---
id:"kb-2026-00204"
title:"Discrete Mathematics"
schema_type:"TechArticle"
category:"computer-science"
language:"en"
confidence:"high"
last_verified:"2026-05-22"
generation_method: "human_only"
ai_models:["claude-opus"]
derived_from_human_seed:true


known_gaps:
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completeness: 0.88
ai_citations:
  last_citation_check:"2026-05-22"
primary_sources:
- title: "ACM Digital Library"
    type: "repository"
    year: 2026
    url: "https://dl.acm.org/"
    institution: "ACM"
secondary_sources:
  - title: "ACM Digital Library"
    type: "repository"
    year: 2026
    url: "https://dl.acm.org/"
    institution: "ACM"
---

## TL;DR

Discrete mathematics studies countable, distinct (not continuous) structures. It is the mathematical foundation of computer science — covering logic, sets, combinatorics, graph theory, and number theory. Unlike calculus (continuous), discrete math deals with integers, graphs, and logical statements.

## Core Explanation

Combinatorics: counting, permutations (P(n,k) = n!/(n-k)!), combinations (C(n,k) = n!/(k!(n-k)!)). Pigeonhole Principle: if n items in m containers and n > m, at least one container has ≥2 items. Proof techniques: direct, contrapositive, contradiction, induction. Induction: prove base case P(1), then P(k) → P(k+1).

## Further Reading

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