Enumerating Binary Strings Without K-Runs of Ones

by JT Cho

Despite having studied mathematics and computer science for quite some time now, I am still amazed to this day at how the two fields can intersect in profound and unexpected ways. This post expounds upon one such case, examining how solving a seemingly simple enumeration problem algorithmically convolves interesting mathematical . . .

Survey of the Fibonacci Matrix

by JT Cho

Back in my high school linear algebra class, I briefly ran into a construct known as the Fibonacci Q-Matrix. At this point I had not discovered recurrences and was pretty astonished that this magical matrix power could produce values of the Fibonacci sequence. For casual readers, a basic knowledge of . . .

Covariance Method for Principal Component Analysis

by JT Cho

I've been working on a couple of side projects recently, so I haven't had much time to do any math or CS related blog posts. However, in my research for a planned side-project involving Self Organizing Maps, I came upon a concept I had seen once before a long time . . .

Trigonometry of Correlation I

by JT Cho

I always find it super cool when recognizing key parallels between different branches of mathematics serendipitously. It allows me to employ techniques I have learned in other classes to derive valuable insight in a new topic, which sometimes (not always) makes the learning a bit easier. Today I will discuss . . .