aadi.ink

If I referred to a date as “zeroth of March”, I bet it would make perfect sense for some but no sense for others. Dates are just arbitrary numbers assigned to each day. That’s not to say that there is no logic within them. Months are sometimes 30 days long, sometimes 31, and 28 once, except 29 every so often. However, within a particular month, adding one to today’s date is still, thankfully, tomorrow’s date.

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?