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.
