rudin-real-complex-analysis
Provides problem-solving assistance for measure theory, functional analysis, and complex analysis using Rudin's methods.
Install
mkdir -p .claude/skills/rudin-real-complex-analysis && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/1685" && unzip -o skill.zip -d .claude/skills/rudin-real-complex-analysis && rm skill.zipInstalls to .claude/skills/rudin-real-complex-analysis
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving with Rudin's Real and Complex Analysis textbookKey capabilities
- →Query Rudin's Real and Complex Analysis content
- →Perform symbolic computation with SymPy
- →Verify mathematical proofs with Z3
- →Reference key theorems and definitions
How it works
The skill uses RAG to query the content of Rudin's textbook and provides interfaces for symbolic computation and formal verification to assist in solving graduate-level analysis problems.
Inputs & outputs
When to use rudin-real-complex-analysis
- →Solve Lebesgue integration problems
- →Verify complex analysis proofs
- →Apply functional analysis theorems
About this skill
Rudin'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.
When not to use it
- →Solving problems outside the scope of the textbook
- →General mathematical research without textbook context
Prerequisites
Limitations
- →Limited to content within Rudin's textbook
- →Requires familiarity with graduate-level analysis
How it compares
It provides a structured environment for applying specific textbook theorems to problems rather than using general-purpose math solvers.
Compared to similar skills
rudin-real-complex-analysis side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| rudin-real-complex-analysis (this skill) | 3 | 7mo | Review | Advanced |
| annas-archive-ebooks | 22 | 7mo | Review | Beginner |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
| worldexams-generator | 0 | 3mo | Review | Intermediate |
Try saying
Example prompts that trigger this skill in your AI assistant.
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