After Olin

Starting this fall, I'll be at Columbia University, pursuing a PhD in the Applied Physics & Applied Math department. I'm in the applied math - atmospheric science track, and I'm really excited about this.

I've known for a long time that I was interested in fluid mechanics and thermal-fluid systems, and my mechanical engineering courses confirmed that these really were my areas of interest. I also found through my courses and projects that Olin that I loved math modeling, and so I started looking into any programs where I could do fluid modeling. For a while, that meant I was looking into lots of different departments, including math, applied math, mechE, chemE, and oceanic and atmospheric science. Through reading geophysical fluid dynamics papers and looking at NYU's Atmosphere-Ocean Science and Math program, I decided that the research I was most interested in was in the atmosphere/ocean space, but my top choices of programs were NYU and Columbia, the two where I would be in an applied math department. After visits to all the programs where I was accepted, I was most excited about and comfortable at Columbia.

A Few Serious and Not-So-Serious Things I Did as an Oliner

In four years at Olin, I did the following:

Palace of Promise

Throughout junior and senior year of high school, Olin was my top choice largely because of its curriculum. I wanted to be doing engineering, not just learning about it, and I appreciated the focus on engineering starting and ending with people. It was the community that eventually led to my decision to go to Olin, but it was the curriculum and education model that initially attracted me.

Identity, Confidence, Community: My Olin Story in Five Graphs

It's been about a month since I graduated! I'll be writing some more general reflections, including one specifically about community, but I was inspired by a conversation with a friend to draw some graphs that I thought were interesting enough to share on their own.

There are five graphs: confidence as an engineer, confidence as a mathematician, identity as an engineer, identity as a mathematician, and sense of community.

The time axis is divided into semesters and summers. My first summer was spent on the Critical Language Azerbaijani program, my second was in Singapore doing chemical engineering research, and during my third summer I was at UCLA doing applied math research in the RIPS program. I was abroad at Budapest Semesters in Mathematics during my junior fall.

All the graphs are annotated, but the annotations are pretty small; click or zoom in to read them!

Thanksgiving Break Adventures

I'm going to see family for Thanksgiving, but I actually haven't left yet because I've been up to a couple of other things! First, I took a quick trip to Toronto, and then there was a fluid dynamics conference in town!

To an Oliner Considering E:Math

My major is not technically Engineering with a Concentration in Math, as often as people may think it is. I'm a mechanical engineer. However, I'm one of only two upperclass Oliners who are E:Math-ish (the other is an electrical & computer engineer), so at the moment I'm one of the best people to give advice about designing a math major. One of the sophomores asked me about being E:Math recently, and this is approximately what I told him.

Spectral Theory

I've already written a fair bit about Inquiry Based Spectral Theory already, but it still deserves a post of its own. It's definitely the BSM class I'll miss the most.

Combinatorics and Topology

Extremal Combinatorics and Topology were my math classes at BSM that had the most fun homework and were generally the lowest stress. Here's a bit more about each:

Analysis and Algebra

Going into BSM, I knew I wanted to take at least one analysis class and at least one algebra class. My analysis ended up being Complex Analysis, and my algebra was Galois Theory. Here are my thoughts on each:

After a Million Miles or So

I'm going to write more detailed posts reflecting on this semester, but here are some more general thoughts on how I ended up here and about going back home.

Why I keep going abroad:

Yes, I keep leaving the United States. I've spent 8.5 out of the last 18.5 months abroad. I knew I wanted to study away for a semester, but I hadn't planned to spend so much time overseas. The Critical Language Scholarship Program was something I found out about during fall of first year and latched onto; it wasn't how I had imagined spending my first summer. Last year, I applied for some mechanical engineering internships and was considering talking to Olin professors about doing research at Olin over the summer when I found out about SERIUS, and less than a week after hearing about the program, I was for sure going to Singapore to do research.

Budapest Semesters in Mathematics (BSM) was the one that was actually planned. Like I said, when I started at Olin I knew I wanted to go abroad, and I was considering BSM, but I was also thinking about programs where I could study in French or Spanish or German. By mid-fall of sophomore year, though, I was pretty set on BSM (more on that below).

Some of my family and friends love to travel, and while I enjoy traveling, it's not something I love. What I've found that I love is living in a place, the process of somewhere new becoming familiar and home. I love the way that dépaysement, the disorientation and breaking of habits by being in a new place or situation, gives way to surprising comfort. I love being a regular at my favorite restaurants, cafes, and bakeries, having church family in four congregations in three countries, and learning cities well enough to give directions when just a few months before, I got a little lost nearly every time I left my apartment.

I love being nearly 9,000 kilometers from my house and yet still feeling like I'm home.

Why I came to BSM:

This is in many ways more complicated than any other reflection I've written here because the why is so different. This wasn't as simple as 'I have to take these classes' or 'It meets a requirement and seems interesting.' I needed to take six more credits of math, but I could have taken a couple of math classes at Olin or Wellesley to do that. So why BSM?

If I Were At Expo

Rebecca Christianson, the Olin prof who organizes Expo at the end of every semester, sent out the email for Expo sign-ups today. Expo is the "end-of-semester celebration of student work," and all on-campus Oliners are required to present something each semester. I'm going to be in Budapest, not at Olin, so I'm not participating, but it made me think about what I would do for Expo were I somehow to be at Olin on December 19th.

A lot of Olin's classes lead to Expo-presentable work because they're project based, and many classes that aren't project based for most of the semester have final projects that are Expo-able. It's a little weird that I've only presented project work at one Expo. In fall 2012 I presented my last ModSim project, in spring and fall 2013 I used my graph theory research for Expo, and last spring I talked about my Passionate Pursuit. For the past three semesters, I've talked about either math or ballet.

So it shouldn't be surprising that if I had to come up with something for Expo this semester, it would probably concern math or ballet.

It's a little tricky, though, because my classes this semester have been very different from Olin classes. There are no projects. Even in Spectral Theory, my most Olin-ish class, nothing I'm doing is original. I'm very proud of the work I've done here, and I've worked harder than I generally work in a semester at Olin, but it's all proving known statements or solving problems with known answers because that's how one learns mathematics. There are lots of things I've proven or seen proven that I think are really cool, and I've considered trying to use a few of them for Midnight Mathematicians talks in the future, but giving that kind of presentation isn't really in the spirit of Expo.

That brings me to ballet. I've seen a lot of ballet here, more in a single semester than I usually see in a year. In Bratislava and Prague I saw two very unusual productions of Romeo and Juliet, and I could easily compare them to each other and to more standard choreographies. I also saw unusual versions of Carmen and Coppelia, so instead of focusing on R&J I could talk about new choreographies of traditional ballets, or I could add in La Sylphide and Merry Widow and explore the structure of story ballets from different time periods.

I think it's a little weird, though not necessarily surprising, that one of the ways I chose to spend my free time would yield at least three potential Expo projects, whereas the hundreds of hours of mathematics I've done wouldn't translate into anything appropriate for Expo. Expo works as a requirement at Olin because of the nature of Olin. BSM is very different, and trying to do Expo this semester with an Olin mindset would be difficult because of that difference.

These Are A Few of My Favorite Things

I planned on listing a few of my favorite things in Budapest. The list I ended up writing is a little longer than "a few."

Midterm Season and Spectral Theory

I'm done with midterms! Galois Theory and Extremal Combinatorics were some of the last classes to have exams; those midterms were on Tuesday. The Complex Analysis test was last Wednesday, and the Topology exam was the Wednesday before that. I've gotten my tests back in all my classes except Extremal Combinatorics, and overall everything went pretty well! While studying, though, I realized that it had been a while since I'd taken normal tests.

In my first two years at Olin, I took sixteen classes and only six exams. If I stretch my definition of exam, that maybe goes up to ten, but one was really a long, cumulative problem set in Transport Phenomena, and the other three were Biology quizzes, which each took a full class period to complete but all together accounted for only 20% of my course grade. Of the six "real" exams, two were self-graded based on effort (Physics of Waves and Bayesian Stats), and three were take home, open book, and open note tests in Dynamics. The last was an in class essay exam for Soviet History.

My exams for Topology, Complex, Galois, and Extremal were all in-class tests, so we had about 105 minutes to complete them. The first three were closed book; for Extremal we were allowed to use our class notes. All four of those classes will have final exams in December. Spectral Theory is exam-less, since it's based around us presenting our work to each other, and Hungarian will just have a final exam.

Prague Photos

I went to Prague this past weekend!

I wasn't there for particularly long; I arrived by bus after dark on Friday evening and then left at about sunrise on Sunday morning, so I really just had Saturday to spend in the city. But I walked around a lot, so here are some pictures!

Okay, this is actually Hungary, near the border with Slovakia. It was really pretty on Friday!

Municipal House

Powder Tower

Snapshots

A couple of weekends ago, Hannah, Philippe, and I went to the Kürtőskalács Festival. Kürtőskalács are chimney cakes, dough baked in a helix around a spit. The festival was held in City Park, so Hannah and I agreed to meet by the 1956 revolution monument at one side of the park. 

Evidently I'm really bad at picking meeting points because it happened to be the day of the Budapest Marathon, and the finish line was right in front of the monument. Oops.

The Chimney Cake Festival mostly consists of a lot of booths selling different varieties of chimney cakes. There's not much to do other than wait in line, get food, and eat, so the lines were very long. The chimney cakes were delicious and definitely worth it, though.

Hannah, Philippe, and I with our mini chimney cakes.

This was the regular (vanilla/sugar) one; I also got one with cinnamon. Note that this is about half the length of a normal chimney cake, and the diameter is smaller than normal, too.

Bratislava!

I spent this weekend in Bratislava, Slovakia! The center of Bratislava isn't very big, so it's a good city for a short weekend trip. On Friday evening after I arrived by train, I walked around the city a bit and went to St. Martin's Cathedral. On Saturday I did a walking tour of the city, went up to Bratislava Castle, and saw a ballet!

Exploring
Bratislava's Old Town and historical center is pretty small; most of it was destroyed under the communist government in the 60s and 70s. One of the things that was built where the rest of Old Town used to be was a highway with this bridge:

They call it the UFO bridge. Because, well... what else would you call it?

I walked around on my own on Friday, and the main place I went was St. Martin's Cathedral (Dom).

The back of St. Martin's Cathedral

The altar!

Ballet and Street Food

Today was my first experience with ballet in central Europe! I went to a matinee at the Opera House to see the Hungarian National Ballet perform Troy Game and La Sylphide. There was also a big festival today on the same street as the Opera House!

The Opera House
The Operaház is gorgeous, and I was sitting in a box. In the theater at home, all the boxes are on the sides, so I think they don't tend to be terribly good seats, but the boxes here go all the way around the circle, and I was near the center.

The Opera House! The screen outside was for a festival going on today.

Inside the theater

Some of the boxes on the Dress Circle level

Non-Mathy Fun!

I've spent a lot of time in class over the first two weeks of school, but there's still been a lot going on outside of class! Here are some non-academic highlights from the past couple of weeks.

Welcome Party
At the end of the first day of classes, there was a BSM welcome party! Lots of the professors and almost all of the students came. This was when I met a lot of the people who had arrived at the end of the last week. I also talked to a couple of professors. The most important thing I had to do was meet with Miklos Abert, the Inquiry Based Spectral Theory professor, and the other students interested in taking the course in order to schedule it. (Scheduling that class is a problem we're still working on...) I also ate a lot of what I think are sajtos pogácsa, a cheesy bread puff.

Supper at Hannah's
Vivienne, a student from Texas whom I met at the welcome party, and I had supper at Hannah's one night last week. Our plans for who would bring what food didn't end up working super well for various reasons, so we had to throw together supper from what Grace had. The final result was pasta with Hungarian white peppers (which are fantastic), peas, spinach, and "pesto" (olive oil and basil), along with some really good garlic bread. It turned out pretty well! Cooking and talking with Vivienne and Hannah for a few hours was a lot of fun!

Evensong
Last weekend the Anglican-Lutheran Society had a conference at Lake Balaton, so the night before the conference started, a Budapest Lutheran church and the Anglican church I've been attending hosted an Evensong service. I'd never been to Evensong before, and I really enjoyed the service. It was almost entirely sung, mostly by the Gabrieli Choir, which specializes in Anglican sacred music. There were a couple of hymns as well, and while I didn't know either one, they were both very singable. One was very fitting for an evening prayer service, and the other was about unity, which made sense in the context of the conference.

Graphs, Open Sets, and Vector Spaces: The First Week of Class

This was my first week of classes at Budapest Semesters in Math!

The first three weeks are a shopping period, which means I could attend as many classes as I wanted in order to decide which four or five to take. Registration will happen during the third week. While math classes started this week, most of the humanities courses don't start until next week, so the past few days were all math for me. I attended seven classes this week: Spectral Theory, Extremal Combinatorics, Complex Analysis, Topology, Galois Theory, Functional Analysis, and Real Functions and Measures. Here are descriptions and my thoughts on each!

Last Week of Summer

Tomorrow is the first day of classes, and I'm very excited! This week, students who weren't here for the language course arrived, the language course ended, and in general things were pretty relaxed. Here are some highlights:

1. Potluck brunch with nine other BSMers at Hannah's apartment today. Hannah is a BSM student who has an apartment to herself about ten minutes from where I live, and she was at a summer program this year with one of my roommates, Sandrine. Everyone brought something, so we ended up with eggs, muffins, multiple kinds of pancakes, fruit salad, nutella, and some other snacks. I think we were all there for about three hours, and it was a lot of fun!

2. Dinner cruise on the Danube on Tuesday. BSM shares a building with McDaniel College, and their convocation was Tuesday and included this dinner cruise. BSMers were invited, and while the convocation was a little awkward, getting to go on the boat was really cool. The food was good, I got to meet a few of the people who hadn't come for the language school, and the views of both sides of the city were excellent. Here are some photos:

3. Supper on Friday night. The game theory professor had planned an event that would involve going to John von Neumann's birthplace and then going to a restaurant with traditional Hungarian food. We never did find the plaque about von Neumann, but we did talk about his work in several different fields. I really enjoyed the restaurant; the food was excellent, and I sat and talked with Hannah and Sandrine as well as Lilian, who had arrived that day. There were several others who had just arrived, so meeting them was exciting!

4. The schedule for the first few weeks came out on Friday! We had all had to fill out a pre-registration survey about which classes we were intending to take, and based on that BSM put together a schedule. We have a shopping period, so for the first three weeks we can take as many classes as we'd like, and then we'll register for classes during the third week. During this next week, I'll definitely be going to Inquiry Based Spectral Theory, Extremal Combinatorics, Galois Theory, Functional Analysis, and Complex Functions. I might shop one or two other classes, but I'm not sure. Humanities courses don't start this week, but once they do, I'm planning on taking Intermediate Hungarian Language and Hungarian Art & Culture.