Washington University Students who have participated in the Budapest Semesters program Igor Konfisakhar, spring 2005 Li-Yang Tan, spring 2005 Alexi Savov, spring 2004 Ben Robinson, 2003-2004 Adam Marcus, 2001-2002 Brig Mecham, spring 2000 Scott Nudelman, 1992-1993 Ben Gum, 1992-1993 Washington University Students who have participated in the Math in Moscow program Igor Konfisakhar, fall 2005 Comments by Washington University students on these programs Li-Yang Tan    (Budapest, Spring 2005) I attended the Budapest Semesters Program in Spring 2005.  There, I took courses in Advanced Combinatorics (algebraic and probabilistic methods), Topics in Graph Theory, and Set Theory.  All three courses were excellent and I recommend them without reservation -- the material was engaging, the homeworks challenging, and the instruction inspiring.  As I am keenly interested in theoretical computer science, these courses were also directly relevant to my course of study:  Advanced combinatorics and Graph Theory are the two courses through which I have developed a storing affinity for combinatorial optimization and computational complexity, whereas Set Theory laid the foundation for me to learn about proof theory and computability theory.  Since Hungary is a traditional powerhouse in combinatorial mathematics (home to Paul Erdos and Laszlo Lovasz, among others), it is hardly a surprise that the semester in Budapest was a formative experience for those of us who attended any of these three classes. There were a few other courses that received rave reviews from my fellow students:  Conjecture and Proof is an excellent course for students interested in Putnam-style problems.  I have to caution you, though, that although it presumes no formal background, it is among the toughest classes the program offers.  If you have had 430 and enjoyed it, you should consider Advanced Algebra and Galois Theory.  Likewise, if you like number theory and have had some complex analysis, Topics in Number Theory would be a good class for you.  The program offers a variety of other classes ranging from functional analysis to differential geometry. All in all, I had a terrific time in Budapest.  Please do not hesitate to contact me (lytan@artsci.wustl.edu) if you have any questions.  Igor Konfisakhar, f(Spring 2005, Budapest; Fall 2005, Moscow) I spent my spring 2005 semester in the "Budapest Semesters in Mathematics" program (with Li-Yang Tan).  This semester (fall 2005) I am participating in the "Math in Moscow" program.  Here, I will present some of my impressions from both programs.  I hope it will be beneficial for other people to read my direct comparisons of the two programs.   BSM (the Budapest program) is a well-established program with about 60 students per semester, while MIM (the Moscow program) is a pretty new program with only around 12 students per semester.  The Budapest program is good for both advanced math students and relative beginners, with an emphasis on problem-solving.  MIM, on the other hand, is intended for more advanced students.  To get the most out of the Moscow program, you should have taken at least two semesters of abstract algebra, the 400-level linear algebra course, and preferably at least a semester of analysis before coming here.   The Budapest program is most known for its classes in number theory, combinatorics and graph theory, and it's Conjecture and Proof class.  Of these subjects, I took their Number Theory I class taught by Csaba Szabo, the Conjecture and Proof class and the Combinatorics II class.  I thought the first two were great.  I think that everyone who enjoys math competition style problem-solving should take Conjecture and Proof, and anyone who hasn't already taken number theory should take Csaba's Number Theory I class.  The Combinatorics II class, while also a relatively good class, however, is really just a hyper-graph theory class.  The teacher was not always prepared for class and didn't grade fairly.  I was also very pleased with my probability theory class.  The Moscow program's abstract algebra classes are probably its strongest.  However, it has top notch professors in just about all of its subjects.  I'm taking Topology I and Advanced Algebra.  I would recommend both of these classes, though I would warn that there is somewhat of a lack of rigor in the Topology class (but the teacher is a great mathematician) and the Advanced Algebra class is hard!  Some other popular abstract algebra classes are Algebraic Number Theory, Representation Theory (a real Russian treat, which you should take if you like algebra), Commutative and  Homological Algebra, and Algebraic Geometry.  These classes are all quite hard--on the order of Budapest's Advanced Algebra class or harder.  The last two should probably be taken together and are the hardest on the list.  You will probably struggle in them almost no matter how good you are at algebra.     The professors in the Budapest program are mostly very good, especially in the popular classes but some professors, such as my professor in complex analysis, are disappointing.  Moscow professors are virtually all top notch mathematicians.  However, this can also work against you, as they may often expect you to understand more and know more than you actually do.  The students in the Moscow program tend to be stronger and more serious about math than in the Budapest program.  I also found them to be more pleasant, but that could be a matter of personal preference.  The Moscow program is run by the Independent University of Moscow (IUM), a university completely devoted to math, which is the strongest math university in Russia, perhaps analogous to Harvard, MIT and UChicago rolled into one.  The students there tend to be really brilliant, as well as friendly and able to speak English.  Class sizes in Budapest vary a fair amount, but average around 15 students.  Classes in Moscow are close and personal with an average of 3-4 students.  Budapest classes run for an hour and a half twice a week, while Moscow classes run for a grueling three hours once a week.  The Budapest program has reasonable text books for most of their classes.  Moscow, on the other hand, almost never has text books. The professors each have their own approaches to teaching their subjects, which differ significantly from textbook approaches.  Instead, they provide little booklets of "class notes."  These "class notes" range from relatively complete and helpful to almost completely undecipherable.  It can therefore be quite frustrating trying to figure out some material that you did not understand from class.  The professors try to be helpful, the program provides a tutor or two (which you should not hesitate to use if you need!), and students work together to figure out material.  As the IUM is such a serious math university, it is a great place to pursue other mathematical interests.  If you have such an interest, make it known to the program director (Irina Paramonova) and she'll do her best to try to hook find something for you.  For example, I have an interest in math olympiad style problem-solving.  I was able to get it arranged that I get a private weekly lesson in problem-solving (in English) from the man responsible for most of the math olympiad activities that go on in the Moscow area (including, I believe, the training of the Russian IMO team).  I couldn't imagine such an opportunity in America.   Budapest has an intensive two-week Hungarian Language course before the start of the semester.  I would definitely recommend taking this course.  It gives you the necessary basic knowledge of the Hungarian language and also provides a good opportunity to get acquainted with the other students from the program. Moscow, unfortunately has no such class.  Therefore, don't expect to be able to get around very well on your own in Moscow for about the first month if you have not already taken some Russian classes.  On the other hand, the  Moscow program tends to have a few people with some mastery of the Russian language every semester, which can help others out.  Both programs have some non-math classes, including language classes.  I didn't hear particularly good reviews of any of the non-math classes in Budapest.  I took the European Films class, which was decent.  Here, I am taking Russian III and Russian History.  The History class is quite good.  The teacher is like an encyclopedia!   In Budapest, students rented apartments at a cost of roughly $400 a month. We had to basically take care of ourselves and we tended to live far apart.  My commute to school was about 35 minutes, though most people's were shorter.  In Moscow, we all live on the 16th floor of the main building of Moscow State University (MGU), one of the most famous and the highest building in Moscow. The commute to school is about 45 minutes.  Each student has his/her own room and we live in two-person "suites" at a cost of $250 per month.  We can eat all our meals at the cheap cafeterias of MGU and the IUM.  Food in Moscow is of lower quality than in Budapest and the average person has some mildly unpleasant experience with it during the semester, though you should be OK if you are careful of where and what you eat.  The water in Moscow is similarly not of good quality.  Life in Moscow, surprisingly, turned out to be cheaper than in Budapest and, more surprisingly, the tuition for MIM was lower than for BSM. For the Moscow program, there are also five $5,000 AMS scholarships given out per semester.   Both cities are pretty interesting.  Budapest has a fair number of tourist attractions as well as other sources of amusement.  You can also reach several nice cities such as Vienna, Prague, and Pecs via busses or trains from Budapest. Moscow, of course, is a considerably more exciting city with numerous tourist attractions and tons of interesting things to see and places to go.  MIM provides several excursions into the city, as well as a couple of trips (which I found quite worthwhile!) to other cities.  This semester we took one trip to St. Petersburg and one to two old Russian cities.  Also, there are cheap night sleeper trains (about #35 each way) from Moscow to many cities including St. Petersburg, Novgorod, Tallin, Kiev, and more.   If you are interested in either program, I would be glad to tell you anything I know about them.  My e-mail address is ikonfisa@wustl.edu. Adam Marcus  (Budapest, Fall 2001 and Spring 2002) I am spending my entire Junior year here in Budapest and it is one of the greatest experiences in my life. The teachers are amazing, love teaching bright students, and practically glow with excitement when they are at the board lecturing. And they are good, too – perhaps one of the greatest concentrations of mathematical minds in the world today. They also live in a beautiful and exciting city deep within the heart of Europe, which only makes the entire situation that much more enjoyable. The Budapest Semester takes Juniors and Seniors during the first semester and Sophomores and Juniors during the second semester for either one or two semesters of study.  They teach both first level and advanced courses, courses not offered in most American schools, and also a normal fare for those needing to complete any requirements for their home universities. The first level classes include Probability, Statistics, Topology, Analysis, Algebra, Combinatorics, Graph Theory, Complex Analysis and Number Theory and the more advanced  topics include Hypergraph Theory, Set Theory, Functional  Analysis, Differential Geometry, Measure Theory, Advanced Complex Functions, Advanced Number Theory, Galois Theory and perhaps the most intensive Algebra course offered to undergraduate students anywhere. Of course the classes depend mainly upon interest and new classes are created every year- if there is interest in a subject, they will find someone to teach it. As for prerequisites, I was well prepared for most of the advanced course---having taken a full year of Advanced Calculus and Topology---but most of the students did not have such an intensive background. A course with the same flavor as Math 310 and then probably Multivariable Calculus would give you the basic background you would need. Those taking the Advanced Algebra course all had at least a year of Algebra but most of the courses try to be self-contained (though all of the advanced classes expect at least a small amount of experience in the subject). Other non-mathematical courses are offered as well, including two levels of Hungarian Language. A 3-week intensive language course is also offered before the semester begins, but all of the courses are taught in English and there are always a few students who complete the entire semester without knowing a word of Hungarian so that should hardly be a source of concern. On the non-academic side, the city of Budapest is amazing. You can choose to rent an apartment downtown or live with a Hungarian family (I did the latter and would strongly suggest it to anyone even slightly interested). Public transportation can take you within a block of any spot in the city for $15 a month and living itself is far less expensive than in the US. Movie tickets cost around $3, dinner at an Applebee’s-type restaurant will run around $5 and a .5-liter beer goes for about 50 cents at the supermarket. I found the entire experience to be enjoyable and would recommend the program to anyone interested. I would be happy to answer any questions, and Professor Freiwald would be a good resource if you have any questions concerning credits, eligibility and other similar inquires and I hope to supply him with some more information upon my return. I hope to see Wash U sending bright contributions to the program in years to come. Comments by students from other colleges and universities On the Budapest Program On the Moscow Program