rudin-real-complex-analysis

rudin-real-complex-analysis is a skill for Claude Code from parcadei/Continuous-Claude-v3. It costs 18 tokens per session (616 once invoked), scanned A, original, MIT.

A reference guide for solving advanced problems from Walter Rudin’s Real and Complex Analysis textbook. It covers measure and integration, functional analysis, complex analysis, topology, and related algebra.

In plain words
What is it for?
Use it to work through textbook exercises involving limits, metric spaces, measure theory, integration, analytic functions, residues, and compactness.
Why use it?
It gives a structured way to approach graduate-level analysis questions when the relevant theorem or technique is not obvious. It also explains the mathematical setting behind topics such as Lebesgue integration and contour integration.

Skill for Claude Code

Written for Claude Code: allowed-tools in frontmatter. Also seen: reads .claude/ paths.

Needs its repository: it runs a file that does not travel with it, so clone the repository first. The line is uv run python scripts/ragie_query.py --query "YOUR_TOPIC measure integration" --partition math-textbooks --top-k 5.

Good fit Use it to work through textbook exercises involving limits, metric spaces, measure theory, integration, analytic functions, residues, and compactness.

Compare 6 skills from other repositories ↓
About the project

Continuous-Claude-v3 is a Claude Code development environment that preserves working context between sessions, coordinates specialized agents, and stores project knowledge through ledgers, handoffs, and analysis tools. It is for people using Claude Code on ongoing or complex software work. Its catalogue entries are the skills, agents, hooks, plugin, and setting that provide its workflows and orchestration.

parcadei/Continuous-Claude-v3 · 3,938 stars · on GitHub

Install

Getting it into your agent

It runs from inside its repository, so the clone comes first — what it calls does not travel with the file alone.

Clone the repo
git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3
agentmods
npx agentmods add skills/parcadei/continuous-claude-v3/rudin-real-complex-analysis

Made for: Claude Code.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

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README.md
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Per session 18 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 616 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe. Third-party audits
  • NVIDIA SkillSpector warn 7 Sept 2026
SkillSpector: 1 finding, up to medium

These are SkillSpector’s own severities. On a checked sample its high-severity flags on skills were ~96% false positives — a documented command, a public API, a “never do X” rule — so we show them as a caution to read, not a verdict. Why →

  • medium Agent Snooping · line 88
    Skill enumerates or reads other installed skills. Access to other skills' SKILL.md files or the skills directory reveals prompt instructions, capabilities, and secrets that should be invisible to peer skills.
    Fix: Remove all code or instructions that list or read other skills' files or directories. Skills should operate independently; cross-skill access is a privilege escalation.
How audits are shown
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00018 $0.00616
Opus 5 $0.00009 $0.00308
Sonnet 5 $0.00004 $0.00123
Haiku 4.5 $0.00002 $0.00062

Measured 9d ago against content hash 0ae3165d7389, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-12, from the pricing page.

Security

Grade A, and why

rudin-real-complex-analysis scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 9d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

.claude/skills/math/rudin-real-complex-analysis/SKILL.md · 89 lines

How it starts

The opening of the file, as written. The whole thing — 89 lines — stays where its author put it; the contents beside it link to each section on GitHub.

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

  1. Measure/Integration Problem?

    • Use Lebesgue dominated convergence
    • Check Fatou's lemma for liminf/limsup
    • Apply Fubini-Tonelli for iterated integrals
  2. Complex Analysis Problem?

    • Check analyticity via Cauchy-Riemann
    • For integrals: residue theorem
    • For mappings: Schwarz lemma, conformal properties
  3. 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

Read the full file on GitHub · 89 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 9d ago First seen · 89 lines · 18 tokens per session scan A 0ae3165d7389

Subscribe to this mod's changes

rudin-real-complex-analysis is a skill published in the GitHub repository parcadei/Continuous-Claude-v3 (3,938 stars, last pushed 7mo ago), licensed MIT. It adds 18 tokens to every session and 616 once invoked, about $0.0001 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.

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