# Hacker Calculus

Understanding Math Rather Than Merely Learning It

# Imaginary Numbers

FINAL EPISODE (13) – Riemann Complex Plane : 4 dimensions but viewed in 3 dimensions

Example:

$\boxed { f (z) = z^2 + 1, z \in \mathbb {C}}$

Episode 1 – 9 : History

Episode 10: Complex function

Function : 1 input mapped to 1 output.

Multi-function : 1 input mapped to (n > 1 ) outputs.

# Mathematician Couple’s Wedding Math Questions

It is fun for the guests who are also mathematicians like the wedding couple…

Why don’t the IT couples do the same with computer questions (eg. private cloud, serverless, containers, DevOps,… ) , lawyers with legal cases, doctors with medical questions …

Example 1 is obvious to this guest whose PhD research topic is in Differential Geometry “Chern Class” invented by Prof S. S. Chern (陈省身) :

Example 2 is obvious to this guest unless he/she can’t count the number of sides (8):

Example 3 is to the guest with some background in secondary school organic chemistry but forgotten, definitely not linear…

Example 4 to the hobbyist of Rubik’s cube, but the answer can be guessed easily by elimination: definitely not 2019 (this year), or π.

Answer in multiple choices (Only 1 answer is correct, the other 2 answers are obviously wrong) :

# The Error Function & The Integral of e^(-x^2)

$\boxed{ \displaystyle erf(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} {e^{-{t}^2}dt}}$

The Bell Curve:

$\boxed{\displaystyle y = e^{-x^2}}$