Atok's Math Blog

For example, with x = 20 and y = 50:

20% of 50 is 10

50% of 20 is also 10

This holds true for any two real numbers x and y, and you can easily see why by simply looking at the definition of percentage:

It’s been like... 8 months since I last posted on this blog, whops.

Here’s what I’ve been up to since then:

Got my Bachelor’s degree in Mathematics-Economics!

Got a student job at a big energy trading company!

Started on my Master’s degree in Mathematics-Economics, specializing in Financial Engineering!

Passed all exams of the first semester!

Considering doing a PhD!

Moving in with my girlfriend in two months!

Feeling good!

I’d like to actually keep this blog more active from now on, as well as provide interesting posts (now and then), so I’m considering changing it up slightly by posting :

Updates from my semester project; I’ve been wanting to try making a summarized (perhaps interactive?), more accessible version of a project, to practice communicating math and data science

Updates from my courses; this semester I’m taking Data Mining, Quantitative Finance, and Bayesian Inference and Mixed Models ― maybe if we learn something particularly interesting, I could post about it

Stuff related to R (the programming language)

Ideas?

I don’t think I’ll have very much time for providing math help, so don’t expect immediate answers if you inbox me (you’re still very much welcome to ask questions anyway, of course).

I’m currently halfway through my exams; nailed both Time Series Analysis and Financial Engineering, but next up is Spatial Statistics, and I’ve not been this nervous about an exam since Analysis I...

If you’ve seen this image:

(likely with comments such as “why didn’t we learn this in school!?”), perhaps you’ve wondered which numbers this would work for, and why. 

It turns out to be a result of simple algebra that works for any two numbers, as long as you’re interpreting the method correctly.

The image explains very little, but algebraically here is what’s happening:

So with the numbers used in the image, it looks like

Basically, by expressing two numbers as a difference from 100, their product can be calculated in a way that’s easy to do in your head. Be careful though; from the image, one might thing you’re just concatenating the red and the blue parts of the number, but you’re actually adding them together.

As I said above, it works for any a and b. For example, we could choose a = 105 and b = 5 and get

That said, since the purpose is to make it easier to calculate, it’s limited which values this method is actually practical for.

Hmm, I’m not really sure, but it could sound like you’re evaluating something else than the line integral, since you’re fixing y and integrating only wrt x.