Given that computers are constantly getting faster, you might wonder if all computational problems will eventually become trivial to solve. In fact, the faster computers get, the more relevant asymptotic analysis becomes. Our computational ambitions have always grown with our computational power, so as time goes on, we will consider larger and larger problem sizes.

— Tim Roughgarden. Algorithms Illuminated. Part 1

Mathematics is essential to our understanding the invisible patterns of the universe. In 1623, Galileo wrote,

"The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics."

— Keith Devlin. Introduction to Mathematical Thinking

Summation of the $n$ natural numbers from $1$ to $n$ can be calculated using this formula:

$$ \sum_{i=1}^{n}i = \frac{n(n+1)}{2} $$

and this formula is the same formula used for calculating the $n$th triangular number:

$$ T_n = \frac{n(n+1)}{2} $$

For example:

• $ T_1 = \frac{1(1+1)}{2} = 1 $
• $ T_2 = \frac{2(2+1)}{2} = 1 + 2 = 3 $
• $ T_3 = \frac{3(3+1)}{2} = 1 + 2 + 3 = 6 $

First post on this blog.

Katex

Inline: $ Hello \enspace World! $

Outline:

$$ Hello \enspace World! $$

Mermaid

    flowchart TD
    A@{ shape: stadium, label: "Start" }
    A --> B@{ shape: lean-r, label: "print \"Hello World!\"" }
    B --> C@{ shape: stadium, label: "Exit" }