1. Big O Notation

Very short notes for the first chapter; not much to talk about.

Big O Notation seeks to estimate the runtime of the algorithm in terms of the input size. The main things to remember are...

• Constants don't matter
• If we have a series of multiple terms such as $n+n^{2}+n^{3}$, only $n^{3}$ matters, i.e. the most expensive time complexity
  Formally, let $f(n)$ and $g(n)$ be functions from $\mathbb{Z}^{+}\to \mathbb{R}$. Then, $f=O(g)\iff \exists c\in \mathbb{Z}^+$ that is constant such that $\forall n\in \mathbb{Z}^{+}$ we have $f(n)\leq cg(n)$.