Math Researcher Teacher

• 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)