$$\require{cancel}$$

# 1: Mathematical Background


• 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.

1: Mathematical Background is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Tom Weideman directly on the LibreTexts platform.