Have you ever tried to perfectly pack a suitcase to avoid going over the weight limit? That’s similar to the challenge I faced for my university project – fitting scientific experiments into a high-altitude balloon without exceeding its capacity.
Instead of clothes and souvenirs though, I had to pack equipment like spectrometers, imagers, and detectors. The goal was to launch atmospheric research experiments 20+ miles into the sky without the balloon breaking apart!
When planning a new shopping mall, where should you place the most popular stores? Getting the layout right is crucial so friends can easily shop together across their favorite spots. I helped mathematically optimize this for a client using an integer programming approach.
The problem has some key details. There are 4 sought-after stores that each need to be assigned to one of 4 vacant mall locations. The distance between each spot is known.
In my applied mathematics work, I often want to approximate complex functions with simpler ones that are more tractable to analyze. One common technique is to use a Taylor series expansion. This approximates a function as an infinite sum of terms involving the function’s derivatives at a point.
In my latest research, I investigated using higher order Taylor series, specifically up to the fourth derivative, to approximate the derivative of the cosine function.
Remember the story of Goldilocks and the Three Bears? Papa Bear, Mama Bear, and Baby Bear each had their own bowl of porridge. Now imagine the Three Bears started a porridge company! As their assistant, I helped them determine the optimal production plan to meet customer demand over the year while minimizing costs.
This may sound like a fun fairy tale problem, but it draws on some sophisticated operations research concepts!