Mathematics

#concept-pamphlet #todo: fill in the terms #todo: fill in the cheat sheet

History §

• Zeno
  • paradoxes
• Cantor
  • diagonalization proof
  • set theory CS103
• Hilbert’s Principia Mathematica
• Lewis Carroll’s “What the Tortoise said to Achilles” (1895)
• Godel
  • Godel’s completeness therorem (1929) (enderton)
  • godel’s incompleteness theorems (1931) (enderton)
• Turing
  • On Computable Numbers (1937) - Church-Turing thesis, Halting Problem. Turing machine CS103
  • Computing Machinery and Intelligence (1950)
• Church
  • lambda calculus (1932, 1933)
• Claude Shannon (1940s)
  • Information Theory
• Hoefstatder’s GEB
• Peano
  • peano axioms
• Zermelo and Frankel
  • zermelo-frankel set theory
• MDPs
  • CS229 Lecture Notes Questions
• Linear algebra

On math taught in basic schooling §

Cheat sheet https://x.com/mathladyhazel/status/1572682795230629889

• delta

On math structured in a format I learned §

MATH 51

On formal systems §

#todo : develop a deep, simple, timeless intuition on completeness, soundness, consistency.

• formal system

• successful formal systems

  • peano axioms

• first order logic

• second order logic

• completeness

• soundness

• consistency

• decidability

On set theory §

#todo: add axioms

• set theory
• Zermelo-Fraenkel set theory (ZFC)
  • axioms of ZFC

On category theory §

• category theory

On type theory §

More prevalent, and seemingly more compatible, in computer science (I wonder why)

• type theory (created to avoid paradox in a mathematical equation)
  • lambda calculus

Proofs §

• direct proof
• proof by contradiction
• proof by contrapositive