another long day....

COA at 8 in the morning. Today we did even more with characteristic polynomials, and even solved a Diff EQ, which was a very easy one. The process is a big complicated but with practice it should be fine.

Then I got caught up on the Num Theory class I missed yesterday. Tried to work on Indiana REU application, but after an hour-ish of writing, accidentaly hit backspace and lost all my work. Foolishly writing on an IE page!

Paid my $350 to take an extra math class! Had a not very good lunch of hard macaroni pasta.

Then had NUM1. Ah, number theory makes me happy. Highlights include Wilson's Theorem, and the fact that a number can be written as the sum of two squares iff the primes in the form 4k-1 are raised to an even power. We talked a bit about groups and stuff as well- referring to Fermat's Theorem, but Csaba was convinced that the number theory approach was much more beautiful.

Then was LOG. The professor had misplaced our homework from last week, haha. Today only 3 people came to class. And 1 might drop. Which means the class may not eventually exist. How sad. Anyway, today we discussed Godel's Completeness Theorem in depth.

Went to a friend's to 'work' on CHA. I sat and watched while they thought. I really didn't know what was going on......

Had a sandwich for dinner with the leftover shrimps and fish balls. Finished applying to the REU at Indiana! Which will be the last one I apply to, unless I don't get into any by the end of next month.

Tried to do homework, but was tired. Instead cleaned- washed the dishes and took out the trash. Its been a looong time since I did that.

Then I wasted time looking at operas playing in Hungary. Their is a showing of Carmen in the middle of April which is supposed to be utterly extravagant. Cheapest tickets are $30. I almost bought a ticket, but then they asked me for the postcode. I don't know my postcode. So.... one day soon I will go to the venue to buy a ticket!

Tomorrow I will get up early since a friend from highschool, who is studying in Prague, is visiting me. Her train arrives at 7 AM, and I'm meeting her at the station at 8. So I must get up early yet again! Otherwise I would be up now trying to finish homework. Instead I get to sleep!

I hate the morning

So, I got up around 7:15, having to go to a Budapest housing office to register my address. Since I already had the student visa (unlike some others), the process was supposed to be much easier.

We were supposed to leave the college at 8, we didn't leave until 8:40 AM. I should have known that didn't bode well.

I was able to buy my set theory book while waiting, though. And it wasn't too expensive!

So we journeyed along, by metro, then bus, to the office. Nobody was there, except us. The office was closed on Wednesday mornings to everybody but students. I should have realized that something was wrong when Anna, our student coordinator, was talking furiously to the lady in Hungarian.

Apparently in that section of town, the phone cables and phone lines had all been stolen!!! And it would be 2 weeks until they could be replaced! Ah, the joys of being in an ex-communist country. At least it wasn't as bad as stories that we shared about complete bridges in rural Russia being stolen!

This is a picture of where we were. All the apartments looked exactly the same!

So then we decided to go to Obuda to just finish up with all this today, which was far away on the other side of the Danube. We finally got there, I studying some combinatorics on the way, and the process went rather smoothly. I greeted the lady in Hungarian, and she said she spoke English.

By this time, number theory was over. I crossed the street, looked in the Tesco, and had a big lunch at this Chinese buffet place. I had thin noodles with chicken on top, and a very interesting Fanta that tasted just like watermelon.

Then I headed on a bus- while the others still weren't finished- and got off at Astoria, near the Renyi Institute.

So I checked out the library, and there was a little dark study room where I studied Number Theory and did my Logic homework. There was a young man across me, who I don't think was older than me, reading an introduction to algebraic geometry. There was an elderly gentlemen reading a newspaper in Hungarian.

It was all first relatively indimidating- so many math magazines lined the area, even in Russian, Chinese, etc. etc., but it wasn't a bad place to study. I then wandered around the library for 20 minutes, which had all the imaginable math journals, including mathematical logic, operators, mathematical psychology, topology, and numerous more. I was looking through some Journals of Functional Analysis, trying to find Professor Feldman's name, because I thought I remembered he published in that before. I looked, and I checked later and he did, but I couldn't find that exact copy.

So I had CHA. Today we talked about the First Orthogonality Relation in character tables. Pelikan went 10 minutes over, he was really excited.

Got back, was very tired. Didn't want to nap. Watched the season finale of Prison Break!

But I was too tired to do math. I napped for an hour and a half, ate a late dinner (of leftover pasta, and a new tasty coconut desert cake), and did some homework, including reading a lot of set theory.

And OH. The tasty treat I had yesterday was a cabbage strudel. I did a quick google search and I came up with this great article http://www.iht.com/articles/2005/12/29/opinion/edephron.php by Nora Ephron, director of Sleepless in Seattle, about her wonderful thoughts on its taste.

Now I'm tired again. I hate it when I have to get up early in the morning! And I have to do it again tomorrow!!!

a fun day

Woke up at 9:30, did a bunch of h/w in the morning. My mind was doing a lot better. It was warm today and I wore a t-shirt and sandals. Hungarians apparently don't wear sandals now.... but I do!

Went to SET. Had to go across the college to find a classroom in an apartment- it was nice, though. We played with the notion of aleph not and c a lot. c^2=c! It was fun.

Had the HUN1 language class. Learned how to order food and whatnot from different places. We went to the grand market to practice. I had a cabbage pastry (which was absolutely delicious! and it tasted some like sauerkraut) and bought fish balls, yay. It reminds me a lot of China- i.e. lots of fruit stands, fresh fish to buy, but not as crowded~ and Hungarians like pickles a lot, so there is a lot of pickle smells!

Went back home, cooked dinner. Panfried shrimp and fish balls! I was planning to eat it with rice, but it smelled weird. So I cooked some ramen instead. Sometimes I feel like if this whole math thing doesn't work out, I could be a chef! haha~

Didn't feel like working. But I did finish up some number theory. Then I watched Transformers. It was AWESOME! I didn't go in expecting much, but it was a lot of action, and a lot of fun.

Tomorrow I have to get up even earlier to deal with the Hungarian bureaucracy. =(

4 days 'til the weekend!

8 AM NUM1. Way too early for Csaba. We start off with congruences, and spend class on them, and by the end we're at Fermat's Theorem. Elementary number theory- Done! I can't wait to see whats next.

Then was FUN. We talked about measure theory, the Cantor Set (yay!), and the niceness of Borel Sets.

Had a good lunch of pasta and pork. Then had COM. Was lost for pretty much a lot of class, since I was tired and not focused, and I had missed the makeup class, since I decided to attend Number Theory. Did recurrence relations, that wasn't bad. Had some similiarity to the homogeneity and non-homogeneity of ODEs. We defined the Fibonnauci Sequence as a function, which was fun.

Went back. Tried to do homework but wasn't very sucessful. Spent a looong time staring at Stirling Number of the Second Kind and generating functions without much success. Not having much fun with Combinatorics, thats for sure. 'Proved' problem 1 on CHA, and convinced myself I'm right. I'm pretty sure its not.

Did laundry. It takes time to dry and my towel is not yet dry. What will I do?!

Ate some leftover pasta for dinner. Watched American dad, which was fun.

Was very, very unproductive. Did apply to a Cornell REU!

I'll go to bed early today. First class is at noon tomorrow, but haven't even done my Hungarian homework yet. It will be very easy, and I'll take care of it in the morning.

I end with a picture. Notice what Stonehenge is flanked to on the right. I never remember!

An ARGH day

So, I got up, and trekked out as promised.

I started taking pictures of my journey to Gellert Hill, and everything was going as expected. I was seeing lots of tourists.

Near Frederick Tere subway.

The Danube.

Crossing Elizabeth Bridge.

St. Istevan Statue.

Then, while walking up a few stairs, the unthinkable happened. The camera strap around my neck came loose, and my new 300+ dollar camera crashed to the ground. This obviously made me very unhappy. I tried turning it on and off, but it the lens would just extend up and down. I was furious at Kodak for making such a poor quality camera strap. I had followed the instructions how to assemble it as well. I had to resist the urge to throw it into the Danube, seeing it make a teeny tiny splash. I saw the LCD working for a couple of seconds the hundreds of times I tried turning it on. I will be sending it to Kodak for repairs, I will make this be covered by the warranty.

Needless to say, I cut my journey short. I then proceeded to a very touristy restaurant, with a $30 Sunday brunch. Unfortunately I had only brought $20, but had proceeded to spend that on a lovely two legs of duck with a pastry. Yes, I wished I could have taken pictures of it.... The duck may have been a little dry, but it was very tasty indeed, and it was exactly what I need to relax.

I went home, and it was a while before I could bring myself to do some homework. Still didn't finish the Combo homework, but yay for the professor not caring!

Watched the second to last episode of Prison Break. It was good!

At a yummy dinner of Spinach Fusilli with ground turkey. Fortunately I still have my trusty Pentax. Its zoom is only 3x, compared to 12x that the Kodak had. But it will still take great food pictures! It was very tasty, much better than the picture actually looks.

Also applied to some more REUs. Finished off my part of the application to Lafayette.

Then did a lot of logic, including reading about structure homomorphisms and isomorphisms. That was fun!

Did a lot of cleaning as well. My room has been looking like an explosion. Take a look... Now I am decided about what classes to take as well, my life can get much more organized. yay!

And OH. I forgot to mention, yesterday at the store I found Hagen Daas ice cream. It was exciting. They even had Bailey's flavor, which I've only had in London at the Theater. One pint was about $12, though. Maybe when it gets really really hot, I'll reward myself. ;)

Unfortunately tomorrow I have makeup classes. Two to be precise- number theory and combinatorics. I will attend number theory. If I am not there, I will miss the Csaba-ness and not get what we did in class from the notes. 8 AM class on a Monday really really stinks. Well, at least I'm done by 2!

Its Saturday! And warmer too!

I surprisingly woke up at 10 AM! So, I was able to go out by 11. It was a beautiful day, almost 60 degrees outside! Took the metro to the opera stop, looking for the gym that my landlord recommended. I saw the sign, but didn't see the opening. I went in an apartment complex, going up and down the stairs, but didn't see any sign of a gym. Then I went outside, I tried another door. I was accosted by a guard, and I told him I was looking for the gym. There was 'fitness' on the sign, so I said that word over and over. He finally understood, led me to the same apartment, and pushed a button, letting me in.

I saw the word that supposedly means gym pointing to a door. The door was locked. I was confused. Then I decided to abandon my mission for now. Then I went to office max, buying a lot of lined paper, including a little 2-hole punch. Went to Csmeagol and got a tasty looking chocolate hunk of bread. I ended up eating some meat and cheese, and the bread as well. It was only a little more than 50 cents- some of the chocolate had fallen off on the way back, but it was still very delicious!

Did a bunch of homework, including reading a lot of logic. Was thinking about going to Gellert Hill and be touristy. I will do that tomorrow morning!

Watched the newest episode of Lost~~~

Went out to the mall and had a hot chili burger king burger (it was two hamburgers with mayo and some jalapenos on it) meal. It wasn't bad at all. This time I was smarter because I realized I had to order a ketchup packet as well. For one single tiny packet it was about 50 cents! Did a LOT of shopping at the match, buying shrimp, spaghetti sauce, spinach penne, including a bunch of spices including garlic, pepper, and chili sauce. Spent a lot but it was money well spent.

Did some more homework, and finally tackled the dishes. I hadn't done them for a while so there was a lot.

Oh btw.... didn't get into Gallian's REU. :( Ah well.

Check back tomorrow~ there will be lots of non-food pictures! I promise! It sure has been a while....

How much homework this weekend?

Woke up at 11, so had a good 9 hour sleep.

FUN was fun. We played more with ultrafilters, which was absolutely fascinating. Defined an omega-limit. So EVERY function has a limit! We talked more about probability in the urn, and proved the Vitali Theorem. We began the discussion of Borel Sets, which are 'nice', such as open, closed, G delta, F sigma, G delta sigma..... and so on. Next week is measure theory!

The professor is still amazing. He is from the Renyi Institute. According to Csaba, the Renyi people are those who only research, and do not normally teach. Doesn't that sound like a great job? Which means, according to him, they are quite eccentric. He was only 2 years younger than Elek, and they went to the same highschool, and they had fun together, but he says non-mathematicians might not like him. I can't understand why!

So the class is good, but I'm a little concerned because everything is the final. Of course there are homeworks along the way, but they are never formally graded, so you might no be 100% sure you're right, and you don't know his grading style as well. I think soon I'll be buying the book to work hard and understand better.

So we got out like 30 minutes early. I didn't know what to do, so I decided i might as well try langos again. I went to the stand, actually looked at the menu, and ordered a langos with ham and cheese. They were out of that, so they gave the bolognai langos instead. It was like a small pizza, with cheese on top, and tomato sauce with some kind of meat. It was not as oily as before, and it was really quite tasty. I walked around a few blocks, giving myself plenty of time to finish the snack, and still ample time to get to class. I was satisfied, but a little bit too full~~

Then was 1.5 hrs straight of intense CHA. We proved a bunch of stuff, including Wedderburn's Theorem, amd after class was over he couldn't resist continuing for a bit, and we proved two things that he showed the first day of class- the number of conjugacy classes is the same as the dimension, and the sum of the squares of orders of the representations add up to the order of the group! I understand most of it, but since we are going through the book pretty linearly, it will be a good reference.

We also got our new homework. It does look intimidating yet again. I hope I can understand more of it this time- one of the problems comes directly from the book. If I can't do the next couple courses, I may simply have to audit the class. But I'm going to try my best. Auditing= taking Algebra with Siehler next year, which would be fun! I'm still very interested in the subject.

I'm trying to further compare analysis and algebra to see my likes and dislikes. It seems like algebra always make more logical sense to me, and nothing is too far-fetched.

But analysis is always much more mind-blowing! Perhaps it is the infinite that makes it more perplexing, but it seems like this is just as intriguing- albeit in a very different way. I wonder what I will be~

Got back, and was very tired. Tried to nap for an hour and a half but that didn't quite work.

Finished my leftovers from last night for dinner.

Watched Moonlight Mile. Not bad at all. Downloaded

Transformers for next time!

Actually did some homework as well. Reviewed FUN, and did some SET. I hope to actually go around the city some this weekend, if at all possible, and not be holed up in this apartment any further.

Good night!

ps. sorry for the spacing problems. blogger is not very smart on this issue.

my thursday....

So I spent a looong day at the College.

Combinatorics was at 8 AM. Today we talked about exponential generating functions. Not too interesting, but we did solve an interesting problem with them. We proved that the # of partitions of n into distinct terms would always be the same as the # of partitions of n into odd terms.

Had a two hour break, but still had logic homework to do, so messed around with that. Bought my Logic book as well. I got it used so it was 60% of the original price.

Then was another number theory problem session. I wasn't as sharp with the problems today. I would keep on breaking the number up into 2k or 2k+1, then breaking the k up, and was able to only prove certain cases. The answer came much easily with the use of modulus.

Then was logic. This was a satisfying class, since today we had defined enough to define what a group was, which I didn't expect, and was interesting. Groups are elementary, but the natural numbers are not! We also did isomorphisms as well, proving equivalence relations. I liked it when we used a bunch of symbols to show a single number. For example, what is the number x for the statement "for every y, if x=!y, then x less than y"?

Then was the feedback session. Humke was there. So was Deszo, the head of the program, who this term is at Cambridge. They weren't too happy, since Conjecture and Proof, their flagstone, only had 3 people registered. Also there were 18 people in the Combinatorics A section, and 3 in the B section. He said he would tell the A professor to move faster to make people switch.

This lasted much longer than I expected. At least there was snacks! I got a chain of people to pass a 2-liter of coke up the rows to me. That was fun. I relieved a lot of people's thirst.

Then I watched Lost, cooked some good dinner (tofu with vegetables with turkey, and rice).

Then was off to do homework....

Now I must live my Friday~

At least tomorrow is Friday

I've spent the last four+ hours working on Character Theory Homework. This homework has made many people already change their minds and decide to only audit the class~~ I have a very good idea of what is going on in class, but the homework is very different. Now I have some idea about the homework. I shall- for now- trudge on!

I would like to sleep. Its been a long day. It was nice seeing Prof Humke today in his W&L hat~ tomorrow he is giving a talk at a mathematician's 60th birthday party celebration, entitled A little bit of this and a little bit of that. I wish I could go.. I have character theory in the middle. Ah well.

Will definitely give more updates tomorrow morning, if I wake up early enough. My first class is at noon~ I have registered! Yes- I did kill THC.

I saw LOST today as well. How could you Sayid!!!!

Good night~

Choices made!

Woohoo!

Went to number theory at 10. Was a really good class, we did a lot of fun proofs. Including finally quickly running through the Fundamental Theorem of Arithmetic. What made me happiest is when we showed at least 3 ways that there are infinitely many primes,

Then went home for a break. Ate lunch and watched Gordon Brown live at the Parliament on Sky News. That was not very entertaining.

Took the subway to CHA. Today was a shortened class, since afterwards was his office hour. We talked about Shur's Lemma. It was interesting- I had seen it before in much simpler form in Linear Algebra. He mentioned that he knows physicists that think it is an astounding result, while mathematically, it is quite simple. I thought that was funny.

I went to a friends apartment and looked through the logic homework- I had not yet purchased the book. Unfortunately for the Theory of Computing folks I found the book quite fascinating. It contained the Church Theorem, and Godel- we will learn both. So there is little chance of me taking Computing any more. Which means the class will die. My opinions surely seem to change post to post.... but I came in wanting to take logic, and I definitely still want a taste of it.

The friends apartment was near the mall.... so I wandered around the mall for a few hours. Went to a libri and bought 2 nice Hungarian-English and English-Hungarian dictionaries. They come with a CD, which I have not yet opened. Then wandered around some more- including going into an Esprit- and then went into the arcade. Played Sopranos pinball, quickly losing my 200 forint. Then decided on the star wars 1993 sega arcade game, my all time favorite arcade game. I loved it and will definitely go back. The sound was much lounder than what I remember playing when I was small, so I was much more immersed. I only spent like 400 forint on it, and it lasted me 20 or so minutes. I think something was wrong- because the machine kept on saying insert more money after I had died, but I just pressed the start button and it let me keep on going, but finally it told me game over. I think with 1000 forint I can easily beat it. I beat it when I was little, probably with 15 dollars of quarters~

Went to the match and bought some food to cook and some meat and stuff for sandwiches. I figured I was in the mall so I might as well eat there. Got a tasty (but a little cold) chicken leg and potatoes for 699 forint. Then had some ice cream for desert. Its so hard to resist dessert here.....

Went back, took care of some combinatorics problems (not due until Monday, I'm proud~) and did a logic problem. Will finish the homework in the gap tomorrow between classes. Also watched an episode of American Dad.


So... I've chosen on Combinatorics 1A, Functional Analysis, Number Theory 1A, Set Theory, Character Theory of Finite Groups, and Mathematical Logic. I bought the Character Theory book, and the Combinatorics book as well- which is not required, but looks to be a good reference. They were expensive! Ah well, they will serve me well in my days of math.

Theres still a slight possibility that SET won't work, because a room has still not been found to hold the class, but I still have much hope. If that doesn't work, I'll guess I'll go with THC.

Tomorrow is registration-date. Prof Humke (who is already in Budapest!) will be there as well. Everybody thinks I am crazy for desiring six classes, not including the language, but I have faith. I didn't come here to have fun~ I came here to learn, damn it! And since two of the classes are reading anyway, I would only have a total of 22 class hours per week. Keep in mind that there are always breaks, and one hour is pretty much 45 minutes. Let's compare this to my last term at W&L. I took 15 credit hours. This was 18 hours of class, with 55 minutes of class each hour. So its actually less time in class each week. Not all the classes can be that hard, especially the intro ones. I know CHA and FUN will be, but as of now I'd want to learn the material. If its all too much, though, I can easily change to audit, and then I get to go to the class but not work. How fun is that?!

If I was here another semester, I would lighten up my load. But I'm not. I'm sure I'll go to Europe another time in my life, with much less cares, but I'll never be in this same position again.

Not much class, but tired anyway!

Was planning to go to algebra. The alarm woke me up but my nose was stuffy. I thought that was a good enough excuse not to go, and sleep another hour. Later I heard the professor talked about how groups of order p^m*q have normal subgroups, but he couldn't quite get through the proof. He is the kind of professor that doesn't refer to notes while teaching- which I like, but sometimes it can lead to problems. I suppose I won't be attending this class any more. How sad.

Went to class about 20 minutes before class started, and caught the bus right when it arrived. Got to the college a couple minutes before class started. Had enough time to buy a yummy strawberry drink (it was 25% real strawberry!) at the cafe. It was time for THC. Today we proved the pumping lemma, which was really quite simple and obvious. We went on to define context-free grammars, and we went onto define pushdown automaton. This is different because it has an infinite queue, so it can recognize languages such as the same number of 0s and 1s.

I will probably take this class. Will see how logic turns out to be sure, though. Whether or not I take the class is whether or not the class exists~~

Went back home, and distracted myself and ate lunch for a while. Then off to class at 2:15. It was my language class. We learned about adjectifying nouns, more about conjugating verbs, which I really don't like, and things about infinitives. I really don't know what an infinitive is. And I really don't want to know either. We also did miming with vocab words, a staple of language classes everywhere. Not a bad class, but 2.5 hours is just too long.

Had dinner at the mall. My first Chinese food (not cooked by me) here! It was this dark sweet chicken. It came with white rice with some peas and carrots, and I also got a Japanese green tea drink. It wasn't bad at all. Although it was relatively expensive at 1450 forints, I will defintely go back.

Went grocery shopping, but unfortunately forgot to bring enough money, so just bought some essential items. So I'll have to go back tomorrow for dinner! Well, that isn't all bad. I wonder what tasty food is waiting for me tomorrow. Fortunately, the walk to and fro today wasn't all that cold.

Did some work, but not nearly enough. Looked at and pretty much finished all my number theory problems due Thursday, which was a big success. Number theory is so enjoyable, I've always thought it is the most elegant branch of all mathematics. I wonder if I will still think that after I've had a course in it.

Awkwardly spilled a bunch of water on my desk tonight. Fortunately my computer is on a little pad with fans, because otherwise it overheats. I am fortunate I stupidly damaged one of the fans before, so I had to buy the pad, but otherwise my computer might have been flooded! Ah, life sure is funny sometimes!

Tomorrow my first course- number theory, is at 10, but I shall go a little early to get to the director and buy a Combinatorics textbook for reference, and also my character theory textbook. I think I will commit! Commitment is exciting, but also nervewracking as well. Let's see how this journey goes~

A case of the MONDAYs

Ok, not really. Just more like a case of getting up early.

Only five people in CLA today. That isn't that much of a surprise- to Csaba either, because it is 8 AM on a Monday, and some people don't like his teaching style. We talked about inequalities and convex functions and neat stuff that is really helpful that I haven't seen before.

Then was FUN. It was a lot of fun~ We proved the theorem, that any vector space has a basis(following from Zorn's Lemma), and we went on to prove the existence of ultrafilters. This is relatively intense stuff- Godel came up with it. We also talked about how this related to probability. We considere the situation when you have a urn of countably many balls with the natural numbers on the balls. Then what is the probability of drawing an even ball?

During the break, the professor was talking about his area of research, and how it coincides with Terry Tao of UCLA. He recounted how last year in February he was told they were working on the same question. He said he better start working like hell, because Tao was 100 times smarter than him. I think this is really funny, since the Green-Tao theorem is something I admire and can one day, hopefully understand.

Had a good lunch of chicken penne with a yummy lemon lychee drink from the cafeteria.

Then was combinatorics. Not the most exciting class- but I'm going to take it. I'm in Hungary, after all. It never really feels like real math like me, but I have to admit today we did some pretty interesting things. We considered generating functions. With it we can solve questions simply such as the following. We roll 5 dice, how many different ways can we get a sum of 18? Hint- the solution is between 500 and 1000.

Went home, finished up Sam and Max Episode 4, defeating Abe Lincoln. Hooray!

Did a bunch of math- including coming to grips with the last class of character theory. To me, it feels like a challenge I can't refuse. Csaba told me if I pass the class he will take me out for two beers. But I was told last year 7 survived that class, and only 5 survived abstract algebra. So I suppose I should choose what I'm more interested about. That being said, I'll probably sit in on abstract algebra tomorrow morning, and if we do something extremely cool- such as prove there really does not exist any group with order 87, then I might take the class.

Had a good dinner- of more microwaved chicken cordon bleu, and some bread with tasty pesto sauce I purchased. Watched the new Terminator episode, and really enjoyed it.

Got some more homework out of the way- including finishing my Hungarian h/w, and trying to finish my computing homework due tomorrow. I got tired before finishing, oh well. I'll have some time to work on it tomorrow, I hope. Also looked at more REUs I'll apply for later.

That is all for today. Tomorrow class until five....

Tomorrow's Monday? No way!

Got up at 10:30 AM, with the help of my trusty cell phone alarm.

Again did a lot of work today. Finished up my Combinatorics homework, wasn't too hard. Also did a problem of Algebra, which involved copying the exact number six from homework 12 from last term. I didn't start my Character Theory yet- I really need the book to work on the problems, but I think after I succesfully attack these problems, I probably just won't work on advanced algebra any more.

Had a good lunch of a gouda cheese and meat sandwich. Got some new bread, my last bread was very nutty and dark, and was much too dense for my taste. This bread is white, and has a little bit hard crust, but the inside is delightfully fluffy.

Read some, looked at functional analysis as well. I don't think the problems are that hard, but I don't think I'll have the time to work on this class. I am a little intimidated by the format, so I'm becoming more and more convinced that auditing this class is the right choice for me.

Worked on applying to another REU.

Cooked a relatively complicated dinner. I had egg noodles, with fish, and spinach. This is the first time I've had fish (this was frozen) in this country which doesn't touch the ocean. It wasn't bad, but it was a little bit too fishy. The creamed spinach was funny because it was frozen into heart shapes.

Had a good dessert capping off my meal as well. It even had some pineapple bits in the cake!

Watched the second to last episode of Prison Break (will they finally break out?!), and worked on some set theory.

Tomorrow I have CLA, FUN, COM1A. MAP is also offered, but I again won't go. Last Thursday the professor came up to me, thinking that I was in the class. He had talked to me a lot in the info session and had showed my interest. I didn't want to take his class, but I didn't want to tell him. It was awkward. I guess I'll send him an e-mail sometime.

I have to register for classes by Thursday at noon. I'll see how THC goes Tuesday and unless its really bad, I'll just stick with that class instead of LOG. It seems I finally am having some idea of what I want.

Good night~

Its cold~

Got up at 11. Choco-puffs knock offs for breakfast with a croissant.

Actually did a moderate amount of homework today! My theory of computing problems were very interesting, and are motivating more and more for me to take the class. Answered a combinatorics problem that was bugging me for a whole week. Not quite sure about the answer, though. Its not a huge deal, though- for most classes an 80% is an A, and I think with work a percentage close to this should be acheivable.

Played some more Sam and Max Episode 4. Now Max is president. Hooray!

Didn't have any bread yet so just ate meat and cheese for lunch.

More work- including reviewing Abstract Algebra (which wasn't very interesting to me). Went out to the Match to buy a bunch of groceries, including replenishing my big bottle of water, some more bread, cheese, and some very interesting meat -with a picture of a girl holding the meat donning a very strange hat on the package. Got some more delicious desserts and some more breakfast food.

The walk to and fro the mall was sooo cold! Weather.com indicated it was supposed to feel about 15 degrees outside. And the walk there the wind is always blowing heavily. I had my earmuffs and chiefs had on, and my sweater, scarf, and heavy jacket on. It kept everything warm except my face, which felt half frozen after the ten minute walk. Of course when I entered the mall I felt like I was on fire, because I was so hot! Oh well, it is supposed to get much warmer over the next couple of days~~

Then I went to dinner with some friends. Went to a Hummus Bar. I ordered the most, getting a complete plate and some kind of soup. The soup- which I got just because I wanted somethign warm- was a bean soup, and tasted good. The complete plate had falafels, mushroom, chickpeas, and some other grounded mix all with hummus. I ate this with two pitas, and didn't finish a lot, but it was pretty good, especially the falafel. There was some diced pickle dip that came with it, and I thought that made it tastier. I was sort of missing the meats, but it wasn't a bad dinner. It cost 1800 ft, so it was relatively expensive, only because I had ordered so much.

Did my laundry. I also attempted to do homework when I got back. Was already tired, though. I probably did about 3 hours of intensive thinking today. I'm not yet used to that. I want to get up early tomorrow, to do more thinking! Fun, huh?

It's a Friday!

Got up at 11. Today it required the alarm to wake me up~

Had a wonderful bowl of multigrain cheerios, and a croissant for breakfast. Then headed off to College International for my Functional Analysis class.

It was absolutely brilliant. The professor really makes analysis, a class the students typically are not as interested in as algebra, exciting. We talked about the completion of not-complete metric spaces. Then he veered into set theory- a class I think I can now take, because the hours will probably be changed! And talked about the axiom of choice, a somewhat controversial proposition, and the amazing property of ZFC that follows that you can break a ball of radius 1 and construct a ball of radius 2 from the debris! We also talked about the homework, which I had not yet looked it- it is only optional. I think I could handle the course, but I will definitely at least audit at.

Then, I ate a salami sandwich, and was off to the Renyi Institute and CHA. Today was really intense. We talked about and defined what modules are, and defined that representations of G (over F) are simply FG-modules! I didn't completely understand, and I need the book. I think I will buy it soon. We proved Mashke's Theorem as well. I followed some of the proof but not everything. I am still hopeful about this class. We got our first homework, and I will not take this class only if it turns out to be impossibly hard, because this subject matter seems more interesting to me.

Afterwards headed to a pizza place with some friends and had half a 'Bangkok Pizza'. It had pineapples on it and was tasty. The name is still strange sounding, though. Went back and wasted some time, ate some sandwiches to finish off my dinner, and went off to a BSM party. Spent that time eating some snacks, including chocolates- some with irish creme!- and talking with friends. It wasn't bad.

Proudly found my own way back to the flat myself. Took the tram back 1 stop, and then back onto the metro for 2. Now I'm more used to the public transportation. Its unfortunate the subway system closes up a little after 11, I'm sure I got on one of the last trains, since mine departed at 10:59.

I'm much more comfortable with the little parts of the city that I've explored up to now. I still have a lot more to do. This weekend I'm sure I'll be inundated with homework, however. This is especially because I've sat in on 9 classes last week. I have homework in FUN, COM1A, THC, SET, HUN1, AAL, NUM1A, CHA, and LOG. I need to get a lot done, and start making decisions about what to take. I must make a decision by Friday. If I take a 6th math class that will cost $350 extra- but this is not a big deal, since the school will reimburse me. Choices choices choices.... it doesn't look like a fun weekend is ahead of me.

Actually doing stuff other than class...

Got up around 11, without my alarm. That was nice.

Went to NUM1A. Today was the problem solving session. That was a wonderful experience. Had 2 hours to work on a variety of problems, including such as 'For what numbers are 2^n -1 and 2^n +1 both prime? And prove for any integers x and y if x^2 + y^2 is divisible by 4 then both x and y are even.

Then, I went to LOG. It was pretty intense. The professor was scrawling many definitions up on the board, after we finish first-order logic, with the compactness theorem. Not quite sure I'm going to take the class any more, will see how next week goes. He himself said this stuff is boring, you just need it for everything else. I will also see how the homework is.

Went to the Renyi Institute, and watched N is a Number. This is a documentary about Paul Erdos. He was such an eccentric guy. He had no home, and simply traveled the world to do mathematics, getting paid to give talks, and staying with fellow mathematicians for periods of time. It was awesome seeing him walk down the exact same steps we had just walked up to go into the room to see the movie. One of the best quotes of the movie was, "If there was no math, there would be no Paul Erdos."

Then decided to go and see a concert by the Budapest Concert Orchestra at the Bela Bartok National Concert Hall. Student tickets, although very high up, were only 200 ft- or a little more than 1 dollar! Grabbed a hot dog before, and this was more expensive than the ticket.

Hungarian classical music was played. I listened to KODÁLY: Dances of Galánta, KAMILLÓ LENDVAY: Piano Concerto, and BARTÓK: The Miraculous Mandarin - ballet with animated motion picture. I thought the first was the best, but the second two just didn't match up. This is funny because my metro stop is named after Kodaly. The animation -although unique- was very strange and abstract, and I didn't think it flowed that well with the music either.

Went back home. It took about 30 min to get home. First took the train, then the tram, then the subway. I had never taken the train or tram before, but with my friends' help, it wasn't hard at all.

I saw the Danube for the first time today, and I also saw Gellert Hill, a hill with Hungary's Liberty Statue, erected by Soviets commerating Nazi defeat. I shall definitely visit this later, perhaps when it is warmer.

Tomorrow I only have 2 classes as well. What a wonderful life~

Keeping the vampires away

AAL- first hour we talked about Sylow's Theorems. I knew exactly what was going on, since this was pretty much a repeat of the last bit of last term. For example, we looked at the group of order 77, and we proved that it is cyclic. For a h/w we have to generalize this situation. The second hour, after the break, we talked about the "Correspondence" thm. There were lots of bars, and discussing of images, and I completely lost focus.

Then I went to NUM1B. Csaba couldn't come today, so I went to the other professor. He was a fine profesor, but I think I shall stay in Csaba's class.

Went to the cafeteria and got an excellent lunch of curry pork with cabbage, and rice. Got a coke to help keep me awake as well.

Then I tried out C&P. The class is Conjecture and Proof, a mainstream of this program. Only five people- not including me, were in the class. The normal professor could not teach this year due to health reasons, so they had to do a lot of juggling in the schedule to make it work. Now it looks like the class might be canceled.

The class involved a lot of problem solving. I.e., have a 8x8 chessboard, when you lay 3x1 dominoes on it, how can you cover the board, leaving only one space empty? Today the homework was due and the students were presenting their proofs, and I was sitting and watching. The professor was sitting there, commenting on their proofs, and the such. It seems interesting, but I prefer a class with more structure. I got the homework for next week, and it involved problems such as proving log base 10 (3) is irrational.

Then was character theory. On the way, with a friend, I stopped for a tradition Hungarian snack called Langos. http://en.wikipedia.org/wiki/L%C3%A1ngos It sounded like a funnel cake, except without the sugar. I got it- this big deep fried piece of dough, and it was very oily. I started eating it. It had a garlic topping, which was something I did not expect. The garlic flavor was so strong! It was pretty much the exact opposite of a funnel cake. Later the snack gave me indigestion. I don't think I'll be trying it again, unless I go try it with the cheese and ham topping. But I probably won't know how to order it by myself, anyway.

Then came the class. It was absolutely astonishing. We talked about how these characters of the group held all the information of the group. We talked about how the conjugacy classes would create a character matrix which was essential to tell whether or not it is simple, and how the columns and the rows are orthogonal. We also defined what a F-Algebra is. He has been introducing much of the overview of the course, and soon we will start to prove many of the results he has shown us.

The professor is a really amazing guy. I was looking through my real analysis book and in the back- Undergraduate Texts page, there is a text authored by him, Discrete Mathematics. What is really amazing, however, is his placing in the International Mathematics Olympiad. Apparently this is a int'l high school math competition. His freshmen year, he got silver. All remaining years, he got the gold. He is number seven on this list http://en.wikipedia.org/wiki/List_of_International_Mathematical_Olympiad_exceptional_participants. When you are not only brilliant, but a great teacher too, I think that is a rarity. This gives me even more incentive to take CHA.

Got home, took a nap for an hour and half or so, and then did some math studying/ reviewing. Had a simple dinner of a sandwich since I was still pretty full from my day. Tomorrow my first class is at noon! What a wonderful day that will be~

The long days continue...

First AAL was supposed to have office hours from 8-9, but everybody showed up, and I awkwardly slept in and came at 8:40. The first class wasn't very useful, and in the second hour we started talking about Sylow's Theorems- tomorrow we shall prove them. The class is still good, but it seems that the professor doesn't provide much motivation- he simply goes through the notes on the blackboard, leaving me not completely satisfied. That is another check that goes to CHA.

Then I had THC. Unfortunately this time only 3 people, including me, were in the class. It still seems pretty interesting, as we were getting more focused on the idea of regular and nonregular languages. If there are less than 3 people this class will not be offered, and it seems really unique, so I'd still like to take it. SET still might change its time, so it is contingent on a lot of things.

I then had a two hour break where I attempted to work. That didn't work out so well. Breaks in the schedule are not much fun.

Then I had my 2-5 Hungarian Language class. It was long. We worked with more verb conjugations and the such. Why do languages even have verb conjugations in the first place? It seems so useless. Chinese is really the best, grammar wise. Read some dialogues as well. Before class, during the break, and while eating, I had memorized the numbers 1-10 in Hungarian. They go something like this: egy, kat, harom, negy, ot, hat, het, nyolc, kilenc, tiz. That made me proud. I'm not very good at learning languages....

Got back, played a bit of Sam and Max, episode 4. It is titled 'Abe Lincoln must die.' http://www.youtube.com/watch?v=4khnsrhXjLU It was getting late so I decided to head out to the mall, yet again, for dinner. This time I went to a grill place, and got a 'steak' on a bed of fries and some chopped cabbage and onion. The steak turned out to be grilled chicken, and there was some white sauce on top of it, but it was really tasty- probably the best thing I've eaten at the mall so far.

Got back, and did my AAL h/w. That wasn't very much fun. I had to prove the orbit-stabilizer theorem, which I conveniently copied from last term's notes. The notation is probably 'wrong', but its the right way anyway, and if the professor doesn't like it he can tell me.

Tomorrow will be another AAL class, and I will have CHA as well. A good day to compare them, perhaps.

I actually didn't nap today! I did have an tasty Italian Espresso from the coffee machine at the college. But now I'm tired, and I have to wake up early again tomorrow. No fun! So good night!

Yay Dollar!

A pretty excellent day. Had only two classes, classical algebra, and then functional analysis. Classical analysis was about polynomials, and was pretty much a recap of my first and second day of Galois, and ome number theory.

I talked to Csaba a bit about the algebra courses. They both sound very daunting. AAL currently has 18 or so, usually only 6 survive. CHA now has 8- and he says only 3 survive that course. The funny thing is that Csaba had the CHA prof Pelikan when he was an undergraduate, and he didn't get an A!

Functional analysis was good. Got our first homework, which actually is never due, but still needs to be done. We discussed the Arzela-Ascoli Theorem, the Baire Category Theorem, and found some weird analysis examples that tend to confuse.

Went home, exuberant that classes had finished so early, and ate lunch- the leftover mexican sandwich, and some mushroom chips. They were actually pretty tasty. They had enough non-mushroom flavor to taste good, but still retained their mushroom-ness.

For the first time I tackled doing the laundry. A bit complicated, and hard to close, but it was a pretty easy process. 2.5 hr later it was still going, and finally I realized I had not turned the water on! Then I did, and it was a simple process. I'm in the bathrom taking pictures- I figured I might as well show you what the hot water heater thing looks like.


Took a nap. Paid rent. Realized that the dollar was doing extremely well. Both times I withdrew I got the same amount of forints, but when I checked my bank statement, this time was 7.3% less US dollars. When you're withdrawing a lot of money, that can be a lot. Now 1000 forint is about $5.50. So you can easily buy a meal for less than that. Today I had dinner at the mall, got a weird spaghetti thing with a fanta. I thought the spaghetti had meat, but to my chagrin the meat was actually sun-dried tomatoes! But it was still tasty. And it only cost 910 ft!

Watched the new episode of Lost as well. Not as crazy as the last one, but still pretty exciting, and couldn't believe it was over.

And did an abstract problem! Yay! For the first part I pretty much copied the solution out of last term's homework. Good thing I brought the notes, the homework, and the book here!

Tomorrow I will be much busier. :(

Now I recharge.

A two-day weekend is just too short

Went out to Octogon today for the first time, in pursuit of a grocery store, since I didn't feel like going to the mall yet again. Seems like a relatively touristy area since I heard a few English speakers. At the store, a lady came up to me, talking, and I had no idea what was going on. Then she asked if I spoke English. I nodded, and then she asked me if I knew where the butter was. I had no idea. I was confused, and looked at the cheeses for a while, and then slinked away.

Bought a bunch of strange things- including the mushroom chips. I am curious to see how they taste. I also bought a prepacked mexican sandwich, which I ate for lunch. It tasted pretty good- like a chicken taco! Except in a sandwich!

Did a lot of skyping. And some mathing. My math feels rusty. I better get up and running soon! I also applied for Joseph Gallian's REU at UMN-Duluth.

Had a dinner of chicken cordon bleu with vegetables. Had just bought a frozen package of them, I cooked too much but I ended up eating it all. I also really enjoyed the pear drink that I had. I don't even think that exists in the States.

Only 4 hours of class tomorrow! That will be very nice.

Good night!

Finally- a day without class!

Got up late and had a relaxing day! Reviewed some math- not nearly enough, though. Finished Sam and Max, Ep. 3. That was fun!

Went to dinner at the mall. Had a yummy spicy gyro. The conversation with the lady was very awkward, since she knew a little bit of english, but not enough, and she kept on saying the wrong word. Afterwards had my excitement of the day -- a wonderful berry flavored ice cream cake desert, topped with three berries and some pretty decoration. I wish I had taken my camera.

Was going to go shopping, but the store in the mall closes at 9. Had enough time to go to the media mart- a Best Buy like store, with tvs, computers, laundry machines, etc. to buy batteries for my mouse and calculator, which were relatively expensive.

Watched Star Trek 3. Not bad!

Tomorrow maybe I can get more done. But I need to get caught up on not working.

It's the weekend!

Started off my day with Graph Theory, taught by Miklós Ruszinko. We went through walks and powers of matrices, the Brasford Search, and the definiton of a tree. It is a fine class, but it seems very difficult, not too exciting, and altogether not that rewarding enough. I will take Combinatorics instead.

Got the notes to Set Theory. There aren't enough people interested in the course as of now, so plans are to change it to a reading course. They also are thinking of shifting the time slot to go against the number theory class. If that happens, as much as I want to, I simply won't be able to take it. I hope that's not the case!

Sat in on Differential Geometry. The professor seems great, but there were lot of integrals and sins and cosines on the board, which means my attention will slowly but surely start to drift. I didn't take notes, but I remember them working on a problem involving path integrals and the formulation of a cycloid. Just not my cup of tea.

I then got a big lunch of some kind of fried chicken with rice, and a delicious many layered huge piece of cake for my desert. I ate this during my second FUN class. We continued on talking about compactness, and solved the hotel problem. It i apaprently called the Tihonov Theorem. The concept of infinity really can boggle the mind- I'll have to think about it some more, thats for sure.

We then talked about some things that he said really weren't relevant, and they involved Ramsey Theory, and the proof to Ramsey Theory. I had never seen this before, and although not understanding it 100%, it really was interesting. He also stated that there were some ramsey numbers so difficult to find, that if the aliens came down, and asked us we for R(5,5), or they would kill us all, we would have to connect all the computers of the world, and pray. If they asked us for R(6,6), we should just connect all the nuclear bombs and kill them all.

We then briefly discussed the Cantor set, and how that it creates the numbers in binary, and has all the properties of addition and multiplication, so it is actually a ring!! He almost let us go before he told us this neat fact, but he then beat his hand with his hand, and remembered. We have class Monday only if he doesn't die over the weekend- because with his age (he is not even that old), who knows what might happen! Oh, and we briefly discussed the E-D def'n of continuity- what he called the geeky definition, and that is why people don't like mathematicians. He is such a unique guy- how can I not take the class?

Then I went to the Renyi Institute to sit in on Characteristic Theory of Finite Groups (CHAR). Took the subway there, and on the way there, passed the tranin station, to the right.

The Reny institute is a great place for mathematics, and even includes a glass elevator reaching to the top floors. While going up the stairs to the classroom, we would see the pictures of famous professors who had passed on, such as Paul Erdos.

The class was taught by József Pelikan. He is a great guy, a bit more excitable than the AAL professor. I thought there would be absolutely no way I would understand what was going on, but for the most part I did, and I really enjoyed it as well. We talked about matrix representations of groups, such as D4, and A5, and what it meant for the representations to be equivalent. In algebra I really enjoyed the matrix problems, and perhaps this class holds even more of them. We went on to discuss Manschke's Theorem and irreducibility.

I talked to the professor, and he basically said I needed to understand basic group theory, and basic linear algebra as well (we discussed invariant subspaces a lot today). I think after this class this tops my AAL class, but hopefully I can get a clearer picture of the classes after the next week.

I did some wandering after that. I headed in the direction I thought home was, but instead, I headed toward Buda. I saw the White Bridge that took cars above the Danube. I decided to wait and have that journey at another time. I walked back to the Opera subway, and didn't really see much exciting, and decided to take the train back home.

Ate dinner from this pizza place, and randomly selected a pizza, which ingredients were in Hungarian. I saw the guy throw up the crust, and put the sauce on it. I got disturbed and frightened when I saw the sauce was not red, but white. In the oven it went. I waited, flipping through some Hungarian magazines, and it was soon done. It had pepperoni, celery, and a few tomatoes on it as well. I picked off the tomatoes, and reluctantly took a bite, when I was back home, in front of my computer and watching the last new Moonlight. It tasted great. The pizza made me happy.

Well, this week is over! I've pretty much seen all the courses. I just might sit in on Conjecture and Proof next week, which is supposed to be one of the prominent courses here, but for now I think I have a better idea of what I'm going to take. Class lists follow:

CHA/ AAL
FUN
COM1A
NUM1A
SET/THC/LOG
HUN1

I think I must choose between CHA and AAL. I just don't have the spots to take both. I also think I will choose between SET, THC, and LOG, with them currently ranked 1), 2), and 3).

I have been thinking too much about classes recently. That makes me tired. I think I shall go to sleep soon.

Hello!

(In Hungarian hello and goodbye are the same word. Therefore, sometimes Hungarians say "Hello" for bye! That happened today in the pizza store, after she knew I spoke English. Saying "Hello" for "Goodbye" is fun! Try it out sometime...)

-Isaac

A day from Hell

So, hopefully today is the only day in my life I have to sit through 10 hours of class. 8 hours, I think is not too horribly long, since it is the length of a normal work day. But anything longer than that, and the mind starts completely shutting down. Mine, at least.

So, my first class was CO1A. I'm definitely enjoying this class more than I thought I would, and the professor was a much more awake today. We did combination with repetition, worked occupany problems, talked about Stirling numbers of the second kind, and went through the Multinomial Theorem, a generalization of the binomial theorem. Next week the professor is going to Pisa, Italy, to attend conference, so we won't be having class, and will have to make it up in the future. If I still choose to be in the class, that is.

Then was the Graph Theory- Set Theory block. A friend of mine was going to sit in on GRT and get the syllabus and take notes for me, so I decided to try out set theory. This is taught by Peter Komjath, the same class/professor that Prof Siehler had when he was BSM-ing. I know little about set theory. The aim of the course is to prove "everything" on infinite sets, show the foundation of math on sets, and prove interesting theormes about the reals, etc. We started up with axioms, such as Ax 1 (Existence)- There is a set. We then began to have theorems, our first was: "There is an empty set", and we began to prove these statements. Slowly but surely, we were building, building, building up on our foundations, and we ended class with a neat proof that if A and B are sets, so is AxB, by showing a set which contains (a,b) as a subset.

I think I would like to take this course. I am interested in GRT as well, but next week there will be some time shifts, so I would be able to take both of them, if I want to. I think I enjoy constructions from the basics, and seeing what kind of complexity can be built up from such simplicity.

Later on, I copied the notes from GRT. Unfortunately the class is not very popular, and the professor is supposedly the least-liked among BSM. Almost every one who takes the class has a negative impression eventually, and I suppose the professor is important in a mathematics class, but the subject is important as well. We got our syllabus and our h/w, and defined many basic properties of graphs, such as simple, bipartite, matching, chromatic numbering, and played with incidence and adjacency matrices. It looks interesting, but simply just OK. I don't want to waste my time slot with a poor class, but I think it would be interesting to study Prof Dymacek's speciality as well. I might sit in on class tomorrow, unless I feel really set-theoretical.

Then I got some vegetarian pasta thing with fries for lunch, and went to NUM1A. Having a class with Csaba is so different since you cannot always trust what he writes on the board. We first discussed the notion of primes and irreducability when you only examine 2Z, and he doesn't just tell you the answer- he really makes you think, and when it comes to proofs, the class must be a part in proving them. Sometimes in math I drift off, scribble whatever is on the board, and figure out I can understand it later. This is not true for this class, since at times the notes are worthless, and you must really understand what is going on. After the break we talked about and went through the proofs for divisibility, the divison algorithm, and euclids lemma. Sometimes he is not so thorough with the proofs, but hey, that is what the book is for. Next Wednesday we will not have class since he has a court date since another car ran into his and is claiming it was his fault, so I think I will try the other professor's class then. We will have a make up session later.

Then I went to Mathematical Logic, LOG. By then I was starting to fade. We discussed "What is truth?" - in mathematics, and made many definitions. This class was taught by Miklos Szabo. We pretty much went through my whole 100 level philosophy class in an hour. We defined tautologies, showed Modus Ponens, and we defined provability, and then finally showed the Compactness Thm. Logic uses really cool symbols! But by then I was losing a lot of focus. It definitely seems like a good class, and seems like a great parallel course to take with set theory, since they rely on each other. I will go again next week after studying (and hopefully completely understanding) this weeks notes, and doing the homework (one problem involves the island on which there are only liars and truth tellers!). Unless I am completely lost next week, I think I will take it.

That class ended early at 3:30, and after I spent some time on the internet, and I went in to MAP at 4:15, but apparently I was late. I didn't feel like starting to take notes, especially when I was late and mentally tired. We were talking about logic in lattices, and I was completely uninterested and lost as well. I also didn't really get the connection to Quantum stuff. I kept on looking at my watch, but time seemed to tick by very slowly. I pulled out and ate two sandwiches I had packed in the hope that food would make time go by faster. It didn't. Class ended at 5:55- he had taken more time than he should have. I'm sure it can be interesting, but I had seen what I thought was much more interesting things today. So, although the professor was a great guy, that will be my last MAP class.

Got home at 6:30 after a relatively long and really crowded bus ride back, and I completely crashed at 7- napping for 3 hours, and got up and cooked myself a very late dinner. Finished up my pesto pasta and added some chicken. I thought I was going to go to the pizza place about a block away, but I guess I'll try that tomorrow instead.

So tomorrow is the last of my new classes. I will go to Differential Geometry to see how that is, and I will also go to Character Theory of Finite Groups. I think the chance of me taking these courses are minimal to none, but they deserve a shot, anyway. That means tomorrow I have class from 8-4:30, and afterwards I guess is my naptime again.

Next week should be better, because my course list is already smaller. But I have to narrow it down to five courses- I think anything more is just too much, unless, perhaps, 3 of the five turn out to be reading courses (i.e. meet only once a week). I will definitely take number theory, am very confident about taking set theory and advanced abstract algebra (unless Character Theory somehow blows it away, or some other unthinkable thing occurs), so that only leaves 2 spots open! Perhaps logic and combinatorics/graph theory? But that leaves functional analysis amiss. And THC was enjoyable as well! That might be reading, so could I handle adding that in? I will have another FUN class tomorrow, to decide more on the future of that. I think how the schedule works out is somewhat important as well. I would prefer not to have 8 straight hours of class one day, unless I have one whole day free, for example.

Choosing is hard. Is it better to take an intro course on something you've never seen, or continue on in a subject you've already studied a lot of? Especially after tomorrow, when I shall know about all the courses, and the real future schedule, I must start to choose. Perhaps you can help me as well.

Hooray! A light day!

Trying to see how far I can push it before being late, I got up at 7:30 AM, leaving at 7:45. I excitedly got to the 76 bus right when it came, and in the end, I was still plenty early for class. Perhaps I was still a bit too sleepy for algebra, however. Why is it always so early in the morning?!


Today in AAL we discussed faithful and transitive actions. Nothing very complicated- but it was some new terminology and ideas, and I'm sure I won't have a problem understanding the notes when I review them. We also have our first 3 h/w problems, due next Wed. He holds office hours the first hour of class on Tuesday, but I'm sure I've solved some of them last term. Good thing I brought my notes and h/ws with me! For example, one problem was to show the conjugates of G formed a subgroup of G.

Then was my first number theory class, NUMA. There are two sections, one taught by all of your favorites, Szabo. I decided to give the other a try, but many had experienced his teaching style in CLA and were reluctant to take him. There were 19 people in the other prof's section, and 4 in his. He came over to our classroom, said something to the Prof in Hungarian, and asked for some of us to come over. Number theory is important to me, so a good class is important to me, but I decided to give him another shot. Me and some others went to the other classroom to try him out.


Szabo teaches in the department of number theory and algebra, and is an algebraist, but his first love is number theory. He says it is "big fun!" When he was 17, there was a soccer game after school, but it was canceled, and instead he solved a number theory problem that was proposed by Erdos, and had since been unsolved. He didn't realize the significance of it, though, but later when on to publish his work. However, he failed his second term in number theory, and the undergrad level, and that affected him, so he decided algebra was his future.


So, you can see, he is a really smart guy. That class I sat in on was absolutely great. He asked us some very interesting questions about cannibals eating scientists. Say you have n scientists that are captured by hungry cannibals. They will eat them for breakfast. They are cruel, so they will put a green or red hat on each scientist's head. The n will be lined up, and the first to answer will be in the back. Every guy can only see all the hats in front of him. The scientists can say, "Red," or "Green." If your hat matches what you say, you live. How many scientists can be saved?


The answer is quite tricky, and it does require some thought. You can see Szabo emphasizes problem solving. Of the 2 classes each week, the second will be a problem solving class. This is what is important in number theory. For the second hour, we briefly discussed Mersenne and Fermat primes, and how little is known about prime numbers. I heard the other section of number theory was discussing primes more, but I think I am very likely to stick in his section. This is the book I bought for the course. He says it is not required, and he hands out .pdf notes, but this is a very high quality book, and will be a great reference for me as well as I continue number theory.


I was wanting to try Conjecture and Proof today (which I heard showed a couple ways to show that the square root of two is irrational), but due to the great number theory class, I chose to try Galois one more time. I ate a yummy 400 ft pasta for lunch before class started, and Szabo started off class with his greeting, "Welcome boys and girls!"


This time class was much better, and we went through some proofs and the like. That being said, I don't understand fields and rings well enough to take the class. The last 45 min I completely zoned out, unless Szabo started telling one of his jokes. His favorite involves meeting girls in a bar. He says to never tell them that you're a mathematician. Just say, my work involves Unique Factorization Domains, or Quaternions, and then they will be impressed and like you.


Even though class was done at 2, I was stil tired. I went back, napped for 3 hours, and made myself my dinner. I finished up the old rice, and made stir fry with shrimp. The shrimp were really small and I could barely taste them, but it was still good. I also drank the milk I had bought yesterday. This one tasted extremely normal, which made me happy.

I then did the dishes, and I reviewed the first month and a half of material from last term's group theory course. It will be very important for me to be extremely comfortable with that material.

Tomorrow- class from 8 to 6!! Including my first Logic and Graph Theory classes. I hope I survive.....

When 1 day of lots of class just isn't enough....

Woke up at 7:15ish after snoozing, got into class plenty early.

First class today was AAL, or Advanced Abstract Algebra, taught by Peter Hermann. The class will cover advanced theories of groups. We started off by review groups- order, subgroups, index, the normalized, and factor groups. We went on to homomorphisms, permutations -- in which the right way, such as x(Pi) was voted against 2-14 :( -- the symmetric group. We then started what he called was new material. This included group action, which is not a very difficult concept, and after some examples, including trivial ones (i keep on remembering.... trivial examples earn trivial points!), we talked about the stabilizer and the orbit. Apparently next class, which is tomorrow, we will talk about the Orbit-Stabilizer Theorem, another topic I covered last term. Apparently that is a very important theorem in our studies this term.

This is a great class. I feel very prepared for it, and have done even more than other students whose professors stick clearly to the textbook. Hermann is a great professor. I remember him saying something about "this is how groups live and breathe", and I thought that was so great. I will definitely be taking this.

Afterwards I sat in on Theory of Computing (THC) taught by Gyula Katona. I didn't come in with many expectations- I had little to no desire to take the class, but the lecture was quite interesting. We talked about finite automaton- and how machines can be built to answer questions such as whether or not a string contains 001 as a substring, when the computer has 2 choices. It was very logical but also very different, and I have never seen anything like it before. We then briefly touched on non-deterministic finite automaton, or NFA, and these seemed even more interesting. I wonder how they choose. Terminator, anyone?

Katona is not the greatest professor- he copies a lot from the book, but the course is unique and is now on my would like to take classes. I'll also see how the next lecture, which isn't until next week, goes.

Then I got a tasty lunch of rice and pork with vegetables (tasting a bit like pot pie mix), and sat in on Galois Theory (while eating!), taught by the interesting prof Szabo. He spent the first 45 min talking about Galois' exciting life, then we discussed the last 45 min what a polynomail was, and what fields and rings are. I don't exactly known what they are myself, and I don't feel that confident about them. He was much more relaxed today, only pacing back and forth a lot, and his writing was much neater too, but I don't think I have the background to take the class. It is an exciting subject, though- but I still have grad school! I'll give it one more shot tomorrow.

Then it was 2, and I had my Intro to Hungarian class. It was 2.5 hr long. We learned basic pronounciations, grammar, the to be verbs, some basic vocab, and the numbers. It is interesting since some conjugation depends on whether the words are front or back, which depends on the last vowels in the word.

Finally got home 5:30ish. Went to the mall, eating a McDonalds chicken nuggets and a large coke (this was actually large!). I tried to order the meal with fries but I guess they didn't understand me. Then got a piece of cake at another place, and did some shopping at match. Then went home to look at some math!

Tomorrow is another algebra class, my first number theory class (which I will surely take), and more galois theory. The characteristic theory of finite groups is canceled on Wed, and the first class of that will be Friday.

Its almost the weekend! ha~

a MATH day

Well, I woke up on time! That is always a relief. Waking up at 7 AM does leave me incredibly tired, however. I only got to watch one quarter of the Super Bowl, and I went to bed knowing the Giants were ahead 3-0, but the Patriots being yards away from scoring.

Woke up and quickly started up my computer- saw the Yahoo headline about how Bellichek was a poor loser, and was happy, although still tired. Had some spreadable cheese with yougurt for breakfast.

Took the trolley bus to school, arrived a little before 8 AM. The classes are as follows- 2 hours long, starting at 15 past every hour, and at the hour we get a 15 minute break. So the 2 hours class is really an hour and a half. Not saying this is little, though.

So, the first class was Classical Algebra (CLA), the review class, taught by Csaba Szabo. (In English, this is pronounced Chaba Sabo). He is one crazy entertaining guy, scribbling on the blackboard in his almost illegible handwriting. The blackboard in the room is the type which can be moved up and down -he throws it up and down with such force that it BANGs every time. If there is an equation on the top side of the board he wants to refer to, he chucks a piece of chalk at the top of the board, hitting the equation, and then catches it on the way down. I don't know if I've ever known anybody as eccentric as that (and thats saying a lot!).

Today we just reviewed complex stuff. Its been about a year since I had complex analysis, and today definitely brought back the memories. We started off with the easy stuff.... just for a bit, and then moved on to taking roots of complex numbers, and roots of unity. I slowly started to remember. I'm not sure I can learn much from this professor, however, since after the hour and a half class- I only have a page of notes. He also teaches Galois Theory and a section of the Number Theory 1 class. I'm going to sit in on the Galois Theory class and see how that goes. I think I work better with a much more typical teacher.

Then came Intro to Functional Analysis (FUN). This class I'm planning on taking, unless there are just too many other things that are interesting. It seems somewhat intense, but perhaps its just been a while since analysis. We discussed compact metric spaces, and although I recognized many of the definitions, I didn't know sequential compactness, or what it meant to be totally bounded. From what I understand, we were simply discussing the Heine-Borel Thm (i.e. compact iff close bounded) for metric spaces. We also discussed a problem involving a infinitely high hotel, with finite floors on each floor, and fire escapes connecting some of the rooms on the floors. We are supposed to prove, I think, that we are able to go up without ever going down. Somehow this has to do with Konig's Lemma.

Our professor in this class is Gabor Elek. He is a very dynamic and excited guy, but gives very good notes as well. I didn't follow some of his proofs, but I'm sure it won't be a problem with some review. He also said he goes on Terrence Tao's blog, and we will get a lecture that has been posted on that, after we have enough understanding! For this class, 100% of the grade is the final! I've never had anything like that before... but since it consists only of previous h/w problems and theorems, I don't think it should be that bad.

I went got a sandwich, and then sat in for Combinatorics (COM1). Hungary is well known for its combinatorics, but the subject has never intrigued me all that much. Our professor was Attila Sali, and he was much more subdued. Perhaps it was because he stayed up until 4 AM to watch the Super Bowl. Our first problem involved the score, 17-14, and involved how many different ways this could happen. The answer, for those interested, is 30. We spent the class talking about the power set, permutations, combinations, the binomial theorem, and proving equalities with and without induction. Nothing too exciting, or too hard, for that matter. We got our first homework problems as well, which are due next Monday. I'll be sitting in on a couple more classes to see what I think about the class.

Then was Mathematical Physics (MAP), which will cover Quantum Information Theory and Quantum Probability. I've already learned much about quantum stuff, but this class seems very different. Yes, it will cover Hilbert Spaces and operators on the spaces, but at least for today, we did something very different. We spent a lot of time with POSETS- a special type of set, and we discussed a strange kind of logic involving lattices in which distribution does not necessary hold. We ended with the double slit experiment. How many times have I seen that? We also have our first homework, which involves bijections and De Morgan's Laws. This professor here is Mihaly (Michael) Weiner. He is the youngest out of my professors today, but he seems very enthuasiastic about the subject.

Tomorrow will be Advanced Algebra (all group, apparently the first things we do are group actions, and then prove the Sylow Theorems, very simply, with these), Theory of Computing (at the same time is Differential Geometry, which I'll sit in on Friday), and Galois Theory- my roomate will be sitting in on Conjecture and Proof, a popular class, which is at the same time. Then I will have Hungarian 1 for 3 hours, so my day ends at 5!

By the time classes were over for me today, it was 4. Even after two cups of coffee, I was tired. After getting home, I did some reviewing, and then had my leftover tofu, and watched Pieces of April, a movie which surprised me and was actually pretty good.

Well, tell me what you think about my classes! Perhaps you can inspire me to some path I didn't think was that special. I think I'm going to try to give even the classes I have little-no interest in at least 3 chances for me to start liking them. I have to choose by Feb 22nd, so I pretty much have 6 chances to sit in on each class. I can audit too, if I am interested but don't want to do the work~

I'd like to call it a day early today, so I can get more sleep in preparation for an even longer day tomorrow.

Have a good day~

A lazy, lazy day

So... I set my alarm for 9:30, wanting to go visit Buda today. (Buda is west of the Danube, Pest is east of it- where I am.) I snoozed and snoozed until 2:15!!

For some reason it seems my bed is very, very conducive to both sleeping- but especially dreaming. I remember dreaming about Professor Vinson being a baseball pitcher up on a high raft, and pitching really fast to me. I had another dream where the Terminator girl from the Sarah Connor Chronicles was kicking some serious ass.

After all that excitement- woke up, watched the second to last episode of Moonlight, read The Minotaur, reviewed some of my analysis book, and cooked myself a tasty dinner of tofu, and then watched the new episode of LOST- who are the last three Lost six??

Hope to finish the analysis book tonight- I'm halfway done, and I might sit through some of the Super Bowl as well. I believe it starts at 11:30 PM here.

Tomorrow I'm planning on class from 8 AM- 4 PM. 8-10 AM Classical Algebra, a 3 week class with review of easy math stuff- such as polynomials over fields, 10-12 of Functional Analysis, a class I'm planning on taking, 12-2 Combinatorics, a class I'd like to see how goes, and then Mathematical Physics (Quantum) from 2-4. I hope I have time inbetween classes for some food breaks!

Tomorrow the math starts.... I am excited~ I am a little nervous about getting up though! I will be getting up when most of you go to bed!