Tags » Primes

The Möbius function proof, part 2 (the subset parity lemma)

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


Number Spirals Part 2

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

Sharing Kelsey Houston-Edwards's philosophy of math video with kids

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

What I Learned by Reading "Gamma: Exploring Euler's Constant" by Julian Havil: Index

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


Topological proof of infinitude of primes

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


A Sketchy Overview of Green-Tao

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


What I Learned from Reading "Gamma: Exploring Euler's Constant" by Julian Havil: Part 17

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