Master discrete mathematics, logic, formal proofs, and computational thinking.

Apache-2.0Auto-check passed

Install Cs Foundations

skills CLI
$ npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install foryourhealth111-pixel/Vibe-Skills cs-foundations --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/foryourhealth111-pixel/Vibe-Skills.git skills-src && mkdir -p .claude/skills && cp -r skills-src/bundled/skills/cs-foundations .claude/skills/cs-foundations && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
cs-foundations
GitHub stars
3.6k
Token cost
~832 tokens
SKILL.md length
281 words
Files
5 (incl. scripts, references, assets)
Skills in repo
81
Repo updated
First seen
Licence
Apache-2.0

At a glance

Master discrete mathematics, logic, formal proofs, and computational thinking.

  • Works in 5 steps: Prove by induction that 1+2+...+n =… → Prove √2 is irrational → Show A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) → …
  • SKILL.md covers Skill Metadata, Quick Start, Learning Path and Practice Problems, plus 4 more sections
  • Runs Python scripts from its folder

What it does

Cs Foundations is an agent skill from foryourhealth111-pixel/Vibe-Skills. Master discrete mathematics, logic, formal proofs, and computational thinking. Build the mathematical foundation for all computer science.

Its SKILL.md is about 830 tokens, which your agent loads only when the skill is triggered. The skill folder holds 7 other files, including scripts, reference files and assets (for example `assets/proof-template.md`, `references/PROOF-TECHNIQUES.md` and `scripts/proof_validator.py`).

The repository describes itself as: Intelligent Skill routing and workflow orchestration for AI agents — +21.12 pp reward, −29.6% tokens on SkillsBench with DeepSeekV4Flash-VE. The licence is Apache-2.0.

Example prompts

  • “/cs-foundations”

Requirements

  • Python 3

Workflow steps

5 steps, taken from the first numbered list in SKILL.md.

  1. Prove by induction that 1+2+...+n = n(n+1)/2
  2. Prove √2 is irrational
  3. Show A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
  4. Count functions from {1,2,3} to {a,b}
  5. Solve: x ≡ 5 (mod 12) and x ≡ 3 (mod 8)

What it can do on your machine

Read from SKILL.md and the folder at commit ddcaa2a. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Ships 2 files in scripts/ (Python), which the agent can run.

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Cs Foundations loads about 832 tokens when it runs, and up to ~1.7k if it reads all its reference files. Until then it costs about 38 tokens; SKILL.md has 281 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~38
When it runs · the whole SKILL.md, loaded when a task matches
~832
With references · SKILL.md plus every file in references/, read only if the agent opens them
~1.7k

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check passed

The automated check found no risky patterns in SKILL.md.

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); the scripts in this folder are not scanned.

SKILL.md

The full file from foryourhealth111-pixel/Vibe-Skills at commit ddcaa2a, republished under its Apache-2.0 licence (© foryourhealth111-pixel). 281 words, ~832 tokens.

Download SKILL.mdSave it as .claude/skills/cs-foundations/SKILL.md (or your agent's skills folder). This skill also uses 4 other files; get the full folder from GitHub.
name
cs-foundations
description
Master discrete mathematics, logic, formal proofs, and computational thinking. Build the mathematical foundation for all computer science.
sasmp_version
1.3.0
bonded_agent
01-cs-foundations-expert
bond_type
PRIMARY_BOND

CS Foundations Skill

Skill Metadata

yaml
skill_config:
  version: "1.0.0"
  category: theoretical
  prerequisites: []
  estimated_time: "6-8 weeks"
  difficulty: intermediate

  parameter_validation:
    topic:
      type: string
      enum: [logic, proofs, sets, functions, combinatorics, number-theory, graphs]
      required: true
    depth:
      type: string
      enum: [intro, standard, advanced]
      default: standard

  retry_config:
    max_attempts: 3
    backoff_strategy: exponential
    initial_delay_ms: 500

  observability:
    log_level: INFO
    metrics: [topic_usage, proof_verification_rate, exercise_completion]

Quick Start

Computer science is built on mathematics. Master these fundamentals:

Core Topics

Discrete Mathematics

  • Set theory and operations
  • Logic and proof techniques
  • Combinatorics and counting
  • Number theory basics
  • Relations and functions

Computational Thinking

  • Problem decomposition
  • Abstraction and generalization
  • Pattern recognition
  • Algorithmic thinking

Formal Logic

  • Propositional logic
  • Predicate logic
  • Proof by induction
  • Truth tables and logical equivalence

Learning Path

Week 1: Logic Basics

  • Boolean algebra
  • Truth tables
  • Logical operators
  • Inference rules

Week 2: Proof Techniques

  • Direct proof
  • Proof by contradiction
  • Mathematical induction
  • Strong induction

Week 3: Set Theory

  • Set operations (∪, ∩, complement)
  • Cartesian product
  • Relations
  • Equivalence relations

Week 4: Functions

  • Function notation
  • Domain, codomain, range
  • One-to-one and onto
  • Function composition

Week 5: Combinatorics

  • Counting principles
  • Permutations
  • Combinations
  • Pigeonhole principle

Week 6: Number Theory

  • Modular arithmetic
  • Prime numbers
  • GCD and Euclidean algorithm
  • Congruence

Practice Problems

  1. Prove by induction that 1+2+...+n = n(n+1)/2
  2. Prove √2 is irrational
  3. Show A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
  4. Count functions from {1,2,3} to {a,b}
  5. Solve: x ≡ 5 (mod 12) and x ≡ 3 (mod 8)

Troubleshooting

IssueRoot CauseResolution
Proof stuckMissing case or wrong directionCheck base case, verify induction step
Set operation confusion∪ vs ∩ mix-upDraw Venn diagram
Counting errorOvercounting duplicatesDistinguish P(n,r) vs C(n,r)
Modular arithmetic errorForgot wraparoundWork with remainders explicitly

Key Concepts

  • Axioms: Statements we assume true
  • Theorems: Statements we prove
  • Lemmas: Helper theorems
  • Corollaries: Results that follow easily

Why It Matters

These foundations enable:

  • Understanding algorithm correctness
  • Analyzing computational complexity
  • Designing new algorithms
  • Proving algorithm properties
  • Understanding what's computable

Interview Prep

  • Explain mathematical induction
  • Prove that a function is injective
  • Count permutations with constraints
  • Solve modular equations
  • Apply pigeonhole principle

© foryourhealth111-pixel, Apache-2.0. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

SKILL.md and 4 other files (scripts, references, assets) in bundled/skills/cs-foundations of foryourhealth111-pixel/Vibe-Skills.

  • SKILL.md
  • assets/proof-template.md
  • references/PROOF-TECHNIQUES.md
  • scripts/proof_validator.py
  • scripts/verify-proof.py

Open the folder on GitHubat commit ddcaa2a

Compare with similar skills

Cs Foundations next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Cs Foundations compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Cs Foundations this skillforyourhealth111-pixel/Vibe-Skills3.6k—~832Automated safety check: PassApache-2.0
Foundations Of Computational Mathematicsbrycewang-stanford/Awesome-Journal-Skills1.2k—~2.1kAutomated safety check: PassMIT
Mathematical Foundationsbrycewang-stanford/Auto-Empirical-Research-Skills4.6k—~4.1kAutomated safety check: PassCustom licence
Principle Foundational Thinkingcursor/plugins11k8 repos~383Automated safety check: PassNone
Moai Foundation Thinkingmodu-ai/moai-adk1.2k—~4.1kAutomated safety check: PassApache-2.0
Ito Computeaffaan-m/ECC277k1 repos~1.7kAutomated safety check: PassMIT

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Questions about Cs Foundations

What does Cs Foundations do?

Master discrete mathematics, logic, formal proofs, and computational thinking. Cs Foundations is an agent skill from foryourhealth111-pixel/Vibe-Skills. Master discrete mathematics, logic, formal proofs, and computational thinking.

How do I install Cs Foundations in Claude Code?

Run `npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -a claude-code`. Or copy the skill folder (bundled/skills/cs-foundations in foryourhealth111-pixel/Vibe-Skills) into .claude/skills/cs-foundations in your project. Claude Code loads it when a task matches its description.

How do I install Cs Foundations in Codex?

Run `npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -a codex`. Or copy the skill folder (bundled/skills/cs-foundations in foryourhealth111-pixel/Vibe-Skills) into .agents/skills/cs-foundations in your project. Codex loads it when a task matches its description.

Can I use Cs Foundations in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/cs-foundations, .gemini/skills/cs-foundations, .github/skills/cs-foundations and .opencode/skills/cs-foundations in your project.

What does Cs Foundations need to run?

Going by SKILL.md and its folder, Cs Foundations needs Python for the scripts in its folder. Our summary lists: Python 3.

Does Cs Foundations access the network?

SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.

Is Cs Foundations safe to install?

Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. The check reads SKILL.md only: the scripts in the folder are not scanned, so read them before running anything.

What licence does Cs Foundations use?

Cs Foundations is published under the Apache-2.0 licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Cs Foundations use?

About 832 tokens (SKILL.md is roughly 3.3k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full. Its references folder adds about 882 tokens, read only when the agent opens those files.

What are the alternatives to Cs Foundations?

Skills that share tags, products or a category with Cs Foundations: Foundations Of Computational Mathematics (brycewang-stanford/Awesome-Journal-Skills, 1.2k stars), Mathematical Foundations (brycewang-stanford/Auto-Empirical-Research-Skills, 4.6k stars), Principle Foundational Thinking (cursor/plugins, 11k stars) and Moai Foundation Thinking (modu-ai/moai-adk, 1.2k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Cs Foundations?

foryourhealth111-pixel (a GitHub user) maintains it in foryourhealth111-pixel/Vibe-Skills, which has 3,627 GitHub stars. The repository holds 81 skills in this directory. The repository was last updated on August 31, 2026.

Source: foryourhealth111-pixel/Vibe-Skills on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.