The little things

First a little bit of background:
* Apartment buildings in Budapest tend to be nestled in the city, so the door into an apartment building is frequently right next to the door to a shop.

* Locks here are exciting. Sometimes you have to turn the key around 3 full turns to get the lock to open. Sometimes you have to do a half turn in the wrong direction and then a 1 and a 1/2 turn in the right direction. Sometimes you have to have the door handle in a certain position when you put the key in and a different position when you turn the key. Sometimes the door to apartment buildings is so heavy that you can have it unlocked and not realize it if you are not expecting it.

Now for the first story:

One night last week Christina, Kyle, Tom and I went to dinner at the Hummus Bar (a small restaurant with really tasty falafel) . After dinner, we walked back to Christina's apartment and along the way came upon an interesting situation. An old man in a wheel chair was sitting in the middle of the sidewalk and a lady was standing in the door of a shop just staring at him. As we approached he greeted us with "Szép estét kivánok!" and proceded to rattle off a long string of Hungarian that was clearly asking us something. We stopped and tried to explain that we did not understand. The lady standing in the shop door called out to him that we were not Hungarians and I think she was telling him to just not bother, but he was not deterred. He proceeded to continue speaking in Hungarian and gesturing wildly until we understood that he was in front of his apartment, but there was a step that he could not get up, so he could not get back in. Christina and I took his key and figured out how to coax the door to the apartment building open while Kyle and Tom got him up the step. Being able to be helpful makes me happy :-).

***
Friday night, as usual, we decided to go out somewhere for dinner. Christina threw each of us a guidebook and we thumbed through them looking for restaurants. We eventually decided on an Italian place in Buda that was described as being popular with the local college students. The menu was in Italian, Hungarian and English (by the way, I love the attempts at English translations of menu items, it frequently results in such dishes as "crashed potatoes"), but the staff was clearly not as fluent in English as the waiters on Ráday street. We were able to successfully order and communicate, but it was clearly slightly frustrating on both sides. (I had a cold raspberry soup and lasagne - a huge slice served in a ceramic bowl that it appeared to have been baked in. It was amazing). After dinner I caught the man who did not appear to be a waiter, but seemed to be there to wander around the tables and make sure everyone was happy and told him "Kösönöm, nagyon finom volt!", ie "Thank you, it was delicious" and he responded with a huge grin. Even though I am far from fluent in Hungarian, I am glad I have picked up enough to be able to be polite. :-)

"As I told you, I have no idea how to prove theorems, so we will suppose it is not true and hope for the best." - Professor Komjáth

Midterms have started!

The first was geometric graph theory. Now leading up to this midterm, we all agreed that we had no idea what to expect. After the midterm, we all agreed that it was definitely not what we were expecting, despite the fact that we did not know what to expect. The problems were actually much easier than I was expecting, but because of this it kind of threw me for a loop and had me constantly second guessing myself. Combined with the fact that I feel like I am good at graph theory mostly because I am persistent, not because I see what to do quickly and that writing things up well and quickly is challenging for me, I'm really not sure how I did on it. I'm not really that worried about it, I just feel like I ought to have been able to do better (of course, I still don't have it back yet, so we will see).

Yesterday was the Conjecture and Proof midterm. I'm quite happy with how it went. The problems were fun and the sort of clever that I am coming to expect from this class.

This morning I had the Topics in Geometry midterm. It was another one that really had more questions that I would say a test with its length of time should have, but it also had questions that honestly did have rather short, easy to write up answers, so I am fairly confident about it :-). Class periods here are two hours. We had the test for the first hour and then an introduction to Spherical Geometry for the second half. Since next Thursday is a holiday, they are giving us next Friday off, which means that tomorrow is next Friday. This means that I have two hours of Geometry tomorrow and then another two on Monday. It should be exciting, expecially since we are going to try to cover everything we are doing for spherical by the end of class on Monday!

Set Theory has not had a midterm yet. Set Theory has not scheduled a midterm yet. I have no idea whether Set Theory will have a midterm or not. The class amuses me endlessly. Theoretically, we are supposed to be meeting every Wednesday. We had class on October 3, and then not again until this past Wed, but we also met on Friday this week. On Wednesday, Professor Komjáth started class with "As usual, I will not be here next week. I think we will have class this Friday instead" (the class was originally a 2 days a week class, but got switched to 1 when there were only 4 of us - Friday was originally a normal class day). Thus we had set theory twice this past week, and Bridget and I are planning to meet on Sunday afternoon to go over the handouts he passed out today and make cookies. It should be fun. Aside from the fact that the class has no schedule, Professor Komjáth has a wonderful subtle sense of humor and the material is fun. We spent the last two class periods on Ordinals. We have defined what it means to "add one" to an ordinal (which is defined as the order type of a well ordered set) , proved that the class of all ordinals is not a set, and introduced the concepts of transfinite induction and recursion. Oh, and once we had already done all sorts of stuff with ordinals he decided that we should actually give a formal set theoretic representation of the ordinals... As he put it "I never said my classes are non-contradictory."

Jó reggelt kivánok

First, a few pictures from the Hungarian dinner party since I never managed to get them added to the relevant post…

Now, for the new stuff :-).

I’m living in a city that actually has seasons. This makes me far more excited than it really has any right to. The leaves have been turning colors, the weather has taken a definite turn towards the colder, and there are people selling roasted chestnuts (which are quite tasty incidentally) and hot wine from carts in the parks. The obvious correct response to this is to spend more time walking around outside enjoying the existence of autumn. On Thursday we went for a walk in Nepliget – a beautiful park that manages to forget that it is in the middle of a city. Here are some pictures from that walk:

On Friday, we decided to go for a walk in the evening before dinner (we had had a late lunch), and since it has been getting dark early, we decided that it would be fun to climb Gellért Hegy (a large hill in Buda) to see the view of the city at night. We walked to Deák Tér, got a couple pictures of the sunset and rode the blue metro line to Kalvin Tér. From there we walked across Szabadság Híd (Liberty Bridge) and then up the side of Gellért we had not previously climbed. We have concluded that some afternoon we need to pack a picnic dinner and take blankets and watch the sunset from the top of the hill and stop to play on the giant slide park on the way up (it was a bit dark when we found the slides on Friday). At any rate, the view from the hill is just as stunning at night as it is during the day.

When we decided we were ready for dinner, we walked back to Kalvin Tér in Pest, wandered down Ráday utca and picked a café for dinner. I had hideg gyümöcs leves (cold fruit soup, in this case strawberry) and gulyas with fresh bread. It was wonderful. We have been cooking dinner most nights, but Friday is our night for going out to dinner and most every week we pick some restraunt or cafe on Ráday. With the exception of when we go to the Pink Cadillac (an amazing pizza place), I usually opt for something that is traditional Hungarian.

Saturday, Christina and I headed to Keleti train station to catch the train to Romania to visit my friend Roxana (a MathCamper from Baia Mare, a city in the Transylvania region of Romania). I love the little tunes that the trains play as they are arriving and leaving from the station – they all sound so happy. We took the train from Budapest to Satu Mare and Roxana’s dad picked us up there. When we got to Roxana’s flat, they had bread, a tray with meat and cheese and delicious eggplant salad waiting for us. On Sunday we had breakfast and then went to the village museum with Roxana. It was a really cool outdoor museum with lots of traditional Romanian houses from different time periods. After the museum we stopped at Roxana’s favorite ice cream place (ice cream is good even when it is cold out) and had big bowls of delicious vanilla/chocolate swirl ice cream with huge mounds of amazing fresh whipped cream topped with fudge sauce. It was heavenly. From the ice cream place we went to the mineralogy museum. Baia Mare is Romanian for “large mine” and the region is known for its gold mines and mining in general. The museum had lots of really shiny crystal formations, most of which had come from mines in the region around Baia Mare. I really enjoyed it. Around 2 we went back to her flat for Sunday dinner. The meal started out with the meat and cheese tray, bread, eggplant salad, a plate of tomatoes and crackers. Roxana warned us not to eat too much as there was more food coming – I don’t think either Christina or I realized just how much more food was coming. The next course was soup – on a cold day there are few things tastier than soup. Then her mom brought out a huge platter piled high with mashed potatoes and topped with fried chicken and roast beef (having roast beef and mashed potatoes was exciting, I have not come across anything resembling roast beef in Hungary). Oh, and a plate of what are best described in English as cheese crepes. All of it was wonderfully delicious. After all of this her mom brought out a cake. Her dad runs some sort of delivery service that includes things for bakeries, so they get all sort of free deserts. The cake had two layers of chocolate cake with a rich cream frosting between them and then it was topped with caramel and chocolate decorations. The whole concoction was tasty, but rich enough that I don’t think I could have eaten a larger slice than I was served (and I usually have a very high tolerance for rich foods.

After dinner (which had taken at least two hours) we hung out with Roxana and her family. We played backgammon with her dad and then she and her dad taught us a fun Romanian card game. We played it twice, first with Roxana and her dad and then with her and her brother. Her brother was very entertaining. He knows just enough English slang to be really funny when he tries to use it (which he was doing constantly). For supper, the meat and cheese tray and eggplant salad came out again, this time accompanied by chocolate filled crepes, large mugs of warm fresh milk that her grandmother had sent and muesli (a granola and fruit cereal).

Monday morning Christina and I worked on HW while Roxana’s family was all at school/work. Around 2:30, they came home and we had “lunch” which was just as involved a meal as Sunday dinner, and just as delicious. We went for another walk to see more of the city itself and then came back and looked at pictures Roxana had of things like the chestnut festival and the region at other times of year. It was a fun and relaxing evening. For supper we had pizza and more milk with muesli, followed, of course, by dessert.

The train station at Keleti and pictures taken from the train:

Pictures from the village museum:



Wait...that's not a European license plate... We saw it while walking around in Baia Mare


Her family (minus her mom who was taking the picture) and the cake we had on Sunday

Tuesday morning we caught the train back to Budapest. Overall it was a wonderful trip. Visiting a friend and staying with their family is also definitely a wonderful way to travel. We got a very different view of Romania (and one that is probably much better at portraying it accurately) than we could have gotten visiting it any other way.

Interestingly, the trip also made me realize just how much Hungarian I have learned and how used to Hungary (and Budapest in particular) I have gotten. I could understand and read bits of Romanian because of my Latin background, but I was very aware of the fact that I did not know how to say even simple things like good morning. It was almost disconcerting to see the blue, yellow and red vertical stripes of the Romanian flag everywhere rather than the red, white and green horizontal stripes of the Hungarian flag and when we walked by a bank that had flags from several nations flying I noticed the Hungarian flag before noticing the American flag (which always looks so out of place amongst the European tricolors…). When we were getting the seat reservations (separate from the train ticket, it is an interesting system) for the train back to Budapest I automatically responded “igen”, Hungarian for yes, when the ticket lady asked, in Romanian, if there were two of us. I also never thought it would be so nice to be greeted “Jó reggelt kivánok”, Hungarian for “Good morning,” by the boarder guards when we crossed back over the boarder into Hungary and realized that I actually understood (and not just from the context) when he asked to see our passports and commented that I have the new version of the US passport while Christina’s is older (Speaking of which, I now have several stamps in my passport – it is exciting). It is going to be interesting to see what sorts of little things like these stand out when I come back to the US at the end of the semester.

Hideg van

The internet at school is broken, so I am typing this from Christina's balcony where we get a spotty, insecure wireless connection. And feels like it is definitely below 10 degrees C. Yeah. Oh, and I am going to Romania to visit a MathCamp friend this weekend, so I will probably be away from the internet until Wed. I will update properly when I get back and actually have internet access somewhere that my fingers don't start get stiff when I try to type.

Szia!

szilva túró süti

Has it really been two months? It doesn't seem possible, but my current (second) 30 day metro pass expires today (so I need to remember to get a new one tomorrow morning), so it must be true. It is strange how fast I manage to settle into a place. Budapest really does feel like home. It feels natural to catch the bus to the metro to get to school in the morning. Signs in Hungarian no longer inherently look strange. I still can't read most of them (though the number I can is ever increasing), but they at least look as though they have reasonable words on them. I know my way around the city well enough that I am frequently able to give directions to tourists and only have to pull out my map if I am trying to find some place in a part of the city I have not yet explored. Life is definitely good.

This past weekend Chelsey threw another dinner party - this time with our attempt at creating traditional Hungarian food. She made a vegetable stew called lecso that we served with rice as the main dish, which was quite tasty. For appetizers we served lots of bread with a Hungarian cheese spread called körözött and "egg foam" (fried whipped egg whites with yolk spooned over them and then baked) as toppings. And then there was desert... Tom made cookies, which were quite tasty, though it was questionable whether they counted as traditional Hungarian, and I decided to go crazy...

My host mother had made a delicious curd cheese and plum cake as part of the huge lunch she made on St. Stephen's day, so I decided that would be a good candidate to make for desert for the party. But I needed a recipe. I asked google for a plum and curd cheese cake...and it did not come up with the correct recipe...so I googled the phrase "szilva túró süti" and was directed to a recipe. A most definitely Hungarian recipe and the picture is definitely what I was looking for. The only thing on the ingredient list I did not recognize was "darált mandula" (which I now know means ground almonds) and I figured that I know enough about baking that I could probably pull something off, so I saved the recipe to my computer and attacked it with the dictionary. It took quite a while and some amount of guess work, but I eventually extracted something that looked like a reasonable set of instructions. Now just this was crazy enough, but we add to it the fact that the only measuring implements I have access to is a set of three funnels labeled 8oz, 4oz, and 2oz. The whole process was quite exciting, but the end product came out quite amazing, it slightly over browned on top. I have to admit that successfully baking a cake from a recipe in Hungarian is very satisfying. I got no HW done on Saturday - but I definitely practiced my Hungarian.

I will add pictures later when I remember to extract them from my camera...

"It's true anyway, it does not matter why." - Prof Elekes

This week's C&P set was...interesting. It decided to throw a bunch of problems at me that did not exactly fit with my normal approach to attacking math problems. It's good for me, but can be frustrating when I am not allowed to discuss them with people. Despite this I still found myself presenting a solution (despite having told myself that I was not going to this week). The set that is currently out seems to fit my style (which I would have no idea how to characterize) better.

The set theory prof is out of town, so we did not have class this week.

Geometric graph theory never fails to amaze me. This week we talked about rigidity of graphs and why infinitesimal motions (not just physical) motions are important to engineers. We had proofs in terms of engineering concepts. Prior to this class I knew math had applications in physics and engineering, but I would not have guessed that physics and engineering had applications in math.

I absolutely love Topics in Geometry. The material in the class itself is fascinating to me and is making me look at algebra differently...there is a lot more of algebra that can be visualized than I thought there was. I think my favorite part though is the "office hour". Every Friday we have class as normal for the first hour and then have an hour where we can get questions answered and such. We never have enough questions to fill a whole hour, so Gábor tells us about all kinds of cool geometric things that we are not going to get to in class. This morning he explained how you can use geometry to analyze topological properties of some algebras and how number theory can be used in geometric arguments. Seeing all of the connections is both exciting and frustrating. It is amazing that they exist and you can prove really cool things by drawing the connections, but at the same time it means you never know what kind of math will be used in the nicest proof of any given statement and there are currently so many branches of math and so much in each branch that is no way to know if you have the right background and certainly no way to know everything that could possibly be useful.

Szeretek a BKV

I love Budapest public transportation (if you follow the link you can listen to the amusing little tunes the buses and metro and such play when the doors are closing or we are arriving at a stop, etc) and the magical 30 day metro pass that gives me unlimited usage. Take last Friday as an example:

I left the apartment and caught the 16 busz (which stops almost directly across the street from my apartment). I rode the busz to Déak Tér where I transfered to the red metro line and rode it to the Keleti Pályaudvar station which has an exit onto the street College international is located on. At school I went to class, checked my email, etc and then Christina and I caught the 74 trolley busz to her apartment. We hung out briefly at her apartment and then walked a couple of blocks to Déak Tér where we met up with Mandi and took the red metro line to Batthyány Tér where we transfered to the HEV commuter train which we rode to Obuda (an older region of north Buda. In Obuda we went to an op art museum dedicated to Victor Vasarely. After the museum we wandered around and came across a Roman amphitheater and what appeared to be some sort of gathering of college students. They were clearly in teams (each team had matching shirts) and they had all sorts of random junk (a traffic cone, a vacuum hose, the shell of a lawn mower, an old motherboard, a broken guitar, etc) which they were using as play weapons. It was quite the event. When we got board with watching them, we walked back to the 1A tram stop we had noticed and took the tram to a blue line metro station . We rode the blue line back to Déak Tér where we met up with Kyle and then continued along the blue line to Kalvin Tér, which is near Raday street (a street known for its restaurants). We had dinner at the Soul Cafe (I had a cold raspberry soup with lemon sorbet and then csirke paprikas, it was delicious. The only problem is that I am not overly fond of having to pick my chicken off the bone, but it is not a big deal. ) and then caught the blue line back to Déak. We walked back to Christina's and hung out for a while before I caught the 16 busz back home. I am really going to miss having this kind of public transportation when I get back to the US.

It was Chelsey's birthday this past week, so we made her a cake. It turns out that raspberry jam works reasonably well for coloring butter cream frosting and that even though it makes it slightly runny, I can still successfully use a plastic bag with the corner snipped off to write with it.

While wandering around Obuda, we found this statue. It is surrounded by pansies. I have lots of pictures of the pansies, but I will spare you that.

A restaurant we passed called csaszarkert, literally, Caesar Garden. It turned out to be interesting forshadowing.

A street in Obuda. They have the same green signs with white writing that we have in the US.

The amphitheater

Another view of the amphitheater

One of the crazy college students arriving

Sunset picture taken from the amphitheater

"I can call anything anything I want - this is math."

The title is a quote from my Set Theory prof.

It is always interesting when classes overlap :-)

Example One:

Conjecture and Proof: Prove that a cube cannot be tiled with smaller cubes of all distinct sizes.
Geometric Graph Theory: We can use graphs with rubber band edges to find ways to tile rectangles with squares. Here are some examples, including one that shows a way of tiling a square with smaller squares of all distinct sizes.
Conjecture and Proof: Passes around a picture of how to tile a square with smaller squares and explains how to create an electrical circuit that represents such a tiling. This electrical circuit is what would result from viewing our rubber band graph in the context of an electric circuit.

Example Two:

Set Theory: Lets play with cardinalities and different kinds of infinities and such!
Conjecture and Proof: Which of the following sets are countable?

Example Three:
Topics in Geometry: We are looking at affine spaces instead of just linear spaces, so we need generalizations of things like "independent vectors" and "basis". Some of these generalizations involve a configuration known as general position, so we are going to explore it.
Conjecture and Proof: Consider a set of half planes in general position that cover the plane...

I guess by classes overlapping, I mostly mean that conjecture and proof keeps being related to my other classes... But at any rate, I am still very much enjoying my classes. They are providing a nice balance of challenging me and yet not sucking all of my time. Set theory is particularly nice in this regard as it is constantly making me think in new ways, but once I figure out how I am supposed to think, the HW does not take that long.

And now Christina and Mandi and I are going to go find a part of the city we have not yet been to to explore, so I will leave it at that for now.

There are somethings that are present everywhere in the US, some of them are just as prevalent here...one of these things is road construction



I had another conversation with an old Hungarian woman on the bus. This one started when she commented on the fact that the plants by the bus stop that are usually just greenery suddenly had little flowers. I understood just enough words that with her gesturing I knew what she was talking about. She asked if I knew what kind of flowers they were. I responded that I did not. My "nem tudom" must have sounded less that confident because she then asked "Magyarul?", I responded "Tudom kiscit magyarul." She pondered this for a second and then asked if I was from Slovakia. When I responded "nem" she asked if I was from Romania before I could add that I was American. When I told her I was American she looked shocked. She asked if I was visiting a sibling here, and I responded that no, I am just here to study. She asked what I am studying and when I responded math she told me that she has a sibling who does math and physics. These conversations are nothing very deep, but it is nice to know that I can at least understand and answer basic questions.

One day last week Christina, Kyle and I went to a gyros place for lunch. Incidentally, there are as many gyros places here as there are burger places in the US. I have to admit that the gyros are better than fast food hamburgers though... Anyway, I mentioned this because while we were eating Kyle suddenly sat up alert and asked incredulously "Is that...csipp csepp...?" We listened for a minute, and sure enough, the music playing in the gyros shop seemed to be a techno-remix of the Csipp Csepp song. This would be roughly the equivalent of a techno remix of the eensie weensie spider playing at a fast food place. It was interesting to say the least.

Friday night a group of us decided to go to a classical concert at the Palace of the Arts. The concert hall is incredible. We were sitting in the very last row of the top balcony and could still hear everything perfectly. The only thing that was at all out of balance was the organ, and even that was not badly out of balance. We also experienced an interesting cultural phenomenon. After the last scheduled piece in the concert, the applause did not die down and instead everyone started clapping in unison, apparently calling for an encore. This happened 3 times! None of us had ever seen anything like it and it was all we could do not to burst out laughing when it happened the third time. It makes me wonder if this is normal here.
Here is the view from where we were sitting

and the outside of the Palace of the Arts


On Saturday, Christina, Bridget, Leslie and I took a train out to Lake Balaton and a thermal spring that is near it. It was amazing to get out of the city. I am enjoying Budapest immensely, but I really don't think I am a city girl. The best anecdote from the trip occurred when we were getting on a bus to go between two small towns near Lake Balaton. The bus driver realized that we did not know much Hungarian and told us that the fare for the four of us would be ein thousand forint. "Ein" sounds an awful lot like "nine", so we were a bit worried for a minute, but we figured out what was actually going on quickly. It make sense that the native Hungarian speakers would be just as likely to mix their foreign languages (German and English) as we are to blend the other languages we know with our meager Hungarian, but it can certainly make for interesting communication issues :-) Here are some of the pictures I took during the Lake Balaton adventure: