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cs-foundations

Study the mathematics behind computer science through a structured learning path and practice problems. Covers logic, proofs, sets, functions, counting, and number theory, connecting these foundations to algorithm correctness and computational thinking.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

원문원문 설명 보기

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

foryourhealth111-pixel/Vibe-Skills

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설치 방법 보기

이럴 때 유용합니다

Learning the mathematics behind computer science
Practicing induction and proof by contradiction
Reviewing sets, functions, and counting
Preparing for mathematical interview questions

포함된 파일(5)

SKILL.md3.3 KB
assets/proof-template.md1.4 KB
references/PROOF-TECHNIQUES.md3.4 KB
scripts/proof_validator.py2.2 KB
scripts/verify-proof.py5.0 KB

SKILL.md(원문)

설치하기 전에 에이전트에게 전달되는 지시 내용을 확인할 수 있습니다.

CS Foundations Skill

Skill Metadata

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

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

Troubleshooting

Issue	Root Cause	Resolution
Proof stuck	Missing case or wrong direction	Check base case, verify induction step
Set operation confusion	∪ vs ∩ mix-up	Draw Venn diagram
Counting error	Overcounting duplicates	Distinguish P(n,r) vs C(n,r)
Modular arithmetic error	Forgot wraparound	Work 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

리뷰

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로그인 없이 쓸 수 있습니다. 사용 후기, 질문, 작동하지 않은 환경 등을 편하게 남겨 주세요.

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설치

명령으로 설치

npx skills add https://github.com/foryourhealth111-pixel/Vibe-Skills --skill cs-foundations

터미널에 붙여 넣고 실행합니다(Node.js 필요). Claude Code, Codex 등 설치할 에이전트를 고를 수 있습니다.

에이전트에게 부탁하기

다음 Agent Skill을 설치해 주세요.
https://github.com/foryourhealth111-pixel/Vibe-Skills/tree/main/bundled/skills/cs-foundations

먼저 SKILL.md와 첨부 파일의 내용을 확인해 수상한 처리(외부 전송, 인증 정보 읽기 등)가 없는지 확인한 뒤 Claude Code는 ~/.claude/skills/cs-foundations/, Codex는 ~/.agents/skills/cs-foundations/ 에 배치해 주세요.

이 문장을 그대로 Claude Code나 Codex에 보내면 내용을 확인한 뒤 설치해 줍니다.

GitHub에서 소스 보기

저장소: foryourhealth111-pixel/Vibe-Skills
스타: 3,760
포크: 341
카테고리: 리서치·학습
라이선스: Apache-2.0
원문 언어: 영어
최종 업데이트: 2026년 10월 23일

스킬은 에이전트를 위한 지시와 스크립트의 묶음입니다. cccskills는 내용의 안전성을 보증하지 않습니다. 설치하기 전에 내용을 확인하세요.