Examining the Mathematical Formalism of Quantum Mechanics

This is a primer on the mathematic foundation of quantum mechanics. It seeks to introduce the topic in such a way that it is useful to both mathematicians and physicists by providing an extended example of abstract math concepts to work through and by going more in-depth in the math formalism than would normally be covered in a quantum mechanics class. The thesis begins by investigating functional analysis topics such as the Hilbert space and operators acting on them. Then it goes on to the postulates of quantum mechanics which extends the math formalism covered before to physics and works as the foundation for the rest of quantum mechanics.