Hungary is famous for it's wine. They have been creating wines for thousands of years, so they really know what they're doing. http://www.winesofhungary.com/history.htm. Yestery I went to the Hungarian House of Wines to wine taste. It was astounding. It's located in Buda, rather near Fisherman's Bastian. You enter and are greeted by a very distinguished gentleman in a three piece suit. The price for admission is 4000 forints, which is around 20 US dollars. It was worth every penny. With admission you are given a wine glass, a bag of bready croutons that cleanse the pallet, and a map of the wine cellar. You descend some concrete stairs to a well-lit, impeccable basement absolutely filled with wine. There are over 700 varieties to try, with about 60 bottles open at a time. You walk through a labyrinth of passage ways and little caves filled with wine bottles. Whenever you see an open bottle that you'd like to try, you uncork it, and pour as much as you desire into your wine glass. The wines are arranged by region with a mural behind them describing their history and taste in German, Hungarian, and English. I was happily wandering the halls, and I stopped to try a white wine that had an interesting bottle (because, unfortunately, that's as much as I know about the quality of wines). I sipped it, trying my best to look like a connoiseur, and rather vacantly read the history of this particular region. I was startled to realize that the very wine I was drinking used to be drunk on wedding nights to encourage the birth of a male heir. Needless to say, I moved on past this particular exhibit. You are allowed 2 hours in the cellar, but no one really checks up on you, so realistically, you could sample wines for hours at a time. It was a very interesting place to people watch. There were men who looked as if they live in mansions and smoke cigars, but there were also foreigners with backpacks who were thrilled at the "all you can drink in two hours" rule. There were families with mothers carrying young children, holding hands with smiley fathers. There was a bachelorette party getting a guided tour. It was definitely a cross section of the world.
On a vastly different note, we finally have heat and hot water after 5 days of going without it. We noticed one night that we didn't have hot water, so the next morning we called our landlord, who told us that that problem had happened last semester, and gave us a fix for it. We were happy, took showers in peace, and assumed the problem was fixed. Two hours later there was no hot water again, and the fix didn't work; rather it made our hot water heater emit disturbing, sputtering noises. We woke the next morning in frosty conditions. Suddenly, it occurred to us that we hadn't paid our utility bill!! After much deliberation we figured out how much we owed, and ran to the post office (where you pay the bills). We handed the bill to the lady behind the counter, and she started speaking rapid Hungarian and gesticulating madly, waving around a yellow sheet of paper. We assumed that maybe we needed such a piece of paper, so we returned to our apartment, unearthed a yellowish tab, and ran back to the post office. We handed over the money and the yellow sheet, and she returned a receipt. We waited all day in hope that our utilities would come back on. Over 24 hours passed, and still no heat, no hot water. We asked around, and it turns out that there was no way our utilities could be shut off, so something must be broken in our apartment. So, our landlord came over, and indeed, something was very very broken. They sent over a repair man later that night to fix the problem. It turns out that it was a hugely difficult problem dealing with the inner computer (or something like that) so he had to come back the next day with the correct parts. However, the repair man didn't speak a word of English. Of course he picked me to try to talk to about the problem and he waved a wrench around talking sedatly in Hungarian, as if by speaking veeeery slowly I would magically understand the Hungarian words for things like "boiler" and "thermostat." After a phone consultation with our landlord, we arranged that he would stop by the next morning between 9 and 10 to fix the problem. Around 4:00 he finally came. By this time, our apartment was so icy that it was necessary to wear mittens. I was in a fantastic mood all day, as one can easily imagine. In any case, we now have heat, hot water, and apparently a new water boiler.
Happy Heat and Wine!
PS, I added pictures of some of my friends and I at the Hungarian House of Wines.
Sunday, February 25, 2007
Wednesday, February 21, 2007
The "powers" that be...
Is there a power of 2 that contains every digit from 0-9 the same number of times?
Another way of saying it is....
You have an integer in which every digit from 0-9 appears, and each digit appears exactly the same number of times. Is this a power of 2?
This was a question I was given in Number Theory yesterday, and even though it's mildly trivial, for whatever reason, I really enjoyed it. The answer is no... but I'm not going to explain why until later.
I found out yesterday that next year at Gustavus I get to live with one of my very best friends in the newest, nicest dorm on campus. She was given the position of CF (the same thing as an "RA") in the dormitory called Southwest, and she got to choose one person to live with. We each get our own room, but we share a living area. I'm very proud of her for being given this job, because everyone wants to be the CF in Southwest!
In a couple of weeks, my mom and my sister are coming to visit me. They have an itinerary of three cities beginning in Prague. A neat feature of the BSM program is that they incorporate two four-day weekends into the schedule of classes. Unfortunately this means having class on two Saturdays to make up for it, but it is nevertheless really nice. During the first of these four day weekends, my mom and sister are arriving in Prague, and so therefore, I am able to come and meet them! Not only will it give me an opportunity to visit the Czech Republic, but I also get to spend more time with my family! A couple of days later, I will ride a night train back to Budapest with them, and then be able to show them around this fantastic city for about three days. They go on to Vienna, but I can't go with them since I will have class. I'm really excited!!
Either this weekend or next weekend I am going to go to Krakow. Apparently it's just gorgeous. Some students who were here last semester said that it was their favorite destination. I have a sneaking suspicion it will end up being next weekend because more people will be able to go with us. Also, this weekend there is a very reknowned scholar coming to speak to the mathematics students, and we all want to attend his presentation.
One of my favorite places to do homework is a shop called Kom Kom Czokolad. It's a Dutch chocolate shop where they sell truffles and hot chocolate. This hot chocolate is not the awful, watery American stuff. It is literally melted down chocolate. They give you a spoon to help you eat it since it is so thick. They also give you a small glass of water since it is so rich. It is absolutely beyond belief. However, they have huge tables and multiple levels, so it's ideal for spreading out and doing math either alone or with a group.
Now, here way to solve the problem I posed earlier. Take an integer with digits 0-9. It doesn't matter what order they appear because the trick here is to add them up. So you have 1+2+3+...+9+0. This equals 45. If each digit appears more than once, you know that each digit appears exactly the same number of times. Therefore, this summation of the digits can be simply multiplied by a constant, giving k(1+2+3+...+9+0). Regardless of what k is, we know that the number must be divisible by 3, since the sum of the digits is 45, and 45 is divisible by 3. However, by the fundamental theorem of arithmetic, 2^n will never be divisible by three. Basically, this is merely stating that 2 times 2 times 2 times 2.... etc will never be divisible by three since each positive integer has a unique prime factorization, and a power of 2 will therefore never contain a 3 within it's factorization. Thus, we have proved that an integer containing all digits the same number of times will never be a power of two. Like I said earlier, this is pretty trivial.... but I like it!
Happy (Ash) Wednesday!
Another way of saying it is....
You have an integer in which every digit from 0-9 appears, and each digit appears exactly the same number of times. Is this a power of 2?
This was a question I was given in Number Theory yesterday, and even though it's mildly trivial, for whatever reason, I really enjoyed it. The answer is no... but I'm not going to explain why until later.
I found out yesterday that next year at Gustavus I get to live with one of my very best friends in the newest, nicest dorm on campus. She was given the position of CF (the same thing as an "RA") in the dormitory called Southwest, and she got to choose one person to live with. We each get our own room, but we share a living area. I'm very proud of her for being given this job, because everyone wants to be the CF in Southwest!
In a couple of weeks, my mom and my sister are coming to visit me. They have an itinerary of three cities beginning in Prague. A neat feature of the BSM program is that they incorporate two four-day weekends into the schedule of classes. Unfortunately this means having class on two Saturdays to make up for it, but it is nevertheless really nice. During the first of these four day weekends, my mom and sister are arriving in Prague, and so therefore, I am able to come and meet them! Not only will it give me an opportunity to visit the Czech Republic, but I also get to spend more time with my family! A couple of days later, I will ride a night train back to Budapest with them, and then be able to show them around this fantastic city for about three days. They go on to Vienna, but I can't go with them since I will have class. I'm really excited!!
Either this weekend or next weekend I am going to go to Krakow. Apparently it's just gorgeous. Some students who were here last semester said that it was their favorite destination. I have a sneaking suspicion it will end up being next weekend because more people will be able to go with us. Also, this weekend there is a very reknowned scholar coming to speak to the mathematics students, and we all want to attend his presentation.
One of my favorite places to do homework is a shop called Kom Kom Czokolad. It's a Dutch chocolate shop where they sell truffles and hot chocolate. This hot chocolate is not the awful, watery American stuff. It is literally melted down chocolate. They give you a spoon to help you eat it since it is so thick. They also give you a small glass of water since it is so rich. It is absolutely beyond belief. However, they have huge tables and multiple levels, so it's ideal for spreading out and doing math either alone or with a group.
Now, here way to solve the problem I posed earlier. Take an integer with digits 0-9. It doesn't matter what order they appear because the trick here is to add them up. So you have 1+2+3+...+9+0. This equals 45. If each digit appears more than once, you know that each digit appears exactly the same number of times. Therefore, this summation of the digits can be simply multiplied by a constant, giving k(1+2+3+...+9+0). Regardless of what k is, we know that the number must be divisible by 3, since the sum of the digits is 45, and 45 is divisible by 3. However, by the fundamental theorem of arithmetic, 2^n will never be divisible by three. Basically, this is merely stating that 2 times 2 times 2 times 2.... etc will never be divisible by three since each positive integer has a unique prime factorization, and a power of 2 will therefore never contain a 3 within it's factorization. Thus, we have proved that an integer containing all digits the same number of times will never be a power of two. Like I said earlier, this is pretty trivial.... but I like it!
Happy (Ash) Wednesday!
Friday, February 16, 2007
Last night I went to a movie put on by the BSM program. It was a documentary called "N is a Number" following the life of Pal Erdös, a Hungarian mathematician viewed as a god by the mathematics community, and completely unknown by everyone else. The movie was fascinating! Erdös lived an incredible life, and I'm very disappointed that the world doesn't know more about him. He has done for Mathematics what Newton has done for Physics, however, the general populace doesn't recognize this. I suppose the idea of Newton "discovering" gravity, a force which we all can feel every day, is a lot more palatable to the normal person than Erdös's conjecture of the additive number theory on arithmetic progressions in divergent series. Nonetheless, here is a link to a very good biography of Pal (or Paul) Erdös from wikipedia: http://en.wikipedia.org/wiki/Paul_Erdős. Wikipedia is not a good source for purely credible information, but in a case like this, it's a very useful insight. Also, here is a link for the movie that we watched. I think the Gustavus Math Department should add it to their collection, as it is very very good. http://www.zalafilms.com/films/nisanumber.html.
My classes are simply amazing. I just love Number Theory. It is one of those classes where the answer is always right there, it just takes a flash of light to see it. Sometimes that flash comes after 2 days of work, sometimes after 1 hour. It's an abstract subject, but not nearly as dry as algebra. My teacher actually had lunch with the aforementioned Paul Erdös and he solved one of Erdös's unsolvable problems. I'm in awe.
Combinatorics is really really good. There are two classes offered, Combinatorics A and Combinatorics B. The "A" class moves faster, but I (like the majority of the Combinatorics students) chose to be in the "B" class. I have every ability to be in the faster class, but the fact remains that I can't understand a word of the other professor's English. Oh well, I can't complain as I am in Hungary. My Combinatorics class is really really interesting. However, yesterday we proved the binomial theorem in about 8 different ways. When the professor said, "And now we will prove it using the Taylor Series," I just about vomited. It was interesting, yes, but after the previous 7 proofs displaying the accuracy of the Binomial Theorem, I was simply not interested in the Calculus way of proving it.
Elementary Problem solving is soooo cool. It reminds me a lot of a super J-term class I took called Mathematical Gems. The point of the class is to cultivate logic and train the students to see the less obvious ways of solving obsure math problems. However, they do this by showing us scores of random, absolutely fascinating problems. Remember the trick you learned in 6th grade: if you add up all the digits in the number and that sum is divisible by 9, the number is divisible by 9 (the same with 3). I always thought that was just a bit of a party trick, but nothing more. I have used it countless times in Elementary Problem Solving, and even a couple times in Number Theory. It's amazing what such a trivial shortcut can tell you about the nature of numbers.
The History of Math (or whatever it's called) is mildly boring considering how it's 2.5 hours of straight lecture, but the information is amazing. He really molds the class to the student's interests. The other day he asked if anyone was interested in physics (since studying mathematical history forcesa deviation into physics) and I rather shyly raised my hand, as an interest in physics around mathematicians is often a reason for persecution. He asked me what I was interested in, and I said Astronomy (because I love astronomy more than anything.) He looked at me and said, "Ahh, astronomy. Very good. Today we talk about astronomy. Good?" He is absolutely brilliant, having three Ph.D's and an extra Hungarian title that means he's one of the best scholars. Ask him anything and he'll know the answer.
I went to Intermediate Hungarian Language. I don't like this language at all, but the class will be really really easy, and who knows, maybe I'll learn something along the way.
I decided against topology. I really enjoyed it (sort of) but the teacher didn't work for me, and I had to face the facts, I just don't have the mathematical background for it without a concrete course in Real Analysis.
I went to a store a lot like Walmart that is an English chain. It was wonderful. I found Peanut Butter and flour tortillas. There was one brand of peanut butter, and it took up about a square foot on the shelf. The next aisle over was completely dedicated to cheeses of all different sorts. They really do things differently over here. I love Eastern Europe, but it's tiring needing to go to a million different shops for everything. At this store, they sold shampoo, school supplies, food, books, cameras, silverware.... the works.
Sorry that this was long. I'm just giving an update! Happy Friday!
My classes are simply amazing. I just love Number Theory. It is one of those classes where the answer is always right there, it just takes a flash of light to see it. Sometimes that flash comes after 2 days of work, sometimes after 1 hour. It's an abstract subject, but not nearly as dry as algebra. My teacher actually had lunch with the aforementioned Paul Erdös and he solved one of Erdös's unsolvable problems. I'm in awe.
Combinatorics is really really good. There are two classes offered, Combinatorics A and Combinatorics B. The "A" class moves faster, but I (like the majority of the Combinatorics students) chose to be in the "B" class. I have every ability to be in the faster class, but the fact remains that I can't understand a word of the other professor's English. Oh well, I can't complain as I am in Hungary. My Combinatorics class is really really interesting. However, yesterday we proved the binomial theorem in about 8 different ways. When the professor said, "And now we will prove it using the Taylor Series," I just about vomited. It was interesting, yes, but after the previous 7 proofs displaying the accuracy of the Binomial Theorem, I was simply not interested in the Calculus way of proving it.
Elementary Problem solving is soooo cool. It reminds me a lot of a super J-term class I took called Mathematical Gems. The point of the class is to cultivate logic and train the students to see the less obvious ways of solving obsure math problems. However, they do this by showing us scores of random, absolutely fascinating problems. Remember the trick you learned in 6th grade: if you add up all the digits in the number and that sum is divisible by 9, the number is divisible by 9 (the same with 3). I always thought that was just a bit of a party trick, but nothing more. I have used it countless times in Elementary Problem Solving, and even a couple times in Number Theory. It's amazing what such a trivial shortcut can tell you about the nature of numbers.
The History of Math (or whatever it's called) is mildly boring considering how it's 2.5 hours of straight lecture, but the information is amazing. He really molds the class to the student's interests. The other day he asked if anyone was interested in physics (since studying mathematical history forcesa deviation into physics) and I rather shyly raised my hand, as an interest in physics around mathematicians is often a reason for persecution. He asked me what I was interested in, and I said Astronomy (because I love astronomy more than anything.) He looked at me and said, "Ahh, astronomy. Very good. Today we talk about astronomy. Good?" He is absolutely brilliant, having three Ph.D's and an extra Hungarian title that means he's one of the best scholars. Ask him anything and he'll know the answer.
I went to Intermediate Hungarian Language. I don't like this language at all, but the class will be really really easy, and who knows, maybe I'll learn something along the way.
I decided against topology. I really enjoyed it (sort of) but the teacher didn't work for me, and I had to face the facts, I just don't have the mathematical background for it without a concrete course in Real Analysis.
I went to a store a lot like Walmart that is an English chain. It was wonderful. I found Peanut Butter and flour tortillas. There was one brand of peanut butter, and it took up about a square foot on the shelf. The next aisle over was completely dedicated to cheeses of all different sorts. They really do things differently over here. I love Eastern Europe, but it's tiring needing to go to a million different shops for everything. At this store, they sold shampoo, school supplies, food, books, cameras, silverware.... the works.
Sorry that this was long. I'm just giving an update! Happy Friday!
Wednesday, February 14, 2007
Applause, Please.
Happy Valentine's Day! I read that Hungary didn't celebrate Valentine's Day until 1989. I wonder if that has something to do with the end of the communist era.
On Monday night I went to see the Hungarian Philharmonic Orchestra at the Opera House. It was fantastic. They played three pieces (the last one had three movements) and an encore. I wrote an e-mail home describing the Hungarian style of composure as a bit of a war of winds versus strings. It was very climactic. There was a flute solo unlike anything I had ever heard. It began with one flautist, adding another flute and a piccolo as it went on. As a former French Horn player, I'll admit to not respecting the flute as much as I perhaps should. However, this solo was beyond belief. At the end of the piece, the concert master not only had the flautist stand, but he went back to her and took her hand. It was really touching.
I can't believe I have not written about the Hungarian method of appluading. It's fantastic. At the end of a show, the audience claps their hands in the "normal" American manner. However, somehow the clapping suddenly synchronizes into a single sound. Rather than a cachophany of sounds, there's a definite beat. After a minute or so of this rhythm, the beat suddenly turns half-time for a bit. Then the beat starts to speed up until it's going crazy fast! This might be repeated several times, meaning that the audience desires an encore. It's a really endearing method that displays unity. When a huge number of people work together to do something as cohesive as creating a beat, it's really stunning.
I have to go to class. I'll give a mathematical update later!
On Monday night I went to see the Hungarian Philharmonic Orchestra at the Opera House. It was fantastic. They played three pieces (the last one had three movements) and an encore. I wrote an e-mail home describing the Hungarian style of composure as a bit of a war of winds versus strings. It was very climactic. There was a flute solo unlike anything I had ever heard. It began with one flautist, adding another flute and a piccolo as it went on. As a former French Horn player, I'll admit to not respecting the flute as much as I perhaps should. However, this solo was beyond belief. At the end of the piece, the concert master not only had the flautist stand, but he went back to her and took her hand. It was really touching.
I can't believe I have not written about the Hungarian method of appluading. It's fantastic. At the end of a show, the audience claps their hands in the "normal" American manner. However, somehow the clapping suddenly synchronizes into a single sound. Rather than a cachophany of sounds, there's a definite beat. After a minute or so of this rhythm, the beat suddenly turns half-time for a bit. Then the beat starts to speed up until it's going crazy fast! This might be repeated several times, meaning that the audience desires an encore. It's a really endearing method that displays unity. When a huge number of people work together to do something as cohesive as creating a beat, it's really stunning.
I have to go to class. I'll give a mathematical update later!
Sunday, February 11, 2007
Some new pictures
I added a few pictures that I have taken over the past couple of weeks. Included are the pictures of the cake that failed, the silver tree outside the Synagogue, and inside the Opera house.
Tomorrow is my first Real Functions and Measures class. I'm very very very excited for it! I hope it's as good as I've been making myself believe it will be. If it ends up flopping, I think I will take the Elementary Problem Solving class in its stead, as it is offered at the same time. I only wish Elementary Problem Solving had a more important sounding name. Multi-Variable Calculus sounds very intimidating and important, even though it's not, really. Elementary Problem Solving sounds trivial. Oh well, don't judge a book by it's cover.
I had a very uneventful weekend. I am unfortunately coming down with a cold or something that renders me reluctant to leave my warm apartment. I have cough drops that were recommended to me by one of the Budapest Semesters in Mathematics workers, and it's strange taking medicine whose directions I cannot understand. The high point is that I'm not alone in my ailment. Over half of the students in the program have exactly the same symptoms, making me realize that perhaps we spend too much time around each other.
On Thursday I'll have been here exactly one month. That is very surreal, as I feel like I have lived in this city for years, but at the same time I feel as though I just arrived.
Tomorrow is my first Real Functions and Measures class. I'm very very very excited for it! I hope it's as good as I've been making myself believe it will be. If it ends up flopping, I think I will take the Elementary Problem Solving class in its stead, as it is offered at the same time. I only wish Elementary Problem Solving had a more important sounding name. Multi-Variable Calculus sounds very intimidating and important, even though it's not, really. Elementary Problem Solving sounds trivial. Oh well, don't judge a book by it's cover.
I had a very uneventful weekend. I am unfortunately coming down with a cold or something that renders me reluctant to leave my warm apartment. I have cough drops that were recommended to me by one of the Budapest Semesters in Mathematics workers, and it's strange taking medicine whose directions I cannot understand. The high point is that I'm not alone in my ailment. Over half of the students in the program have exactly the same symptoms, making me realize that perhaps we spend too much time around each other.
On Thursday I'll have been here exactly one month. That is very surreal, as I feel like I have lived in this city for years, but at the same time I feel as though I just arrived.
Friday, February 09, 2007
z=y?
I promise the title of this post isn't a math equation. Actually, it's in regards to Hungarian computers. The school in which I study has a computer lab for student use. It's a very nice lab with printing facilities and fast computers. I bring my computer to school with me, so I don't have much occasion to use this amenity, however, I decided I should set up an account with the school so that I can use the computers should necessity arise. I went to the tech services room and asked if I could set up an account and he replied with the cursory "of course" (side note: in Hungary, in a service-type setting, if you ask for something, they never say "yes," rather they say, "of course." This phrase doesn't have the high-and-mighty connotation that it has in the USA, rather, it's a cordial statement implying servitude.) He asked me to type my last name in a field box (actually he asked for my family name... I love Europe) which I accomplished no problem. Predictably, he asked for my first name, which I was surprised to see came out at Eliyabeth. In Hungary the z and the y keys' places are switched on the keyboard!?! I didn't forsee that! Taking a closer look at the keyboard, the "@" sign is not on the "2" key. Instead there's the pounds sign, as in the currency of England. The @ sign take the place of the quotation marks. In Hungary they don't use quotes. If I were to write dialogue, it would look like this:
,How are you?'
,I'm fine, thanks.'
Europe is just so efficient: they never have superflous stuff like we do in America.
In terms of math, I had my first combinatorics class. It's great! When I asked someone what combinatorics is, they replied, "say you have 6 blue turtles, and 11 red turtles, how many ways can you stack them?" I'm not sure how turtles were picked to be the subject of the example, nevertheless, that's combinatorics in a nutshell. My favorite thing about it is that it has NUMBERS! Math doesn't have numbers anymore, only letters. While keeping math restricted to variables forces generality (which is fascinating!) it's really nice to have such concrete problems! My Abstract Algebra teacher suggested that I take it, knowing that I miss numbers, and I am so grateful that she recommended it! I actually see a lot of computer science in Combinatorics. I am NOT a computer scientist; it's too frusterating and picky for me. However, the ideas behind it are amazing, and so using the techniques of recursion to solve a math problem is really cool.
It was one of my best friend and roommate's 21st birthday last night. A couple of us made her a cake! In terms of culinary techniques, I have no talent. I have been known to ruin "just-add-water brownies" and Macoroni and Cheese made from a box with a cheese powder. Thus, under the best circumstances, baking a cake is a nerve-racking endeavor. Therefore, when my friend Sarah brought the cake mix to my apartment, imagine my bewilderment when I saw that the very long, complicated directions were in Hungarian! There were four packages of different mixes, and we also had to add other ingredients. One of the mixes didn't congeal into frosting like (we think) it was supposed to, and another one turned into a concrete-esque substance. The picture showed that there were cherries in the cake, but the word our dictionary gave for cherries never appeared in the directions. So we guessed an got a bunch of cherries. We poured a package marked "gelezin" into them, hoping that maybe it would turn into a jello-like mix. It didn't. We put the cherries into the soupy frosting thinking that it might help it congeal. It didn't. So we picked the cherries out and put them into the concrete substance, thinking that perhaps they would dilute the concoction. It sort of worked, and so we spooned some of the soupy (now pink) frosting into the concrete and came up with a happy medium that was pink and tasted like.... nothing. As soon as I put my pictures on my computer, I'll upload one of what the cake was SUPPOSED to look like, and what it ended up looking like. They are two very different pictures. Surprisingly, it was edible! But only barely. Maybe I need to continue with my Hungarian lessons.
Happy Friday!
,How are you?'
,I'm fine, thanks.'
Europe is just so efficient: they never have superflous stuff like we do in America.
In terms of math, I had my first combinatorics class. It's great! When I asked someone what combinatorics is, they replied, "say you have 6 blue turtles, and 11 red turtles, how many ways can you stack them?" I'm not sure how turtles were picked to be the subject of the example, nevertheless, that's combinatorics in a nutshell. My favorite thing about it is that it has NUMBERS! Math doesn't have numbers anymore, only letters. While keeping math restricted to variables forces generality (which is fascinating!) it's really nice to have such concrete problems! My Abstract Algebra teacher suggested that I take it, knowing that I miss numbers, and I am so grateful that she recommended it! I actually see a lot of computer science in Combinatorics. I am NOT a computer scientist; it's too frusterating and picky for me. However, the ideas behind it are amazing, and so using the techniques of recursion to solve a math problem is really cool.
It was one of my best friend and roommate's 21st birthday last night. A couple of us made her a cake! In terms of culinary techniques, I have no talent. I have been known to ruin "just-add-water brownies" and Macoroni and Cheese made from a box with a cheese powder. Thus, under the best circumstances, baking a cake is a nerve-racking endeavor. Therefore, when my friend Sarah brought the cake mix to my apartment, imagine my bewilderment when I saw that the very long, complicated directions were in Hungarian! There were four packages of different mixes, and we also had to add other ingredients. One of the mixes didn't congeal into frosting like (we think) it was supposed to, and another one turned into a concrete-esque substance. The picture showed that there were cherries in the cake, but the word our dictionary gave for cherries never appeared in the directions. So we guessed an got a bunch of cherries. We poured a package marked "gelezin" into them, hoping that maybe it would turn into a jello-like mix. It didn't. We put the cherries into the soupy frosting thinking that it might help it congeal. It didn't. So we picked the cherries out and put them into the concrete substance, thinking that perhaps they would dilute the concoction. It sort of worked, and so we spooned some of the soupy (now pink) frosting into the concrete and came up with a happy medium that was pink and tasted like.... nothing. As soon as I put my pictures on my computer, I'll upload one of what the cake was SUPPOSED to look like, and what it ended up looking like. They are two very different pictures. Surprisingly, it was edible! But only barely. Maybe I need to continue with my Hungarian lessons.
Happy Friday!
Wednesday, February 07, 2007
Math classes!
My math classes have started! They are, so far, fantastic. As an update, rather than taking Hungarian Arts and Culture, I decided to take a class called Historical Aspects of Mathematics. It's three hours, once a week, and I think it will be very very interesting. The guy who is teaching it worked at the Mayo Clinic for a long time, so next time I get a chance to speak with him, I'll ask him about his experience. We worked through the way early civilizations found the answer to the quadratic equation using a compass. It was really facsinating, although ancient civilizations didn't know about negative numbers, so they had to use really obscure methods. As the teacher said, "they didn't understand negative goats, or negative wives, so they couldn't understand negative numbers." It really made me think what we might be missing just because we do not have the capacity to understand as of yet.
I attended a class called Elementary Problem Solving. While I'm not going to take it, it was a really neat experience for two hours. We had to find the center of a circle using only the ability to draw another circle from two points and a straight edge. We could not measure. It was really interesting and required extensive use of tangents and knowledge of trigonometry within circles.
I have not had Combinatorics or Real Functions and Measures yet, but I'm really excited for both of them. Today was my first day of Topology. It's intense. I have never had a real analysis course, so I might end up auditing it. It will be a really interesting class alongside my Real Functions and Measures course, but I think I'd prefer not to get credit for it and just learn about it in preparation for my last classes at Gustavus.
Number Theory... I can't say enough good things about number theory. It is the type of math that made me into a math major. We spent all two hours proving properties of prime numbers. When I first read the book Contact by Carl Sagan and learned about the subtelties of primes I knew I was in love. Now that I have a class focusing entirely on primes, parities, and the elegance of numbers I think I'm in love. I'm taking it with the less popular of the two teachers. However, I really like his teaching style, and the other guy is only popular because he's so eccentric. He is the type of teacher who calls students out in class expecting them to give an answer. While that style might work for some students, I prefer not to spend the entire class period nervous that I'll get called on and give an incorrect answer. There are so many unsolved problems in Number Theory, it's positively addicting. I really need to look through my notes though, I'm rusty on the binomial theorem, which is pretty crucial.
Other than class, I went ice skating on the huge ice skating rink the other day. It was a lot of fun, although I used muscles I didn't know I have. I didn't fall though! My ballet training makes it difficult for me to hold the appropriate stance for skating, thus usually leading to fights with gravity, with myself as the defeated party. It was a victorious experience.
I had my first Hungarian Goulash last night. It was fantastic and very inexpensive. It was rather like beef broth with tomato soup thrown in but watered down. It was not spicy in the way Mexican food is spicy, rather, it was flavorful and eclectic. It had beef, potatoes, and carrots in it.
To get to school I have to take Tram number 74. I've never had a commute to school before, other than walking or driving, or perhaps getting dropped off at the school bus. I walk a block down from my apartment and take a turn for two blocks. There's a stop there at which a tram stops every 5-7 minutes. I take it for 3 stops, and it drops me off less than a block from my school. On the way back I have to walk about three blocks to get to the nearest stop, but it lets me off about a block away from my apartment. It's a very efficient system and I feel sophisticated when I use it.
That's it for now. Happy Wednesday!
I attended a class called Elementary Problem Solving. While I'm not going to take it, it was a really neat experience for two hours. We had to find the center of a circle using only the ability to draw another circle from two points and a straight edge. We could not measure. It was really interesting and required extensive use of tangents and knowledge of trigonometry within circles.
I have not had Combinatorics or Real Functions and Measures yet, but I'm really excited for both of them. Today was my first day of Topology. It's intense. I have never had a real analysis course, so I might end up auditing it. It will be a really interesting class alongside my Real Functions and Measures course, but I think I'd prefer not to get credit for it and just learn about it in preparation for my last classes at Gustavus.
Number Theory... I can't say enough good things about number theory. It is the type of math that made me into a math major. We spent all two hours proving properties of prime numbers. When I first read the book Contact by Carl Sagan and learned about the subtelties of primes I knew I was in love. Now that I have a class focusing entirely on primes, parities, and the elegance of numbers I think I'm in love. I'm taking it with the less popular of the two teachers. However, I really like his teaching style, and the other guy is only popular because he's so eccentric. He is the type of teacher who calls students out in class expecting them to give an answer. While that style might work for some students, I prefer not to spend the entire class period nervous that I'll get called on and give an incorrect answer. There are so many unsolved problems in Number Theory, it's positively addicting. I really need to look through my notes though, I'm rusty on the binomial theorem, which is pretty crucial.
Other than class, I went ice skating on the huge ice skating rink the other day. It was a lot of fun, although I used muscles I didn't know I have. I didn't fall though! My ballet training makes it difficult for me to hold the appropriate stance for skating, thus usually leading to fights with gravity, with myself as the defeated party. It was a victorious experience.
I had my first Hungarian Goulash last night. It was fantastic and very inexpensive. It was rather like beef broth with tomato soup thrown in but watered down. It was not spicy in the way Mexican food is spicy, rather, it was flavorful and eclectic. It had beef, potatoes, and carrots in it.
To get to school I have to take Tram number 74. I've never had a commute to school before, other than walking or driving, or perhaps getting dropped off at the school bus. I walk a block down from my apartment and take a turn for two blocks. There's a stop there at which a tram stops every 5-7 minutes. I take it for 3 stops, and it drops me off less than a block from my school. On the way back I have to walk about three blocks to get to the nearest stop, but it lets me off about a block away from my apartment. It's a very efficient system and I feel sophisticated when I use it.
That's it for now. Happy Wednesday!
Saturday, February 03, 2007
Some newly learned advice and what I miss from America
First of all, anyone who is thinking about coming to Budapest for the BSM program, or really any form of study should BRING THEIR OWN SCHOOL SUPPLIES! We went to buy notebooks and such earlier today and it was a very taxing experience. First of all, their notebooks are 70 pages max, and are either wide ruled, so narrow ruled writing on the lines would be impossible, or graph paper. Most Europeans take notes on graph paper, and I'm sure I'd love the system if I was used to it, but for now, I'm sticking to my own system. Also, pocket folders don't really exist. There aren't pockets in any binders or notebooks, and their version of "folders" are rather like fold out boxes in which papers can be placed and then protected by a cover. The fantastic BIC pens and pencils are not available; you must buy pens and pencils basically one at a time. To wrap it all up, 6 notebooks, six folders, six pens, and six pencils cost me around 35 dollars. Again, just remember to bring your own school supplies because it's a pain here!
Now, we've been compiling a list of things we miss from the United States. We love this city so much that we feel like we need to keep in touch with what we like about America so we won't be miserable when we have to leave. So, here goes he list of things to appreciate from America.
**Diet Coke (they only have Coke Light which is much different from Diet Coke)
**Clothes Dryers (everything must hang dry)
**English (pretty self-explanatory)
**Public Restrooms that don't cost money
**Waiters who bring you the check in a restaurant rather than the customers having to ask for it
**Peanut Butter
**Refills on tap water
**cheap cell phone service
**Skim Milk
**Easy internet connections
**Abundant Mexican Restaurants
**American clothes sizes
**Safety and Fire regulations
**sound-proof glass and walls
**No smoking sections
**shower curtains (you have to be creative with shower-taking methods or else the bathroom will flood)
**Being on the same time zone as parents and friends
**TARGET! I wish I could count how many times I say "I need a Target!"
That's a pretty comprehensive list as of now. Enjoy American luxuries!
Now, we've been compiling a list of things we miss from the United States. We love this city so much that we feel like we need to keep in touch with what we like about America so we won't be miserable when we have to leave. So, here goes he list of things to appreciate from America.
**Diet Coke (they only have Coke Light which is much different from Diet Coke)
**Clothes Dryers (everything must hang dry)
**English (pretty self-explanatory)
**Public Restrooms that don't cost money
**Waiters who bring you the check in a restaurant rather than the customers having to ask for it
**Peanut Butter
**Refills on tap water
**cheap cell phone service
**Skim Milk
**Easy internet connections
**Abundant Mexican Restaurants
**American clothes sizes
**Safety and Fire regulations
**sound-proof glass and walls
**No smoking sections
**shower curtains (you have to be creative with shower-taking methods or else the bathroom will flood)
**Being on the same time zone as parents and friends
**TARGET! I wish I could count how many times I say "I need a Target!"
That's a pretty comprehensive list as of now. Enjoy American luxuries!
Friday, February 02, 2007
Language barriers
I'm struggling with the Hungarian language. It has 14 vowels... enough said. I decided not to take Hungarian for the entire semester; rather, I'm going to take a class called Hungarian Arts and Culture. The interesting thing about being in a culture with a language so vastly different from ours is the way in which we compensate. All of the students I'm with find ourselves slipping into Spanish or French depending on what we took in high school. Since we know that English is not an option, I guess it's inherent to try the language that we speak that's not English. People say things to me and I'll reply with Si instead of Igen. Instead of saying bocsenat for excuse me, I'll say perdoname. So strange.
I'm in the process of figuring out what classes I'll take. After talking to students who were here last semester, I've (maybe) decided on taking Number Theory, Combinatorics, Topology, and mayyyybe a class called Real Functions and Measures. Then I'll take the Hungarian Arts and Culture class in addition to the math. The weird thing is that I ended up without class on Fridays, and if I don't end up taking the Real Functions class, I won't have class on Mondays either. There are students here who plan their schedules around not having class on Friday, I was just lucky enough to have had it work out coincidentally.
We have a welcome session and party this afternoon. I think it should be a very good time because we got to talk to the professors and ask questions.
I'm in the process of figuring out what classes I'll take. After talking to students who were here last semester, I've (maybe) decided on taking Number Theory, Combinatorics, Topology, and mayyyybe a class called Real Functions and Measures. Then I'll take the Hungarian Arts and Culture class in addition to the math. The weird thing is that I ended up without class on Fridays, and if I don't end up taking the Real Functions class, I won't have class on Mondays either. There are students here who plan their schedules around not having class on Friday, I was just lucky enough to have had it work out coincidentally.
We have a welcome session and party this afternoon. I think it should be a very good time because we got to talk to the professors and ask questions.
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