# Week 1 – New, New, New

University is entirely different from school. I’ve survived my first day and first week. In the meanwhile, I observed a lot.

## Social Aspects

In my eyes, the most important part in early stages at uni is to socialize. I’d like to make new friends. That’s going to be more and more difficult in the future when people are familiar with each other.

As an introverted and shy person myself, I tried my best. I learned what it’s going to be like.

• It’s difficult to make friends in lectures. Usually, I can engage in superficial small-talk before the lecture starts. However, that’s it. Talking during the lectures almost didn’t happen. When the lecture ends, we all scatter. As there are hundreds of students, it’s difficult to meet the same person again – so how should we connect?
• Mathematicians and physicists are all introverted. At least most of them! I experienced that I have to initiate. Many people just don’t talk a lot or are too shy.
• People are usually only involved in their practice group. We’re divided into small groups of at most 15 students. In those, we would then try to solve the problem sets and stick together in practice sessions. No surprise that each of these groups would form some sort of closed society. You are much more familiar with these people than anybody else.

That’s a problem. The barbeque we had on Wednesday was “advertised” as the perfect opportunity to make new friends. What happened was quite the opposite. Most people only spent time in their practice groups. How should we meet new people like this?

It would probably be better to mix up the groups from time to time.

University has just started – so I’m still striving to get to know more people!

## Food

What to have at lunch? There are many possibilities. Here’s what I did.

• Day 1: Fried Asian Noodles. Apparently what most math students get. It’s quick and only a few steps away from the math building.
• Day 2: Fried Asian Noodles. Why not? It was good.
• Day 3: Fried Asian Noodles. Yeah… I guess you can see a pattern. Today we didn’t watch our time and therefore needed a quick meal.
• Day 4: Canteen. Yup, you read correctly. Not Fried Asian Noodles. We decided that a variation would be nice. The food was okay. It was cheaper than noodles but we didn’t get a lot. A classmate claimed that the salad was horrible. (I had soup as garnish.)
• Day 5: StuCafé. Better than the canteen! Wonderful ambiance. Good and cheap food.

You have to replenish your energy with the best food available!

## Math And Teaching

1. Introduction to logic
2. Sets
3. Sets of numbers $\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}$
4. Functions
5. Equations and inequalities
6. Linear systems of equations and matrices
7. Sequences and series
8. Continuity
9. Differentiation

The lectures are alright. Unfortunately, I couldn’t really learn new math. In most lectures I’d just play with my phone or read – most topics were basics that were familiar to me. Of course, those are good for students that haven’t dealt with it yet. I assume most have not. School math just wasn’t useful.

It’s still kept simple. Most properties/theorems are only noted and not proved. That’s left for the real deal, not the pre-course!

One lecture was interesting, though. (Yes, it was only one mere lecture.) Namely the one about continuity! I’ve never explicitly dealt with this topic – only roughly known some motivation for continuity. So indeed, I enjoyed that one. At the end of the day, we only scratched its surface (only right for a pre-course). I do feel I have a better understanding of it now, though!

The problem sets are okay. As I’ve noted before, they are more difficult than the lectures. There are usually 1-2 interesting problems. The others are trivial – only if you’ve dealt with real math before, of course!

Some category 3 problems (the most difficult ones) are “laughable” for math olympiad students, though.

• Problem 10 in Session 3 is to prove the irrationality of $\sqrt2.$ One doesn’t even have to find the key idea because there are instructions given on what to do.
• Problem 9 in Session 5 is to prove the AM-GM inequality for 2 variables. Again, an instruction is given.

Other questions are more difficult. The continuity problem set was much harder than the other ones. Problem 5bc in Session 7 (Sequences and series) was the one I struggled with the most. It’s a one-trick pony!

Problem 5bc [Session 7, Category 2]. Compute the limit $\lim_{n \to \infty} a_n$ for

(b) $a_n = \sqrt{\frac{n}{2} + \sqrt{\frac{n}{2}}} - \sqrt{\frac{n}{2}-\sqrt{\frac{n}{2}}}$

(c) $a_n = n \cdot \left( \sqrt{3} - \sqrt{3-\frac{2}{n}} \right)$

I got 5b) wrong at first. A novice mistake: Squaring the sequence. There are certain convergence issues that have to be dealt with. Infinity is weird! In contests I’ve barely worked with calculus because of the so-called Calculus Trap. I’m excited to step outside the boundaries now!

Often, I finished early and even left early. Hopefully, that doesn’t concern my classmates too much. Should any of you read this and it does bother you – I’m really really sorry! However, what should I do? I don’t think purposely going slow is a better option.

5 more lectures to go!

As a conclusion: Talking to new people is more difficult than math. So is finding good food.