# Articles by tag: math

I took many notes throughout my undergraduate degree in mathematical physics at the University of Waterloo. Once I finished my last exam, I decided to digitize all of my notes and discarding the physical copies. Below, you can find all my notes from all of my classes at the time.

Differential analysis using sequencing data is, at its heart, a very simple idea that involves a lot of complicated statistics. It makes explaining the simple idea to newcomers in bioinformatics very difficult. Here, I want to break down the motivation behind differential analysis and explain where the complicated statistics come from.

The Central Limit Theorem is a pillar of statistics. We can apply the proof of the CLT to understand how different estimators converge in distribution with large sample sizes.

Mathematical notation is a signature of math. Almost anyone can recognize it instantly, even if they don't know what it is. I want to talk a bit of why notation is useful, why it can be confusing, and tackle some examples in statistics that are often confusin with some clear notation.

Some thoughts about what I'd like students taking the biostatistics course I'm TA'ing to take away from the class.

A brief look at potential functions in 3 dimensions, and how Poincare's lemma can make it easier to solve for vector potentials.

How incomprehensible machine learning models answer questions without providing the solutions we desire.

Why are definitions important, and what makes them "good"? Here I focus on is the topic of definitions being "good" and "well-defined" and how to ask good quantitative questions in biology.

There are many reasons to be excited about scientific progress in the biological sciences, especially if you're a mathematician of almost any kind.

I want to highlight how clever the derivation of Tajima's statistic is, and a great idea he puts forward in his 1989 paper.

"Read coverage" in high throughput sequencing is a bit of an ambiguous term. Here, I make the argument for using the analogous term "support", coming from set theory and its interpretation.

A video project for my fluid dynamics class in undergrad.

A summary of my Undergraduate Summer Research Assistant term in 2015 studying Hamiltonian fluid dynamics.