Continuing from my previous post, we are in the middle of proving that satisfies the same equation as , that is,

and that therefore for all , that is, is the sum of all the th primitive roots of unity. 1,033 more words

Continuing from my previous post, we are in the middle of proving that satisfies the same equation as , that is,

and that therefore for all , that is, is the sum of all the th primitive roots of unity. 1,033 more words

Recall in part one I mentioned the root spiral and prime numbers. I won’t go into the history of how they came about (other than mention that Mr. 396 more words

Kelsey Houston-Edwards is making a series of math videos and the first two are outstanding. We looked at the first one last week:

Sharing Kelsey Houston-Edward’s video with kids… 114 more words

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post.

When I was researching for my… 311 more words

Let’s begin with one of the oldest and most fundamental results in mathematics: there are infinitely many prime numbers. If you’re not aware of what primes are, I’m surprised to find you here. 533 more words

These are the notes of my last lecture in the 18.099 discrete analysis seminar. It is a very high-level overview of the Green-Tao theorem. It is a subset of… 1,065 more words

Let denote the number of positive prime numbers that are less than or equal to . The prime number theorem, one of the most celebrated results in analytic number theory, states that… 284 more words