Quantum mechanics without all the physics

I'll try to explain to you what quantum mechanics is about, without any regard to the real world. You'll need to know how to multiply matrices (and be willing to hold onto your hat). Depending on how we go, I'll tell you about Bell's inequality and quantum probability, make disparaging comments about physicists (it's okay, some of my best friends are physicists), and encourage you to learn about von Neumann algebras.