Math toolkit
Short refreshers on the mathematics the course leans on, each with practice questions and answers. The lessons link here exactly where each one is needed.
Complex numbers
Magnitude, phase, and why a phase factor has size 1
Vectors and normalization
Kets are column vectors; probabilities must add to 1
Inner products and bases
⟨φ|ψ⟩, orthogonality, and |⟨φ|ψ⟩|² as a probability
Matrices acting on states
Gates are matrices; circuit order vs matrix order
Tensor products
Combining qubits: |a⟩⊗|b⟩ as a 4-entry vector
Angles on a sphere
Spherical coordinates, and why the Bloch sphere uses θ/2
Bits, XOR and bit strings
x ⊕ y, x · z mod 2, sums over {0,1}ⁿ, and signs that depend on f(x)