OpenAha
00
All courses
Math · Foundational

Number Theory

Whole numbers hide a surprising amount of structure. Sift out the primes, prove there are infinitely many, learn fast divisibility tricks, master Euclid's 2300-year-old algorithm, solve coin puzzles, discover Fermat's little theorem and the check digits on every barcode, and see how clock arithmetic keeps the internet secure.

9 lessons~50 min0/9 complete
1

Primes

The atoms of arithmetic.

  1. Building BlocksPrimes and factorization
  2. Finding PrimesThe sieve, and infinitely many primes
2

Divisibility

Shortcuts and the greatest common divisor.

  1. Divisibility TricksTest without dividing
  2. Euclid’s AlgorithmGreatest common divisor
  3. Coins & StampsWhich amounts can you make?
3

Modular Arithmetic

Arithmetic on a clock.

  1. Clock ArithmeticRemainders that wrap around
  2. Fermat’s Little TheoremPowers that come back to 1
  3. Check DigitsCatching typos with arithmetic
  4. Secret CodesFrom Caesar to RSA

Courses that build on this

Ready for more? These courses use what you learn in Number Theory.

Math · Intermediate

Cryptography

Crack ciphers with statistics, then build codes that even computers can’t break.

7 lessons3 chapters
Math · Intermediate

Continued Fractions

The secret behind 355/113, leap years, musical scales, sunflowers, gears and eclipses.

7 lessons3 chapters
Math · Advanced

Prime Patterns

How primes thin out, the patterns they make, how to test them, and famous unsolved problems.

7 lessons3 chapters