# Posts

### The Power of Simulation

I’m reading a book that deals with the history of probability theory (Classic Problems of Probability by Prakash Gorroochurn). It is …

### Average Logarithms and the Geometric Mean

I recently came across a surprising connection between the geometric mean and logarithms. At least, it was surprising to me, but isn’t …

In a previous post, I said that an appropriate purgatory for physicists would be to have them read all of the words ever written on the …

### Approximating the Geometric Mean

In my last post, I discussed the geometric mean and how it relates to the more familiar arithmetic mean. I mentioned that the geometric …

### The Geometric Mean

Given two positive numbers $$a$$ and $$b$$, the most well-known way to average them is to take the sum divided by two. This is often …

### Symmetric Difference

I was recently flipping through a real analysis textbook, and came across a notation that I had not seen before. First, the set …

### The Probability Current

Probability Current in Quantum Mechanics In nonrelativistic 1D quantum mechanics, consider the probability of finding a particle in the …

### EPR Mistakes

I am teaching undergraduate quantum mechanics for the first time this semester. One thing I have discovered is that it is very easy to …

### Lines in the Complex Plane

What is the equation of a straight line in the complex plane? There are many different forms, but I want to look at some of the …