Mathematics, Surprisingly

Do programmers need advanced mathematics? And what if they are designing and implementing a programming language? In the talk I will show where I needed mathematics in my work at Jut and how bad job I would have done without understanding it. You can think of this as a small contribution to a discussion about education of programmers and the role of mathematics and other theoretical subjects in it.

Presented at Rubyslava #52 (Data Science Edition).

Video: https://www.youtube.com/watch?v=7cThtM6Yk1A

Details:
http://lanyrd.com/2015/rubyslava-october/sdxdgc/
https://www.facebook.com/events/862212323886828/

Transcript

1. MATHEMATICS
   SURPRISINGLY
   David Majda
   Bratislava · October 22, 2015
   

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2. INTRODUCTION
   

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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 … | (
   reduce -every :5s: max(value) by host | @timechart;
   keep time, value | @logger
   )
   

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8. read … | (
   reduce -every :5s: max(value) by host | @timechart;
   keep time, value | @logger
   )
   read
   @timechart
   reduce
   keep @logger
   

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9. DEMO
   

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10. LOGIC
    ALGEBRA I
    ALGEBRA II
    GEOMETRY & PHYSICS
    

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11. LOGIC
    

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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. Conjunctive normal form
    

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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)
    (nothing)
    

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26. { c: 0, s: ?, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nothing)
    

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27. { c: 0, s: ?, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nothing)
    

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28. { c: 0, s: 0, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nothing)
    

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29. { c: 0, s: 0, m: ? }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nothing)
    

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30. { c: 0, s: 0, m: undefined }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nothing)
    

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31. { c: 0, s: 0, m: undefined }
    read … | reduce c = count(x)
    s = sum(x)
    m = max(x)
    (nothing)
    

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32. Identity element
    

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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)
    (nothing)
    

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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. Associativity
    

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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
    mad
    

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

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48. Monoid
    

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49. Set S, operation ⊕ : S ⨉ S → S
    1. ⊕ is associative on elements of S
    2. S contains identity element under ⊕
    

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50. GEOMETRY
    &
    PHYSICS
    

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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. Affine space
    

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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. Dimensional analysis
    

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68. v = s / t
    η = P
    out
    / P
    in
    

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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. CONCLUSION
    

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79. QUESTIONS?
    

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80. WHERE NEXT?
    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
    

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81. IMAGE CREDITS
    http://commons.wikimedia.org/wiki/File:Torus.png
    

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