My journey.

After four months of living in Budapest, I'm finally leaving. I'm writing this on the airplane over the Atlantic Ocean, although by the time I post it online I will be in America. Now the past semester feels like a wonderful dream: everything was so different in Europe, but now it's all going back to normal. I'm waking up.

Budapest's airport is on the outskirts of the city, so reaching it was a challenge. There is public transportation that could take me to the airport, but the metro doesn't start running quite early enough for me to catch my flight at 7:00 AM. There is also a taxi service we could use, but a taxi could be unreliable. I didn't want to risk a taxi without a back-up plan. (In fact, a few of my friends arranged to go by taxi, but their taxi didn't come; it was quite a scare, but they got to the airport.)

In light of this, a friend and I decided to get a hotel by the airport and stay there the night before our flights, so that getting to the airport in the morning wouldn't be a hassle. We ended up getting to the airport without any problems. On the other hand, getting to the hotel the night before was quite a terror.

The main problem was that each of us had multiple heavy bags. Getting them on and off the metro was hard enough—in fact, it was no trivial task to fit them on the metro at all. Then we had to go from the metro to the bus stop, which involved a long staircase with several landings. We couldn't carry our bags down the staircase all at once, so we took one or two at a time, setting them on each landing in turn and going back for the others. Eventually some kind onlookers came and helped us. They must have thought we looked positively ridiculous, scrambling up and down the stairs with so many bags.

After we finally conquered the stairs and arrived at the bus stop, we noticed the elevator.

On the bus, my heaviest bag would fall over every time the bus made a sudden movement. So would my friend. After getting off the bus, we had some walking to do. This was the worst part, because for some reason one of my bags kept falling. No matter how many times I positioned and re-positioned it, after thirty seconds it would be slipping again. I was getting increasingly frustrated, and my friend couldn't help but laugh at me. Part of our walk was on a gravelly road with no sidewalk, where we had to hope that the oncoming cars saw us in the dark. (Apparently they did, because I survived.) Also, we had to cross something similar to an expressway exit, as well as a railroad.

After that journey, we were positively bushed. We fell asleep soon after arriving at the hotel, only to wake up four hours later for the early airplane. That's where I am now: on a nine-hour flight, writing this journal entry and intermittently sleeping. Was the overnight hotel really a better plan than an early-morning taxi would have been? We can't know for sure, but it was certainly a better story.

That night, when I was walking from my apartment to the metro, it hit me that that it was the last time I would ever make that walk. It was the last time I would see my neighborhood. I almost cried. Budapest was home to me for four months, and I'll never forget it. I've grown as a person, though the change was so gradual that I didn't really notice until it was time to leave. My experience in Budapest will stay with me for the rest of my life, and hopefully Budapest's fatty foods won't do the same.

Things I miss and will miss.

I am going back to America in two days! I am excited to be home, but also sad to be leaving Budapest. I decided to make two lists: one list of things I miss about America and another list of things I will miss about Budapest.

Things I miss about America:

• Milkshakes.
• Understanding what people say.
• The tutoring center at my college.
• Professors who are always available outside of class.
• My friends and family.
• Movies.
• Going places without having to deal with copious amounts of smoking.
• TGI Friday. This restaurant exists in Budapest, but it is ridiculously overpriced, even by American standards.
• My college.
• Free tap water at restaurants without even having to ask.

Things I will miss about Budapest:

• The excellent-quality low-cost food.
• The public transportation system.
• The panini press that came with my apartment.
• The colorful money.
• Being able to go somewhere like Austria for a weekend, just on a whim.
• My new friends.
• The beauty and history all around the city.
• Túró Rudi.
• The thermal baths.
• The palacsinta restaurant.
• Goulash soup.

These aren't in any particular order, other than just the order in which I happened to think of them. Also, after writing this up, I noticed that there are a lot of food ones. I like food.

I have at least two more journal entries left. First, my Logic class. Second, some of the sights that I have seen around Budapest itself.

Salzburg, Austria.

I went here just for a weekend, with one of my friends. Due to a failure to plan ahead, we arrived in the town Friday night without having reserved a place to stay. Fortunately we had a map with a few places we could try; the place we ended up staying the first night had room for only two people for one night; it's a good thing there were only two of us. The hostel was really small, and we had to share a room with two strangers. Also, the door to our room didn't lock from the inside, so we had to sleep with our door unlocked in a strange place in a foreign country. It was pretty unnerving, but none of our things were stolen. Or maybe something was stolen and I just haven't noticed yet. It must not have been important. By the way, I took a picture of our hostel from far away:

Other than the brief lodging panic, we had a great time. Salzburg is known for two main things: it is Mozart's hometown, and it is the setting and the filming location of The Sound of Music. I went to the house where Mozart resided as a young man; it is now a museum with various artifacts from the life of Mozart, including instruments and letters. Since I'm a pianist, it was really exciting for me to see the piano that Mozart used. The experience felt kind of like a pilgrimage.

I also went on a The Sound of Music–themed bus tour of Salzburg. We got to see a lot of the landmarks from the life of the real Trapp family, as well as some important locations at which the movie was filmed. I really like The Sound of Music, so this tour was really fun.

This road appeared in the movie twice: first, Maria danced and sang down this road with her bag and her guitar in hand as she went to meet the Trapp family for the first time; second, the family pushed their car down this road as they were attempting to flee the country.

This is the real-life gazebo that the movie's "Sixteen Going on Seventeen" gazebo is based on.

The villa that was used for filming.

The backyard lake that was used for filming.

The abbey that real-life Maria was from.

The bus tour also took us by beautiful lakes and mountains.

I tried a Topfenstrudel (strudel pastry thing with sweet cheese in it). Strudel is a traditional Austrian food. It was delightfully awesome. This is what it looked like.

I am really glad I was able to visit Salzburg. It was a beautiful mountainous small town, which many would call "charming". I will close with some photographs that I took from Salzburg's fortress.

FUNctional analysis does not live up to its name.

Last summer I learned some quantum mechanics and thought it was pretty interesting. Some of the theoretical parts use a lot of functional analysis, so I thought that functional analysis would be a fun class to take. After all, its name contains the word "fun", so how bad could it be?

While some of the topics in the class were fairly interesting, some other topics were boring and complicated and pointless. The homework problems were extremely difficult, which is not bad by itself. But, more importantly, upon reading the problem I would rarely see why this is a problem that needs solving. There would be so many steps, each one being a small result that I don't care about, which when taken together prove a larger result that I also don't care about. So, since I wasn't motivated to do the homework, halfway through the semester I decided to audit the class.

I did learn some cool stuff, though the specifics often eluded my understanding. I learned the basics of Banach spaces and Hilbert spaces. I also learned about bounded linear transformations; the term "bounded" here means that there is an upper bound on the growth of a vector when it is put through the transformation. In finite-dimensional vector spaces (that is, Rⁿ), all linear transformations are bounded; however, in infinite dimensions this is not always the case, and often it is necessary to consider only the bounded transformations. 

Another cool thing is about eigenvalues. In finite dimensions, all the values of λ for which A–λI is non-invertible are eigenvalues of A; you have probably used this fact many times if you have ever taken linear algebra. With infinite-dimensional linear transformations, there may be some values of λ for which A–λI is non-invertible and yet λ is not an eigenvalue. The former set is called the spectrum, and the spectrum always contains the eigenvalues—but not everything in the spectrum is an eigenvalue. The professor showed us an example of a transformation whose spectrum includes the real numbers in the interval (–2, 0) but which has no eigenvalues at all. 

There are several phenomena like these: two distinct concepts which always happen to coincide in finite dimensions don't always coincide in infinite dimensions. I'm glad that I learned what I did; it gave me a new perspective on some parts of mathematics. I also learned something about myself: analysis isn't really my cup of tea.

Verona photographs.

 

The ancient Roman arena in the early morning.

 

Some ancient Roman ruins.

 

Gnocchi (dumplings) with meat sauce.

 

Real Italian pizza.

 

A bridge from the side at night.

 

Every side street was beautiful.

 

The river is called the Adige (pronounced like a DJ).

 

An awesome bridge, some buildings, and the Adige.

 

The city at twilight, as seen from the San Pietro castle.

 

Candy and more candy.