The Math Every Programmer Needs

Leave your fear of math behind along with the equations and symbols, we're headed to Ruby-land!

Joël Quenneville

Principal Developer at thoughtbot

Schedule Entry

Slides

Attendees

• Josh
• Gary

Relevancy	Interesting
4	5

Notes

• Discrete Math - most useful CS skillset for the rails devs
• Proposition Logic, Boolean Algebra, Graph Theory, etc.
• Practical Problems
  • Unnecessary Conditions => Use Operators!
    • Boolean Algebra focus on Operators
    • Identity, negation, adm, or
  • Propositional Logic Truth Tables
    • 2 expressions are equal if their truth tables match
    • Can use tables in GH PR markdown
    • Makes complex code easier to understand and communicate
  • Broken Auth Logic => Demorgans Law on negation of compound conditions
    • More readable code
    • Catch bugs
    • Unless is a boolean condition
  • How many test cases do I need? => Combinatorics
    • 2 inputs + # states per input
    • Compound states multiply!
    • 2 states x 3 states = 6 tests!
    • Default optional parameters (combinatorics)
    • Insufficient test coverage => Venn diagrams (tests vs states)
    • Add more tests or reduce states (maybe your code is trying to do too much)
  • Which RSpec let blocks actually get invoked? => Graph Theory
    • Visual model. List lets.
    • Add directed relations for dependency / references between them
    • = Dependency Graph
    • Color those being used
    • Can improve performance by simply / optimize dependency between them
  • Work incrementally => Graph Theory
    • Large Task -> Linear List (steps 1 to 5)
    • Graph Theory - evaluating a node requires evaluating all downstream nodes
    • Alternatively, work on leaf nodes. Can be done in isolation. Can be shipped!
    • Dependency Graphs should be evaluated from the bottom up (terminal nodes first)
    • Aka Topological sort
    • Concrete example: Replace image processing gem. Cycles!
    • Cycles cannot be evaluated independently
    • Breaking cycles via new dependency on adapter to create DAG
    • This is the strangler fig pattern
  • What are the risks of a randomly generated ID collision? => Combinatorics
  • Designing a DB schema => Set Theory + Combinatorics