M - D → M
    D - D → D
    

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78. ANALÝZA
    

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79. emit -from 0
    | batch 2 | reduce count()
    | batch 4 | reduce count()
    

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80. emit … | batch 2 | reduce count() | batch 4 | reduce count()
    { time: 0 }
    { time: 1 }
    { time: 2 }
    { time: 3 }
    { time: 4 }
    { time: 5 }
    { time: 6 }
    { time: 7 }
    { time: 8 }
    { time: 2, count: 2 }
    { time: 4, count: 2 }
    { time: 6, count: 2 }
    { time: 8, count: 2 }
    { time: 4, count: 2 }
    { time: 8, count: 2 }
    

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81. emit … | batch 2 | reduce count() | batch 4 | reduce count()
    { time: 0 }
    { time: 1 }
    { time: 2 }
    { time: 3 }
    { time: 4 }
    { time: 5 }
    { time: 6 }
    { time: 7 }
    { time: 8 }
    { time: 2, count: 2 }
    { time: 4, count: 2 }
    { time: 6, count: 2 }
    { time: 8, count: 2 }
    { time: 4, count: 2 }
    { time: 8, count: 2 }
    < 2
    < 2
    < 2
    < 2
    ≤ 4
    ≤ 4
    

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82. Infinitezimály
    

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83. ε > 0
    ∀x ∈ R, x > 0: ε < x
    

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84. emit … | batch 2 | reduce count() | batch 4 | reduce count()
    { time: 0 }
    { time: 1 }
    { time: 2 }
    { time: 3 }
    { time: 4 }
    { time: 5 }
    { time: 6 }
    { time: 7 }
    { time: 8 }
    { time: 2, count: 2 }
    { time: 4, count: 2 }
    { time: 6, count: 2 }
    { time: 8, count: 2 }
    { time: 4, count: 2 }
    { time: 8, count: 2 }
    < 2
    < 2
    < 2
    < 2
    ≤ 4
    ≤ 4
    

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85. emit … | batch 2 | reduce count() | batch 4 | reduce count()
    { time: 0 }
    { time: 1 }
    { time: 2 }
    { time: 3 }
    { time: 4 }
    { time: 5 }
    { time: 6 }
    { time: 7 }
    { time: 8 }
    { time: 2 - ε, count: 2 }
    { time: 4 - ε, count: 2 }
    { time: 6 - ε, count: 2 }
    { time: 8 - ε, count: 2 }
    { time: 4 - ε, count: 2 }
    { time: 8 - ε, count: 2 }
    < 2
    < 2
    < 2
    < 2
    < 4
    < 4
    

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86. TEORIE
    RELATIVITY
    

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88. Minkowského metrika
    

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89. ds2 = c2dt2 - dx2 - dy2 - dz2
    

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90. ds2 = c2dt2 - dx2 - dy2 - dz2
    

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93. ZÁVĚR
    

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94. OTÁZKY?
    

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95. KAM DÁL?
    http://en.wikipedia.org/wiki/Conjunctive_normal_form
    http://en.wikipedia.org/wiki/Disjunctive_normal_form
    http://en.wikipedia.org/wiki/Identity_element
    http://en.wikipedia.org/wiki/Associative_property
    http://en.wikipedia.org/wiki/Monoid
    http://en.wikipedia.org/wiki/Affine_space
    http://en.wikipedia.org/wiki/Dimensional_analysis
    http://en.wikipedia.org/wiki/Infinitesimal
    http://en.wikipedia.org/wiki/Minkowski_space
    

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96. POUŽITÉ OBRÁZKY
    http://commons.wikimedia.org/wiki/File:Torus.png
    http://commons.wikimedia.org/wiki/File:World_line.svg
    

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