My second to last semester in University

Writing this title, all of this is quite surreal to me. I mean, of course I know and have planned for it to be that way, but still.

Anyhow, so a semester has passed, somehow and now I am already doing the introductory and preparatory projects for my master’s thesis.

But before that, maybe a little retrospective as to how I found the university.

A little Review of the University of Hamburg

In one sentence, I would say that the university in Hamburg basically gave me the most important thing of what I wanted (in terms of studies), but not much more.

So, my main goal obviously was to learn more graph theory, as I have - more or less - taken all the graph theory classes that were given in my old university. I would say that I mostly got that. I have great teachers here and it is undeniable that the university is great for discrete math as a whole.

Although, and this is my first point, I guess I didn’t expect discrete math here to be that different to what I am used to in Karlsruhe. Don’t get me wrong, this is not some sort of judgement or gatekeeping as to what counts as discrete math, but the fact of the matter is that the flavour of discrete math I am used to is mostly extremal with some algorithmic and structural touches here and there. Frankly, I thought that was most of it. Like, okay, you can get down the combinatorial optimization route but to me that falls under algorithmic. But with the discrete mathematics I am presented here, I feel like this is only of many things that they study here.

I mean, okay, I only took two classes last semester by people who mainly do extremal and probabilistic combinatorics, so right up my alley. And I really, really enjoyed those courses as well. However, looking at my seminar on matroid theory (a field by the way that I was completely unfamiliar with) and the homepages of the other discrete math people, I feel somewhat alienated. I don’t even really know what you would do in topological graph theory, infinite graph theory, tangles and all those other more structural things they’re specializing in.

And I didn’t expect that I needed to know category theory in a seminar on matroid theory, but there you go.

It is quite wild, and due to my time here being somewhat constrained (mainly by myself and how the master is structured here), it will remain a bit of a mystery for me now, and I will probably never take a lecture by Diestel. :(

Maybe just to emphasize my point, Schacht and Reiher have their own research seminar that is really only on extremal and probabilistic combinatorics. Yes, while under the discrete math group, they are not in any way representative for the discrete math work group here.

Okay, now aside from discrete math, I also have to say that I find the in-depth phase is really short. I mean, I had already started my master’s at KIT, but after one semester here in Hamburg I am now nearly done with taking courses. And I didn’t pick that many courses either, at least not for examination. Point is that I looked forward to broaden my horizon with the math I know but I feel like this kinda backfired. I am now a bit more competent in combinatorics and have my logic basics down again. But I am still fairly iffy with analysis (I still don’t know much about PDE’s, functional analysis and the rest there), and I couldn’t really deepen my knowledge in probability theory.

And that’s the other thing with this university: It may be the best place in Germany for discrete math, but even here that work group is by far not the biggest work group in the department. Actually, the main focus of the math department actually seems to be algebra (especially in connection to physics) and differential geometry. Not much analysis courses are given and the probability courses here aren’t my cup of tea. That’s when I really miss KIT because there they had fairly good courses in probability theory.

As for the learning conditions, ugh… This is not a hot take, but the Geomatikum is hideous. It’s not a welcoming place to learn, has way too few places for people to study and needs a renovation. Although, really, I think at this point constructing a better building would probably be more efficient.

Also, I feel like this university is on the one hand more chill, on the other hand less chill than KIT. There is no real course catalogue listing all the courses one could possibly take and the professors here feel like they are allowed to be less organized. The courses give in general more points than what I would expect at KIT and the professors are - on average - much more chill. But, they also have less grudges to give you a lot of work. I heard what sounded like horror stories from me about classes where the lecturer is the nicest person ever that really wants everyone to be able to follow the lecture, but also expects you to know like whole bunch of things (or I guess speedrun learning category theory for the lols) that then cumulate in an eight hour exam. Like what the hell, what?

Anyway, this has gotten way too long. So, now onto what I want to take.

New semester, new courses

The first week has passed and I will probably stick to the following classes

1. Extremal Graph Theory (EGT),
2. Introduction to Ergodic Theory (ItET), and
3. Computability, Decidability, and Incompleteness (CDI).

The first one really serves to prepare me for the master’s thesis and is also by Schacht. The latter two are more like smaller courses for me to dabble in other things. Ergodic Theory kinda sounded fun, is one of the ways to prove Roth’s Theorem, is used in probability theory, so I guess why not. And the latter is like a greatest hits compilation of the most important results in computability theory (I do miss me some theoretical computer science) and logic from what it looks like (although I guess the class should really be called Recursion Theory apparently).

All of those classes seemed fun up until this point, all of them fairly excited to teach their subject. The downside is however, that there are no lecture notes. For CDI, this is not really a problem, the handwritten notes seem good enough, but for the other courses I plan to write my own notes in - you guessed it - LaTeX. I have (hopefully) found some people to write the notes with. Either way, it’s not too bad (yet). After all, this is a lot less course work than last semester, as I try to focus on the courses that I really want to take instead of starting with a whole bunch of courses to only drop them.

I will also be doing a seminar on extremal and probabilistic combinatorics by Schacht. It will revolve around just one conjecture, and we are only five people, so it should be fun. \s

Seriously though, I guess the upside is that Schacht chose so few papers such that I won’t have to give multiple talks like last time.

Lastly, as part of my preparatory and introductory project I will also be studying and discussing a paper with Schacht (see a pattern?). I have to choose from two fairly cool papers, one about a first exponential improvement in the diagonal Ramsey number, and one about a basically tight bound for AP3-free sets of $\mathbb{N}$.

I think I will probably take the second one, because the methods involved seem fairly interesting.

A (more personal) shoutout

As I have quite a lot of time at the moment, I spontaneously decided to go to a concert on the fifth of April by Paul Beskers, who was actually at the same school as I was. We even shared a club together, the so-called Kompositions-AG. Good times. Anyway, it was a great concert at the JazzHall and I hope to go there more often! In general, I am looking forward to going to some cool concerts, the next probably in the Feldstraßenbunker where on the 19th of April Godspeed You! Black Emperor will be playing!