The Library
Guided tutorials for the mathematical ideas that are hardest to learn from a textbook alone. Each concept includes an interactive component, worked examples, and a self-check.
What is a Group?
A group is a set paired with an operation that satisfies four simple rules. Those four rules are powerful enough to describe symmetry, arithmetic, and much of modern mathematics.
Cayley Graphs
A Cayley graph makes a group visible. Given a group and a set of generators, it draws the group as a directed graph where each edge records the effect of applying one generator. The shape of the graph encodes the structure of the group.
Modular Arithmetic
Modular arithmetic is the mathematics of remainders — counting that wraps around after reaching a fixed modulus. It underlies nearly every cryptographic protocol, hash function, and digital clock you have ever used.