The Math You Actually Need
Course 0: every piece of math the curriculum uses, from powers and probability to complex numbers, radians, and exponential decay — taught from zero, with a real quantum circuit to run in every chapter. Entirely free.
An exponent is a count of repeated multiplications: 2^3 means 2 × 2 × 2 = 8. That single idea explains the most important number pattern in quantum computing — every qubit you add doubles the number of possible readouts, so n qubits give 2^n outcomes.
A probability is the fraction of times an outcome shows up when you repeat something many times. Two rules cover nearly everything in this curriculum: chances of either-or outcomes add, chances of independent events multiply — and the count you expect is just probability × number of tries.
A negative number is an amount with a direction attached, which lets two amounts cancel to zero — and engineered cancellation is the trick every quantum algorithm runs on. The number i adds a brand-new direction, turning the number line into a plane of arrows called complex numbers.
An angle measures how far something has turned, and a radian measures it by the distance walked around a circle of radius 1 — a full turn is 2π, about 6.283. Quantum gates turn a qubit's state by angles like these, and one plain rule — RY uses half the angle you give it — lets you predict a real measured histogram exactly.
A vector is nothing more than a list of numbers in a fixed order, and a qubit's state is a two-number list of amplitudes. The one rule the list must obey — the squares of its entries must add up to exactly 1 — is just "the probabilities must total 100%" in disguise.
Multiplying by the same number over and over makes growth explode — 1.01 a hundred times is about 2.70 — and makes decay collapse: 0.99 a hundred times is about 0.37. That second number rules quantum computing: if every gate succeeds 99% of the time, a 100-gate circuit runs perfectly only about 37% of the time, which is why error correction exists.