We give the example of (affine) group schemes to demonstrate the importance of the Yoneda Lemma. In part 1, we discuss how basic matrix groups relate to algebras via representable functors.

# Math in unconventional places

A short essay about spending time with mathematics in places that you wouldn't expect at first.

# I think I am Asian.

What does it really mean to be Asian or American or German? Are you European-American? German-Asian?

# A digression on categorical notions

A familiar functor from analysis, why rings should have a 1 and intuition on the equivalence of categories.

# What the Coronavirus means for Exchange Students

With the pandemic surrounding the Coronavirus going on, literally everything has been pulled from the ordinary. A small affected group would be the exchange students to whom I relate very dearly and so this essay is dedicated to everyone who ever was, is or will be an exchange student.

# Difficult Books and the Separable Closure of Finite Fields

Still now, I am trying to optimize the ways to study mathematics. One things that has changed for me in recent days is that I'm trying to take up more challlenging books. Now, I occasionally need up to one hour to understand a single page. This blog entry is about some of my experiences with this and a little fact about finite fields.

# Infinite Galois Theory

Once upon a time, we studied finite Galois theory. Now is a time to advance to infinite Galois theory.

# The 90th Theorem

Hilbert's Theorem 90, a classical application on cyclic extensions and an unexpected application in number theory.

# On the Structure Theorem of Finitely Generated Abelian Groups

We talk about the classification of finitely generated abelian groups and a uniqueness result that a friend and I struggled on.

# The bad, but the good.

Studying Abroad #6: Always see the good in the bad. Even when you're saying goodbye to the best time of your life.