Number Theory

The queen of mathematics: prime numbers, modular arithmetic, quadratic reciprocity, Diophantine equations, and the arithmetic that underpins modern cryptography.

Course Overview

Textbook

Niven, Zuckerman & Montgomery, An Introduction to the Theory of Numbers

Chapters

TBD

Sections

TBD

Prerequisites

Abstract Algebra I

Target

Deeper cryptographic understanding, Algebraic Number Theory

Status

Planned

Chapters will be scaffolded when this course becomes active.

Why This Course

  • Cryptography — RSA, primality testing, discrete logarithm are number theory

  • Hash functions — modular arithmetic governs collision resistance

  • Key exchange — Diffie-Hellman is modular exponentiation

  • Post-quantum crypto — lattice-based schemes use algebraic number theory

  • Intellectual depth — Fermat, Euler, Gauss, Riemann all worked here