# Articles by tag: math

Limit of a t distribution

I like to write some proofs when I have need of them but have a hard time tracking them down. Here is one about the limit of the t distribution with infinite degrees of freedom.

Notes from a mathematical physics degree

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.

What is differential analysis, anyway?

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 and estimation of variance

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.

Notation and thinking in math

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.

Teaching stats for statistical thinking

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

Anti-curl and Poincare's lemma

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.

Well-defined biology

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.

Now is an exciting time for mathematicians in the biological sciences

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

The cleverness behind Tajima's D statistic

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

"Support" over "coverage"

"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.

Visualizing layered fluids in a rotating reference frame

A video project for my fluid dynamics class in undergrad.

Quasi-geostrophic models and Hamiltonian dynamics

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