JUST ENOUGH MATH
The minimum linear algebra and complex numbers needed to read a qubit equation — visually motivated, no proofs.
Vectors: Arrows That Describe Qubit States
Building vectors from scratch, and writing qubit states as columns of numbers for the first time.
Complex Numbers Without the Fear
The Argand plane, Euler’s formula, and why multiplying by i is secretly a 90-degree rotation.
Matrices as Machines That Transform Vectors
Matrix-vector multiplication, worked step by step, and your first look at a gate before it has a name.
What Makes a Matrix "Unitary" (Reversible)
The exact test for whether a matrix is a physically valid quantum gate, with full worked examples.
Inner Products: Measuring "How Alike" Two States Are
Generalizing the dot product to complex vectors, and defining orthogonality precisely.
Eigenvalues & Eigenvectors: The Directions a Matrix Doesn’t Rotate
Finally explaining why plus and minus states are named the way they are.
Probability Refresher: Expectation Value, Visually
From dice rolls to Pauli-Z expectation values, the single-number summary that variational algorithms optimize.
Dirac Notation Cheat Sheet: Reading Bras and Kets
A consolidated reference for every piece of notation introduced so far in this module.
Putting It Together: The Math Behind the Bloch Sphere
The capstone lesson: deriving the full qubit state formula and proving every claim from Module 1.