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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.
Your progress
4 lessons
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.
The course — start at lesson one
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.
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