# What's all this, then?

## Educational disciplines: size against market growth

Here is an interactive version of this diagram: (click on the image to show a larger version.)

## Tschirnhausen transformations and the quartic

Here we show how a Tschirnhausen transformation can be used to solve a quartic equation. The steps are: Ensure the quartic is missing the cubic term, and its initial coefficient is 1. We can do this by first dividing by the initial coefficient to obtain an equation $x^4+b_3x^3+b_2x^2+b_1x+b_0=0$ and then replace the variable $$x$$ with $$y=x-b_3/ 4$$. This will produce a monic quartic equation missing the cubic term.