# 1: Mathematical Background

- Page ID
- 16513

- 1.1: Complex Numbers
- The mathematics of harmonic functions such as those used to describe waves of all kinds is intimately tied to complex numbers. We review the basics of this area of mathematics.

- 1.2: Vector Algebra
- We review a fundamental mathematical element of quantum states by comparing the infinite-dimensional vector space known as a Hilbert space with the familiar finite vector space we have used since classical mechanics.

- 1.3: Probability & Statistics
- Quantum mechanics is an inherently probabilistic science, so we take some time in this section to (re)familiarize ourselves with some of the basic tenets of probability and statistics.