When I studied Measure Theory I learnt it in an axiomatic way, lacking context for why the notion of $\sigma$-algebras was introduced and how they arose in the first place. In this post I want to disp...

This post is about Hilbert's basis theorem and the Nullstellensatz (theorem of zeros), which together form the foundational results of commutative algebra––the algebraic part of algebraic geometry––an...

I wanted to brush up on some algebra I had studied several years back which has by now inadvertently dampened with neglect. I'll start from the basics and build up to the Fundamental Theorem of Finite...

Proofs are hard, machine learning is easier, college is over. I still feel dumb, still feel full of myself, here we go. This post about an application of the heat flow equation to ML. Uh... you'll see...

In this post I'll use elements from local theory of curves and surfaces to arrive at Gauss's remarkable theorem ("Theorema Egregium") and highlight the significance of the distinction between intrinsi...