Dan's Math

Very few things in the world are as beautiful as Math. I'm interested in a lot of things (I'm a math major after all). Here, I share some of my thoughts on math and publish some of my work that might be somehow interesting.

My Articles (Drafts!)

Analytic Summation (pt.1)

The question was: given a sequence with a closed-form expression for its n-th member, when is it possible to give a closed-form expression for its partial sums? I started exploring this as I was 16, and in this paper, I have gathered some of my findings. Not all the ideas are brand-new, but there is one thing I would strongly suggest you looking at: The Cherry on Top Theorem (Theorem 4.0.3)

Analytic Summation (pt.2)

Here, I extend the main idea of an antiderivative sequence introduced in the first part. By introducing

Cliques

We define the concept of a special subset of vertices of an undirected graph called a clique and set the rules for when one can"jump" from one clique to another. Such a pair is called a move. An (ordered) sequence of cliques, such that every pair of adjacent cliques form a move, is called a good path if it satisfies specific properties that we define later. The goal is to establish when a good path is exists and, if so, how to construct it.