Math

I enjoy doing some math things in my freetime so I will be posting some here.

Math problems from the Pi Mu Epsilon Journal Problem Department:

I found out about these through my membership in Pi Mu Epsilon in undergrad and found out they post the problems publicly. Here are some of the problems I've done and a PDF of my work. Some PDFs are made in LaTeX, but a lot of them will just be handwritten documents:

Maximizing Batch Crafting in Febuary 2021:

A friend had asked me, if they had a list of items (and amount of each item) needed for crafting in a game and how large a stack of each item (amount of that item that can fit in one inventory slot) is, how many inventory slots are needed? And how many times can you do the crafting (how large of a batch can you prepare) with a certain amount of inventory slots? I did some math to find out the answers to these questions.

To compute the exact maximum batch size would require taking the summation of ceiling function, so I made an approximation. I did this using 2 different approaches. The first approach was just using an approximation function that removed the ceiling function. This eventually gave me an interval containing the maximum batch size.

The other method approximated the function directly with a Fourier Series. This method is limited in that the number of iterations needed to get an accurate approximation increases quickly when the number of items used in crafting increases, but I included it for completion's sake. In the amount of time spent waiting for the second method to compute (see how long this desmos graph takes to compute 1000 iterations to get enough accuracy for 5 items), you could easily do the first method and check each integer value for the correct maximum batch size.

Here are some examples using the first method: Batch Crafting Examples. And if you want to run this calculation yourself, I built a tool for it.