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 counts how many times you multiply a number by itself. So 2^3 means 2 × 2 × 2 = 8. That one 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 share of times an outcome shows up when you repeat something many times. Two rules cover nearly everything in this course. 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. Because of that, two amounts can cancel to zero. Planned cancellation is the trick every quantum algorithm runs on. The number i adds a brand-new direction. It turns the number line into a flat map of arrows, called complex numbers.
An angle measures how far something has turned. A radian measures it by the distance you walk 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. One plain rule — RY uses half the angle you give it — lets you predict a real measured histogram exactly.
A vector is just a list of numbers in a fixed order. A qubit's state is a two-number list of amplitudes. The list must obey one rule: the squares of its entries must add up to exactly 1. That rule is just "the chances must total 100%" in disguise.
Multiply by the same number again and again, and small changes get huge. 1.01 multiplied by itself a hundred times is about 2.70. And 0.99 multiplied by itself a hundred times is about 0.37. That second number rules quantum computing. If every gate works 99% of the time, a 100-gate circuit runs with no mistake only about 37% of the time. That is why error correction exists.