Course 1 · Module 1
Number Theory
This module covers the branch of mathematics that studies whole numbers: which ones divide which, how they factor into primes, and what happens when you count in a loop the way a clock does. You'll be able to reason about divisibility and remainders, follow Euclid's 2,300-year-old proof that the primes never run out, and see how the same ideas now protect every online payment. Number theory is the clearest case in mathematics of questions asked for their own sake turning out to matter enormously.
Module objectives
- Use divisibility and modular arithmetic to reason about whole numbers, including why there are infinitely many primes.
- Explain how number theory secures digital communication and why questions about primes remain open.
Lessons
- Lesson 1 Number Theory: Primes, divisibility, and Euclid's proof that the primes never run out You'll meet the oldest branch of mathematics still being actively researched: the study of whole numbers. You'll work with primes, factorization, and remainders, and you'll follow… 61111h 3m
- Lesson 2 Number Theory: Codes, cryptography, and the Riemann Hypothesis You'll see how the arithmetic of primes and remainders now protects online payments and catches typing errors in book numbers. You'll also meet the questions about primes that… 611111h 33m