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
2. INTRODUCTION
6. { time: "2015-05-03T09:29:15.000Z" space: "default", source_type: "metric", name: "response_time", value: 134.675 }
7. read … | ( reduce -every :5s: max(value) by host | @timechart; keep time, value | @logger )
8. read … | ( reduce -every :5s: max(value) by host | @timechart; keep time, value | @logger ) read @timechart reduce keep @logger
9. DEMO
10. LOGIC ALGEBRA I ALGEBRA II GEOMETRY & PHYSICS
11. LOGIC
12. read status = 500
13. read status = 500 or (status = 404 and url !~ …)
14. read status = 500 or (status = 404 and url !~ …)
15. Conjunctive normal form
16. (a 1,1 ∨ … ∨ a 1,m(1) ) ∧ … ∧ (a n,1 ∨ … ∨ a n,m(n) )
17. read status = 500 or (status = 404 and url !~ …)
18. read (status = 500 or status = 404) and (status = 500 or url !~ …)
19. read (status = 500 or status = 404) and (status = 500 or url !~ …)
20. ALGEBRA I
21. read … | reduce c = count(x) s = sum(x) m = max(x)
22. { c: 3, s: 6, m: 3 } read … | reduce c = count(x) s = sum(x) m = max(x) { x: 1 } { x: 2 } { x: 3 }
23. { c: 2, s: 3, m: 2 } read … | reduce c = count(x) s = sum(x) m = max(x) { x: 1 } { x: 2 }
24. { c: 1, s: 1, m: 1 } read … | reduce c = count(x) s = sum(x) m = max(x) { x: 1 }
25. { c: ?, s: ?, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
26. { c: 0, s: ?, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
27. { c: 0, s: ?, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
28. { c: 0, s: 0, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
29. { c: 0, s: 0, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
30. { c: 0, s: 0, m: undefined } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
31. { c: 0, s: 0, m: undefined } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
32. Identity element
33. e: ∀a(e ⊕ a = a ⊕ e = a)
37. { c: 0, s: 0, m: -Infinity } read … | reduce c = count(x) s = sum(x) m = max(x) (nothing)
38. ALGEBRA II
39. read … value > 0.95 | reduce c = count()
40. Elasticsearch Cassandra read … value > 0.95 | reduce c = count()
41. Elasticsearch Cassandra read … value > 0.95 | reduce c = count()
42. Associativity
43. (a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)
44. count count_unique sum avg min max first last pluck percentile sigma mad
45. count count_unique sum avg min max first last pluck percentile sigma mad
48. Monoid
49. Set S, operation ⊕ : S ⨉ S → S 1. ⊕ is associative on elements of S 2. S contains identity element under ⊕
50. GEOMETRY & PHYSICS
51. read time < :2015-04-01:
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:
53. read time < :2015-04-01: - :1 day:
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
55. Affine space
61. m 1 m 2 m 2 t d 1 d 2
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
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
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
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
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
67. Dimensional analysis
68. v = s / t η = P out / P in
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
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
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
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
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
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
78. CONCLUSION
79. QUESTIONS?
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
81. IMAGE CREDITS http://commons.wikimedia.org/wiki/File:Torus.png