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...
Advanced Topics

Number Theory

Exploring Numbers

Number theory is the study of properties of numbers, especially integers. It explores concepts like prime numbers, divisibility, and greatest common divisors.

Key Concepts

  • Prime Numbers: Numbers greater than 1 with exactly two positive divisors: 1 and itself.
  • Greatest Common Divisor (GCD): The largest number that divides two numbers without a remainder.
  • Modular Arithmetic: A system where numbers "wrap around" after reaching a certain value (the modulus).

Applications

Number theory forms the basis for cryptography, computer security, and digital communications.

Fun Fact

Many famous problems, like the Goldbach Conjecture, are unsolved mysteries in number theory!

Examples

  • Using modular arithmetic to determine if a number is even or odd.

  • Finding the GCD of 24 and 36 is 12.

In a Nutshell

Number theory studies the properties and patterns of integers, with deep applications in cryptography and computing.

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Cryptography and Security