About rudin-real-complex-analysis
A reference skill for graduate-level topics covered in Walter Rudin's Real and Complex Analysis, including measure theory, functional analysis, and complex analysis. It offers topic guidance, theorem references, and commands for querying text and performing symbolic or formal checks.
Key features
- 01Coverage of real and complex analysis
- 02Guidance for measure and integration problems
- 03Decision tree for selecting theorems
- 04RAG queries for Rudin content
- 05SymPy symbolic computation
- 06Z3 proof verification
Use cases
- 01Studying Lebesgue integration and measure theory
- 02Working with contour integrals and residues
- 03Choosing theorems for functional analysis problems
- 04Checking symbolic calculations or propositions
Install
Copy the command and run it in a terminal.
npx skills add https:/After installing, type/rudin-real-complex-analysisin Claude Code to confirm it loaded.
Details
From the project READMERudin's Real and Complex Analysis
Reference skill for Walter Rudin's "Real and Complex Analysis" (3rd Edition) - a graduate-level text covering measure theory, integration, functional analysis, and complex analysis.
When to Use
Use this skill when working on:
- Measure theory and Lebesgue integration
- Lp spaces and functional analysis
- Complex analysis (analytic functions, contour integration, residues)
- Connections between real and complex analysis
Topics Covered
Real Analysis
- Limits and continuity in metric spaces
- Convergence of sequences and series
- Differentiation and integration techniques
- Metric spaces and topology
Complex Analysis
- Analytic functions and Cauchy-Riemann equations
- Contour integration and Cauchy's theorem
- Residue theorem and applications
- Conformal mappings
- Power series representations
Topology
- Topological spaces
- Compactness and connectedness
- Metric space topology
Algebra
- Rings and ideals (in context of function spaces)
Decision Tree
-
Measure/Integration Problem?
- Use Lebesgue dominated convergence
- Check Fatou's lemma for liminf/limsup
- Apply Fubini-Tonelli for iterated integrals
-
Complex Analysis Problem?
- Check analyticity via Cauchy-Riemann
- For integrals: residue theorem
- For mappings: Schwarz lemma, conformal properties
-
Functional Analysis?
- Riesz representation for duals
- Hahn-Banach for extensions
- Open mapping/closed graph theorems
Tool Commands
Query Rudin Content
uv run python scripts/ragie_query.py --query "YOUR_TOPIC measure integration" --partition math-textbooks --top-k 5
SymPy for Symbolic Computation
uv run python scripts/sympy_compute.py integrate "exp(-x**2)" --var x --bounds "0,oo"
Z3 for Verification
uv run python scripts/z3_solve.py prove "forall x, |f(x)| <= M implies bounded"
Key Theorems Reference
| Theorem | Chapter | Use Case |
|---|---|---|
| Dominated Convergence | Ch 1 | Interchange limit and integral |
| Riesz Representation | Ch 2 | Identify dual spaces |
| Cauchy's Theorem | Ch 10 | Contour integrals = 0 for analytic |
| Residue Theorem | Ch 10 | Evaluate real integrals |
| Open Mapping | Ch 5 | Surjective bounded linear maps |
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.