Discrete Math

Study of mathematical structures that are fundamentally discrete rather than continuous.

Set TheoryLogic and ProofFunctions and Relations
Graph TheoryCombinatoricsNumber Theory
Cryptography and SecurityNetwork AnalysisScheduling and Planning
Breaking Down ProblemsUsing Visuals and Diagrams
Set TheoryLogic and ProofFunctions and Relati...Graph TheoryCombinatoricsNumber TheoryCryptography and Sec...Network AnalysisScheduling and Plann...Breaking Down Proble...Using Visuals and Di...
Basic Concepts

Functions and Relations

Functions

A function is like a machine that takes an input and produces exactly one output. In discrete math, functions help describe how elements from one set are related to elements in another.

Relations

A relation shows how elements from two sets are connected. For example, "is taller than" is a relation between people.

Properties of Functions

  • One-to-One (Injective): Each input has a unique output.
  • Onto (Surjective): Every output value is used.
  • Bijective: Both one-to-one and onto.

Importance

Functions and relations help us organize information, model processes, and solve real-world problems in computer science and data analysis.

Examples

  • Assigning a student to their unique ID number is a function.

  • 'Is a sibling of' is a relation among people.

In a Nutshell

Functions connect inputs to unique outputs, while relations describe connections between elements from sets.

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Graph Theory