Perfect Math Notation

Warning: If you are not a big nerd or if you have not struggled over math texts, you may not find this as funny as I do...

Perfect Math Notation

Notation is very important in your mathematical papers. Here are the most famous rules on how mathematicians use notation.
Do not explain your notation. Do not waste your time explaining your notation. Most of them are standard anyway. Your paper will look more impressive if you plunge right into your statements. So a good paper can start like this:

Obviously, p is never divisible by 6 …

Everyone knows that p is a prime number.
Use a variety of alphabets. This way you demonstrate your superior education, while expanding your notation possibilities. Not to mention that it looks so pretty:

sin²ℵ + cos²ℵ = 1.

You also get points for drawing a parallel between alpha and alef.
Denote different things with the same letter. It is very important to maintain continuity with the papers in your references, so you should use their notation. Besides, some notation is standard:

Suppose S is an ordered set. Elements of the permutation group S act on this set: for any s in S, sS is the corresponding action.

Mathematicians secretly compete with each other. The goal is to denote as many different things as possible with the same letter in one paper. My personal record was to denote six different things with the letter G. There are two versions of this competition to maximize the number of different meanings of one letter: it can be done either on the same page or in the same formula.
Use different notation for the same thing. The ultimate achievement would be to change your notation in the middle of your sentence:

Gauss showed that the sum of integers between 0 and k inclusive is equal to n(n+1)/2.

Replace standard notation with your own. Your paper will look much more complex than it is. Besides, if someone adopts your notation, they’ll have to name it after you:

Let us use the symbol ¥ for denoting an integral.

Denote a constant with a letter. Letters look more serious than numbers. You will impress your colleagues.

We will be studying graphs in which vertices are colored in only three colors: blue, red and green. For simplicity the number of colors is denoted by k.

As a bonus, when you prove your theorem for three colors, you can confuse everyone into thinking that you proved it for any number of colors.
Do not specify constraints or limits. When you use a summation or a integral, the limits look so bulky that they distract from your real formula. Besides, it’s time-consuming and too complicated for most text editors. Look at this perfect simplicity:

∑ i² = n(n+1)(2n+1)/6.

Everyone knows that you are summing the integers between 1 and n inclusive. Oops. It could be between 0 and n. But 0² = 0 anyway, so who cares?
Be creative. You can mix up these rules or invent your own.

Let us consider a triangle with N sides. Actually, it is better to replace N by H, because in Russian the letter that looks like English H is pronounced like English N. Let us denote the base of the triangle by X. By the way, that is the Russian letter that is usually pronounced like the English letter H, so sometimes I will interchange them. The height of the triangle is, as always, denoted by H.

By following these simple rules, you will earn great respect from your readers.

Kiev

As our semester begins to wind down, we have all realized how little time left we have to travel (and are starting to get VERY excited about coming home).  Last weekend, a group of seven headed to Kiev, Ukraine for a weekend of exploration and excitement.

We took an overnight train out of Moscow to Kiev on Wednesday night and luckily we met a fluent English/ Ukranian/ Russian speaker who graciously befriended us.  She translated when we were woken up at 3am by the Russian police to see our visas, tickets, and immigration cards.  She helped again when we were awoken at 5am by the Ukranian police who wanted basically the same thing.  The best part of meeting this wonderful woman was that when we arrived in Kiev she showed us to the metro and directed us to our hostel.

A few people had set plans in their mind of what they wanted to do with our time in Ukraine.  I however, was just along for the ride.  We have now been together (ALL THE TIME) in our dorm, in classes, traveling, sight-seeing, etc for almost three full months so there can sometimes be a little tension and bickering.  However, this extended amount of time together has also allowed us to form close bonds.  In our Kiev hostel we all slept in one room with lots of bunk beds.  My "bunk mate" was Caleb who also happens to be my neighbor in the dorm.  In the middle of the night Caleb's blanket was hanging off the bunk.  Below him, in my sleepy stupor, I took (stole) the blanket as my own.  Caleb, being the gentleman he is didn't even get off his bunk to rip it from my sleepy hands and only complained a little bit in the morning.

Kiev was warmer than Mocow, but still chilly and we dealt with a lot of rain and gray skies.  The city was gorgeous and we took lots and lots of pictures.  I forced my fellow explorers to get quite close to a Communist demonstration which was quite exciting.

Despite a couple cloudy days, we did get lucky and have some sunshine.  I stood arms wide, welcoming the much needed Vitamin D into my body for a good minute or so before I allowed anyone to continue walking.

Ukraine was much less expensive than Moscow.  We found a pizza place near our hostel which had delicious food and was only about $10 for a good sized pizza and drink.  We were also directed to пiаза жата (piazza hata) which we thought would be a pizza hut but actually means "big belly house" in Ukranian (which is almost the same as Russian but slightly different).  This cafeteria style eatery was cheap and yummy and allowed us to try some Ukranian food (basically the same as Russian food).

The highlight of our weekend was definitely Chernobyl which deserves a post of its own.

Halloween in Russia

October 30, 2009

Halloween was not very scary and did not include any dressing up, at least not in the traditional American sense.  We dressed up in fancy clothes to go to Swan Lake which was amazing and is currently in second for my favorite ballet.

Lenny, Caleb and me in the Bolshoi Theater lobby.

Earlier in the day we walked around downtown and tried to see the Diamond Fund and Red Square, but red square was closed.  We saw a museum of an old home and generally enjoyed one of the first snows of the year.  Just walking around Moscow made me feel like a local.

Swan Lake is my new (second) favorite ballet!

Catch-Up

October 23, 2009

I have been no good at keeping up this blog, but I will try to recount the last couple weeks since V&S.  The following weekend I took the GRE exam.  I’m not sure how it went and I won’t know for about a month.  However, when taking it, we met a number of Russians.  Everyone we met was impressed that we were studying at the IUM and very confused about why we would come to Russia.  They were all very nice and two of them asked for our emails/ phone numbers because they wanted to show us their home universities.  It was also interesting to take a standardized test with nonnative English speakers.  The first thirty minutes or so was spent filling out the answer sheet.  I have been bubbling in my name and middle initial and address for almost two decades, but I realized during this exam how difficult it must be for those who do not have English as their first language.  For example, “M.I.”  How would you know what that meant?  I’m also sure that the box for social security number confuses them as well as the box where they make you write in cursive that you will not cheat.

My classes have continued to be challenging, but I’m getting along ok.  My Riemann Surfaces professor is incredibly nice.  I was having trouble with an assignment so I asked him via email if there was any way we could meet up so I could ask him for help in person (most of our professors only teach at the IUM once a week).  He ended up inviting me to his apartment and very generously helped me with my questions and gave me a copy of a set of lecture notes he is working on.  He is also tailoring the course toward my research in nonlinear waves.  There is only one person in the course besides myself and Shabat seems to like me best so the class is basically being taught for me.  I asked Shabat to write me a letter of recommendation for graduate school and I hope his famous (in the math world) last name and positive words will help to encourage some schools to accept me.

On Saturday, October 17 a group of five of us went on a little adventure.  We began at bakery called “Volokonsky Keyser” which is famous for their olive bread and pastries.  Each of us got an assortment of delicious items and shared with the group.  It was amazing.   

Next we went to the Moscow Museum of Modern Art.  I really enjoyed this museum and the beautiful paintings which were on exhibit.  There was also a piece entitled “Say I love you” which was a series of speakers set up in a crazy design on wooden boards that were curved into designs.  When you spoke into a microphone at one end of the room your voice was bounced through these speakers and didn’t return to you for an extended period of time.  This museum also had a very cool sculpture garden outside.  Even though it was raining and cold we spent time playing on the statues.

Next, we went to the Gulag History Museum.  This museum was very small but we were able to tag along with another group of English speakers on a quick tour.  Then, we were placed in front of a television and an hour-long movie about the work camps or “gulags” in Russia.  The movies were interesting but the museum was very cold and I was freezing which made it difficult to concentrate on the movie.

This past week was the beginning of midterms.  I had an exam in dynamical systems which was not bad and an exam in my Putnam problem-solving course.  This exam was the worst thing I have ever experienced.  Our professor gave us three hours to work on three questions.  Each question had a part a (2 points) and a part b (3 points) for a total of 15 points on the exam, 9 was passing, 12 was good, and 15 was excellent.  We took our exam in the back of a classroom where our professor was teaching a group of middle school aged boys (in Russian of course).  This exam was IMPOSSIBLE and I only got parts of the first two questions done.  If I’m lucky, I’ll get one point.  I spent most of my time holding back tears and contemplated getting up and screaming at the Russian boys many times.  In this class, I am also one of just two students.  I felt much better when about 2 and a half hours into the exam when I said, “I’m about ready to quit.  How’s this going for you?”  My classmate, Dian responded with, “Me too.  This is awful.”  When we packed up after three hours I learned that Dian had completed just one question (5 points).  We both failed.  We went out to dinner to commiserate the ridiculous and horrible three hours we had just spent beating our heads against a wall.  I’m not sure if either of us will continue the course.  There will definitely be a discussion with our professor this Thursday.  My final midterm exam is Monday in partial differential equations.  I’m not too concerned about this one, but I will definitely devote some time to studying this weekend.

Today (Friday), Bill, John, and I visited the Contemporary History Museum.  This museum had more artifacts and less art so I did not enjoy it as much as some of the other museums I’ve visited.  However, it was very interesting to see the history of Russia presented by Russians and to examine the clothing, weapons, books, furniture, and other belongings of Russians for the last few hundred years.  My favorite piece was a painting (picture below) of the US according to Ronald Reagan.  

Vladimir and Suzdal

October 23, 2009

The weekend of October 3 and 4 our group headed to Vladimir and Suzdal to experience “rural” Russia. We were to meet at 7:45am in the lobby of our dorm ready to leave for the three-hour bus trip. However, I had stayed up till 3 or 4am the night before studying for the GRE and my alarm didn’t wake me. Instead, I awoke to a knock on my door, informing me that it was time to go. I threw my things together and managed to join the group. Not surprisingly, I was not the last one in my group to be ready. This group of students in INCREDIBLY slow when it comes to getting ready and a deadline means very little.

When we got on the bus, we met our tour guide for the weekend, Vladimir. Vladimir began our bus ride (at 8:30am) by offering us wine and cookies. I really believed Vladimir was joking, but no. He came around and gave each of us a plastic glass of red wine. Truly Russian.

Our adventures began immediately upon arriving in Vladimir. We saw the gates that had “defended” the city for many years. Really, it was a hill with a gate. And then we heard about the Mongols who attacked year after year after year and the citizens never wised up and changed anything. Instead, they just continued to be attacked. We saw lots of museums and exhibits including a glass museum and some gorgeous views. That evening we stayed at a nice international hotel. Vladimir challenged anyone to play ping-pong and promised if we beat him he would buy us vodka. Two of the boys took his challenge and won. When he bought them their shots, the rest of us met them at the bar. I’m not sure how it happened, but somehow Vladimir also purchased a shot for me.

The hotel had an amazing buffet style dinner. Usually I detest buffets, but this was actually quite good. There was coffee/ hot chocolate and blini as well as all sorts of cookies and buns and каша (basically oatmeal…just Russianized) which has become a staple of my diet. A group of us just sat around the table and talked for a few hours after dinner. We had a really nice time and I informed our group about the Diva Cup (if you don’t know about it…you should!) although the boys were not thrilled with my explanation…at least I waited till after dinner.

Sunday we bussed over to Suzdal and continued our marathon of tours and museums. We visited a monastery and I saw took this picture.

I’m not sure what root vegetable this is, but I think this truck full of them sums up Russia. We were looking at a church and a flower garden and the next thing we know, a truck full of veges. Unbelievable.

Another spot we stopped had beautiful wooden windmills and a seesaw which we took advantage of. There was also a man carving wooden roses out of birch bark. They were beautiful and I knew immediately I would need to purchase one for Larkin.

We stopped for lunch back in Vladimir at a small restaurant. We were shown into a back room where our tables were bordering the wall and a big spot was cleared. The waitress did not understand “vegetarian” so even though the vegetarians were sitting separately and they had been informed about our “restrictions” we were served chicken soup and a main course of fish. Luckily there was a lot of bread and we were able to laugh it off. The big surprise came when a group of 8 or 10 Russian men and women came in and began to dance. There was singing and music and playing of instruments. It became even more surprising when some of the dancers reached across our table to grab hands and have us join them. They involved different groups of us in different dances and we all enjoyed laughing at each other and ourselves. Near the end, they took all of us out of our small room into a larger dining area where others were eating. Then we danced around in a circle holding hands while people in the center played different games. IN one game, someone was blindfolded and had to walk toward someone in the circle and the person they touched had to come to the center and be blindfolded. For another game two people were in the center with tall hats on and they each had a heavy bag on a string. The object of the game was to swing your heavy bag at the other person and try to knock their hat off. None of us really understood this hour of dancing and laughter, but we all enjoyed it very much.

Things that Don't Work in Moscow

October 15, 2009  

1. Hulu.com

2. Abc.com video player

3. Pandora.com

4. Really, most websites where I watch movies/ TV shows for free don’t work outside the US. Who knew?

5. Computers…even the ones that are used to create our visas

6. My brain at learning languages…I dropped my Russian I class

7. My (nonexistent) stress relieving techniques

8. Mattresses. I have three on my bed as well as a wood plank and I can still feel the springs.

9. Copyrights. It may just be because I’m in a community of math nerds, but I have been given access to two websites where I can download math text books for free and the copies that others have they are VERY willing to share.

10. Dryers. Actually, they don’t exist. I hate hang drying because it makes your clothes feel all crunchy.

11. The Putnam exam. Math in Moscow students are no longer allowed to go to Budapest to compete.

A Home Away From Home (or rather, the dorm)

September 27, 2009

I am amazed again and again by how small the world is.  Not only did Luke Davis and I go to the same elementary school, but apparently his mother does a lot of volunteering at St. Johns and my parents know her decently well.  This connection is on top of the fact that his college roommate and best friend is my dad’s best friend’s son.  And now we are both living in Moscow.  Weird.

I have pretty much moved into the Davis apartment.  My fellow MiMers are joining me here on a fairly regular basis to enjoy the oven, comfortable beds, and washing machine.  It is fantastic for me to be able to get work done while laying on a couch with candles lit and wireless internet.  I’m enjoying their apartment thoroughly and it is going to be tough to give it up when they return from the US in a couple weeks.

This week I finalized my class schedule here and continued the never-ending cycle of homework and applications.  I am getting very close to being pretty much done with grad school applications which is a giant weight off my shoulders.  I am still putting quite a bit of time into applying for the NSF (National Science Foundation) fellowship because they need me to be very specific about past and future research.  I also have less than two weeks until I take the GRE Math Subject Test.  I’ve convinced myself that my acceptance or denial from graduate school is riding on this exam (may or may not be true, but DEFINITELY plausible) so I’m trying to study as much as possible.

Saturday morning I went to the Bolshoi theatre to see a ballet with Dan and Christina.  We learned that if you arrive an hour before the performance there are a limited number of student tickets available for 20-50 rubles (<$2 !!!).  We saw Cipollino, the story of a town of vegetables.  It was very cute and the dancers were amazing.  The Bolshoi main stage is (and has been for 2-3 years) under construction so we saw the ballet on the “new stage.”  I’m bummed I will not be able to see the Bolshoi main stage because the new stage was beautiful and I can only imagine what the main stage looks like.

Week three of classes is complete and I feel like I’m settling in to a normal routine with not many exciting things to blog about.  Next weekend our group is going to Vladamir and Suzdal (two rural towns on the outskirts of Moscow), which should be a fun adventure.