Mathematics Abound

The Quantum Mechanical Harmonic Oscillator In my research, I've been working on a generalization of the quantum mechanical harmonic o...

The Fourier transform arises in many different ways. Historically, it first arose as a sort of limiting procedure for Fourier series. Th...

One question which comes up quite frequently regarding the complex numbers is: why do we define them and their operations the way we do? Ev...

Some months ago, I found myself wondering about abstract sets and how exactly we can put group structures on them. Groups are often pres...

In a previous post, I constructed the split-complex numbers in a somewhat handwavy fashion. It went as so: suppose $j$ is a solution to $x^...