Topic · in development — big ideas below
Discrete mathematics
The mathematics of steps, networks, and code.
Calculus studies smooth, continuous change. Discrete math studies things that come in whole pieces: yes/no decisions, network connections, countable arrangements. It's the native mathematics of computers — which can only ever count.
The big ideas
Logic is algebra on true and false
AND, OR, NOT follow laws as exact as arithmetic. Every circuit and every if-statement is built from them.
Graphs model relationships
Dots and connections — friendships, road maps, the internet. A shocking number of hard problems become walks on a graph.
Counting without listing
How many possible passwords? Poker hands? Routes? Combinatorics counts astronomically large sets with a few clean principles.
Induction climbs infinite ladders
Prove a fact for step one, prove each step hands you the next, and you've proven it for all infinity of them — recursion's mathematical twin.
Out in the world
Route finding
Maps apps run shortest-path algorithms on road graphs — discrete math, billions of times daily.
Cryptography
Online security rests on number theory: primes, modular arithmetic, and problems that are easy one way, hard backwards.
Databases & scheduling
Query planning, deadlock detection, and exam timetabling are all graph problems.
The planned course
- 01Logic & proofTrue, false, and how to be sure.soon
- 02Sets & functionsThe vocabulary of collections.soon
- 03CountingPermutations, combinations, and the art of not listing.soon
- 04Graph theoryNetworks, paths, and the bridges of Königsberg.soon
- 05Recursion & inductionSelf-reference, tamed.soon
- 06Number theory basicsPrimes, remainders, and the math inside encryption.soon
While you wait — this connects to material that's live now