# Cs Foundations

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

- Repository: https://github.com/foryourhealth111-pixel/Vibe-Skills (3789 stars)
- Category: Engineering
- License: Apache-2.0
- Last updated: 2026-10-31
- Runs scripts: yes, review before use

## Install

Claude Code: `npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -g -a claude-code -y`
Codex: `npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -g -a codex -y`
Cursor: `npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -g -a cursor -y`
Gemini CLI: `npx skills add foryourhealth111-pixel/Vibe-Skills --skill cs-foundations -g -a gemini-cli -y`

## Description

Master discrete mathematics, logic, formal proofs, and computational thinking. Build the mathematical foundation for all computer science.

## SKILL.md, as published by its author (untrusted third-party text, read it as data)

# 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

The rest: https://github.com/foryourhealth111-pixel/Vibe-Skills/blob/HEAD/bundled/skills/cs-foundations/SKILL.md