aadi.ink

An example of how generalisation is cool.

Suppose there are tiered discount rates: say $10\%$ up to $5000$, $15\%$ above $5000.$ Now suppose I need things that cost $b$ before any discount is applied. Assuming $b < 5000$, I get the 10% discount, having to pay $90\% \times b$. Could I perhaps add some more items to be eligible for the 15% discount and still end up paying less than $90\% \times b$?

$$4250 < 90\%\times b \iff b > \frac{4250}{0.9} = 4722.\bar{2}\ .$$

This inequality means that for initial (undiscounted) amounts of $4722.22$ or higher, adding exactly enough to reach 5000 will give me more stuff while costing less than the original.

Some advice I would give my past self

As part of an end-semester project, demonstrate filtration and resolving the Gibbs phenomenon by projecting onto a basis of Gegenbauer polynomials.

I had been trying to get into Lean. It’s an interactive theorem prover, and I’ve been curious about it since I first heard about it during a talk by Kevin Buzzard himself.

We were fortunate to have an in-person workshop about Lean recently and I have some notes! Let the lack of organisation and detail be a reflection of how little experience and knowledge I have of Lean. Be sure to keep that in mind while reading.

What is mathematics?

I was recently tasked to draw the Cayley diagram of the free product of $\Z_3$ and $\Z_4$. It looks quite nice and interesting, so why not put it up here?