By name: math-researcher-teacher description: "Advanced, research-oriented mathematics expert system. Provides rigorous symbolic computation, numerical simulation, and proof assistance across four major pillars: Analysis & PDE, Algebra & Geometry, Stochastics, and Discrete Math."
Math Researcher Teacher
A comprehensive, research-oriented AI assistant for advanced mathematics. It acts as a meta-skill, routing queries to specialized sub-domains for rigorous analysis and simulation.
Target Audience: Undergraduate/Graduate Mathematics Students, Researchers.
🏛️ Domain Architecture (The Four Pillars)
This skill is organized into four major departments. The Agent should determine the user's mathematical field and route to the appropriate subdirectory.
1. Analysis & Differential Equations (domains/analysis-pde/)
- Calculus & Analysis: Limits, series, integrals, metric spaces.
- Real & Complex Analysis: Measure theory, residues, conformal mappings.
- Differential Equations: ODEs (stability, phase portraits), PDEs (heat, wave, laplace).
- Functional Analysis: Banach/Hilbert spaces, operators.
2. Algebra & Geometry (domains/algebra-geometry/)
- Linear Algebra: Vector spaces, eigenvalues, matrix decompositions, spectral theory.
- Abstract Algebra: Groups, rings, fields, Galois theory.
- Geometry & Topology: Differential geometry, manifolds, curvature, homotopy/homology.
- Number Theory: Primes, congruences, elliptic curves.
3. Stochastics (domains/stochastics/)
- Basic Probability: Distributions, expectations, limit theorems.
- Stochastic Processes: Markov chains, Brownian motion, martingales.
- Advanced Stochastics: Random matrices, large deviations, random graphs (Erdős-Rényi).
4. Discrete & Combinatorial (domains/discrete/)
- Combinatorics: Counting, generating functions, partitions.
- Graph Theory: Connectivity, coloring, flows, spectral graph theory.
🚀 How to Use
Step 1: Identify the Domain Read the user's request and map it to one of the four domains above.
Step 2: Navigate & Load
Navigate to the domain's folder and read its SKILL.md for specific instructions on using its specialized agents and Python scripts.
Example Routing:
- "Simulate the eigenvalue distribution of a Wigner matrix" -> Go to
domains/stochastics/(Advanced Stochastics). - "Calculate the curvature of a surface" -> Go to
domains/algebra-geometry/(Geometry). - "Solve this Heat Equation numerically" -> Go to
domains/analysis-pde/(Differential Equations).
🛠️ Common Tools
All domains share access to the common/ library for standard operations:
symbolic_engine.py(SymPy wrappers)numeric_engine.py(NumPy/SciPy wrappers)plot_engine.py(Visualization tools)