Index

• Set theory

  • Set[ZFC]

  • Numbers

  • Infinite Set

  • Hyperreal/Surreal Numbers

• Mathematical logic

  • First-Order Logic[completeness]

  • Formal number theory[incompleteness]

  • NBG Set Theory[consistency]

  • Computability

  • Turing's Proof(to AI)

  • Second-Order Logic

  • (ml legacy):

    • MathematicalLogic

    • Enderton

• Proof Theory

  • Ordinal Analysis for PA

  • (pt legacy):

    • Proof Theory(Takeuti)

    • Proof Theory(Pohlers)

    • Ordinal Analysis for PA(Pohlers)

    • Ordinal analysis(Arai)

    • Human Analysis

• Operation

• Polynomials

• Linear Algebra

  • Vector Space

  • Linear Transformation

  • Matrix Operation

  • Determinants

  • Diagonalization

  • InnerProduct Spaces[½]

  • InnerProduct Spaces[2/2]

  • Canonical Forms

• Analysis

  • Analysis in R

    • Real Numbers

    • Sequence and Series

    • Topology in R

    • Functional Limit

    • Continuity

    • Derivative

    • Function Sequence and Series

    • Integral

  • Metric Space

  • Analysis in Rⁿ

    • Topology in Rⁿ

    • Differentiation

    • Extrema

    • (ann legacy):

      • Matrix Calculus

  • Differential Equation

  • Calculus of Variations

• Topology

  • Set

  • Topological Space

  • Connectedness and Compactness

• Study of Uncertainty

  • Probability

  • Probability Distribution

  • Statistics