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Math Foundation

by @smseow001

Contemporary mathematics core knowledge system - 6 dimensions + Grand Unified Programs + milestone achievements. For complex math problem solving, financial...

Versionv1.0.0
Downloads376
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clawhub install math-foundation

πŸ“– About This Skill


name: math-foundation version: 1.0.0 description: Contemporary mathematics core knowledge system - 6 dimensions + Grand Unified Programs + milestone achievements. For complex math problem solving, financial engineering, algorithm design.

Math Foundation Knowledge Base

1. Logic & Axiomatic Foundations

  • Mathematical Logic, Set Theory, Axiomatic Systems
  • Godel Incompleteness Theorems, Formal Proofs
  • 2. Algebraic Structures

  • Groups, Rings, Fields, Modules, Category Theory
  • Homological Algebra, Langlands Program
  • 3. Geometry & Topology

  • Topology: continuity, homotopy, homology, manifolds
  • Differential Geometry, Riemann Geometry
  • Poincare Conjecture (solved by Perelman 2003)
  • 4. Dynamics & Analysis

  • Real/Complex Analysis, Functional Analysis
  • Differential Equations, Dynamical Systems, Calculus of Variations
  • 5. Random & Statistics

  • Probability Theory, Stochastic Processes, Martingales
  • Stochastic Differential Equations (SDE)
  • Law of Large Numbers, Central Limit Theorem
  • 6. Discrete & Computation

  • Combinatorics, Graph Theory, Number Theory
  • Algorithm Complexity: P/NP/NP-Complete
  • Cryptography: RSA, Elliptic Curve
  • Grand Unified Programs: Langlands Program

    Connects: Number Theory, Algebraic Geometry, Representation Theory, Analysis

    Financial Mathematics Core

  • Black-Scholes: dS = mu dt + sigma dW
  • Ito's Lemma, Girsanov Theorem
  • Feynman-Kac Formula
  • Milestone Achievements

  • Poincare Conjecture (2003)
  • Fermat's Last Theorem (1994)
  • Green-Tao Theorem (2004)
  • *For advanced AI problem solving*