More Math-y Adventures

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I started this blog a year ago to help me get ready for two adventures that involved a whole lot of high-level math, in two places I’d never been, with a lot of people I’d never met. I was preparing for my summer at SMP in Minnesota and then my Fall semester at BSM in Hungary.

A year ago, I was questioning my abilities in math. I was in the depths of my Real Analysis course which was the first math class I really struggled in and had to work for. I was incredibly nervous about spending the next summer and semester surrounded by all this high-level math and all those math geeks. What if I didn’t fit in? What if I didn’t like math that much? What if wasn’t smart enough?

A year ago, I couldn’t have imagined the ways in which SMP and BSM would change my life. I made so many new friends and met so many new people who I have laughed with, loved with, cried with, and worked with. These math people? They’re my people. I am now so confident in my math abilities and love of the subject. I’ve learned what it means to DO math, as opposed to just study it, and have found the joy in learning and doing as much of it as I can. I’ve become one of those people I used to joke about who read their math books for fun.

A year ago, I couldn’t have imagined I would ever feel that I’d “outgrown” my liberal arts math department. Even though there are still courses I haven’t taken, I’m jealous of my BSM friends who go to University and have more than two options of 300-level math courses, and I miss being in class with other students who want to use their math education to be mathematicians. The level of intensity I learned while at SMP and BSM makes me feel like I don’t really belong here.

I’ve spent this semester transitioning back into New England, suburban, liberal arts college life. I’ve been taking a math course on optimization, learning the headaches of debugging hardware in my robotics workshop, writing for my journalism class, and trying to finish up my music minor.

And now I am SO ready for more math-y adventures!

This summer I am going to Boston to work in a bioinformatics lab group. I don’t really know what I’ll be doing or who I’ll be working with, but I am excited to live in the city that my sister calls home, and to be part of a research group again!

Just like a year ago, I can’t know what’s coming my way, but I’m ready for the challenge.

Me and my sister.

Me and my sister on the Bp metro.

A completely incomprehensive list.

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I leave my home in Bp for my home in the States in three days. (three days!) I’m sad the semester is over.

I made a list of some things–excluding friends and family– that I will miss from here, things that I won’t miss from here, and things that fall into both categories.


What I love about Bp:

Turo Rudi.
The most brilliant snack/dessert every invented. Yet impossible to describe in a way that makes it actually sound appealing.

Turo Rudi even has a CAR! It's that good.

Turo Rudi even has a CAR! It’s that good.

The courtyard in my apartment.

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My courtyard.

Being Surrounded by math majors.
Sometimes I make math jokes by accident and I’m not the only one who thinks they’re funny!

Hungarian.
Some favourite words: cica (kitty), Jó buli. (good party), igen fun (not a real Hungarian phrase!), egészségedre! (cheers!)

Parliament, the Chain Bridge, Gellert Hill lit up at night.

Parliament at night.

Parliament at night.

Espresso.
What is drip coffee but a dilution of deliciousness?

The baths.

Everything cherry (meggyes) flavoured. cherry jam, cherry yogurt, cherry pastry, cherry beer, …

Ruin Bars.
Carrots, anyone?

Travel.
Being able to get to Vienna in three hours.

Vienna.

Vienna.

Grid-ruled A4 paper.
It’s everything I could ever ask for in a sheet of paper!

The Danube & Margit Island.

Forints.
Their colours. Their funny pictures of men, The novelty of carrying thousands and thousands of forint in your wallet. Being able to say “Dude. You owe me some forint.”

The freedom of not knowing what’s going on around you.
Freedom to J-walk like a non-Hungarian. Freedom to look at a stature and make up its story because there is literally literally no way you will ever know. Ever.


Things I miss about home:

Lunchmeat.
Please, please, let me have something that is not a derivative of sausage!

IMG_0713English.
I am tired of not being able to ask for what I need, tired of being laughed at or glared at when I don’t know what someone is saying to me, tired of “speaking” in a mix of *broken English* and charades.

Cell phones.
No more “Meet me on the left side of the statue of John Calvin at 5:53pm, standing directly under his arm. Wear your red Rudolph hat so I can see you. If we don’t find each other by 5:57, then…” (JK. Sort of…)

Not being surrounded by math majors.
See: sometimes I make math jokes… ;)

0.5mm pens.
To go with my A4 paper.

Finding the info you need on the internet.
Information that is online, in English, and actually correct? No way.

Not enough drying rack.

Not enough drying rack.

Dryers.
For nights when I realise I want to wear something that seriously needs washing.

Soup/pasta/bread without sour cream!

Vegetables that are not pickled!
I had no idea that I would miss SALAD. Who misses salad?!

Home. <3

Home for Chsistmas. <3

Graph theory is to BSM as Jesus is to Church School.

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For those of us who attended Church School every week growing up, we quickly learned that if you didn’t know the answer to a a question being asked, you should just say “Jesus.” And much of the time, that was actually the right answer. As we got older that fact became more and more of a joke.

SacredSandwich.com

At BSM, a similar sort of joke has evolved, but replacing the “Jesus answer” with graph theory! A friend here told me that he has decided one of the reasons Hungarian mathematics is so strong is because they know how to simplify *any* question to one about directed graphs, connected graphs, simple graphs, bipartite graphs, etc. and then apply those theorems.

effx0When a professor asks how we should approach the problem, and you don’t know, you should probably say “represent it as a graph.” ;)

Liberal Arts Students in a Semester of Maths?

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I’ve never questioned my liberal arts education until this semester.

When I was in the process of searching for colleges I was torn between choosing to study music or to study something in the sciences– so I didn’t make a choice… I went where I could do both. I decided to go to a liberal arts college and became a math major with a minor in pipe organ performance.

I still feel like this was the right choice for me, but I am no longer as certain as I used to be. What if I had gone to a tech or research university instead?

Spending this semester at BSM is making me realize how much math I simply don’t know. And it makes sense: the students who go to university and take 4 or 5 STEM courses a semester where I normally take two should know more math and science than I do.

However, it’s causing me to struggle here. There are so many things I don’t know. So many “famous” proofs that I have not seen. So many “rudimentary” theorems I’ve not heard of before. I take longer on my problem sets than many other students because I need to do the background scut work at the same time. It makes me be the embarrassed student in the room who raises her hand during the colloquium in response to the question:

–Who doesn’t know that proof the area of a parallelogram on a grid is equal to the determinant of its two component vectors?

At BSM, unlike at home, I sit toward the bottom of the class here. I sit in lecture and feel kind of stupid in terms of my mathematical knowledge. My liberal arts education has not prepared me mathematically for the intense program at BSM. I’m having a hard time. I imagine this is what graduate school in maths might be like, and that I will have to work exceedingly hard to fill in the gaps in my maths education if I choose to pursue graduate studies.

However, my liberal arts education has given me breadth of knowledge, if not mathematical depth. It has taught me how to learn anything I want or need to, and it’s allowed me to follow my multiple passions.

I have to remember that although I might feel stupid in the maths classroom, there is so much else I get the chance to study that science-only students don’t:

  • I have classroom discussions on gender and sexuality.
  • I take advanced-level French and have become completely conversationally proficient.
  • I write papers on the importance of memorilization in a post-genocide society.
  • I give recitals and lead entire worship services from behind a pipe organ.

This is all important too!

I think that neither the liberal arts student nor the science student is better than the other– they’re just different. I am beginning to understand that we probably need both kinds of academic citizens in this world.





Feature Photo: Last Light, by Felix Gonzalez Torres. “The work of Cuban-born artist Felix Gonzalez-Torres, whose family emigrated to the US in 1979, revolves around themes both personal and political, such as racism, homophobia, history, and international politics. Inspired by Christmas decorations, his lightbulb installations suggest both celebration and memorial. Untitled [Last Light] alludes to his friend Ross Laycock’s death from AIDS in 1991, evoking not only death but also renewal, bulbs always being replaced as they burn out.” (Le Centre Pompidou.)

The Secret Pre-rec to BSM

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Hands down, the course I am most thankful to have taken before coming to BSM is my Discrete Mathematics course.

I’ve been really surprised at how much I am relying on the things I learned in discrete math. The only official pre-rec to BSM is having taken either Abstract Algebra or Real Analysis, and that’s really just to ensure you have learned enough math and are at a high enough mathematical level for the courses offered.

Yes, I’m very glad I took Real Analysis– I use the thought processes developed in that class all the time. Real Analysis was the first math course I took in which I genuinely struggled; it taught me how to work through confusion and persevere. It began to teach me what it actually means to do math as opposed to just learn math.

But I use the topics covered in Discrete Math every single day at BSM. After this week, I have officially done some degree of graph theory in ALL FOUR of my math classes! My friend’s response upon hearing that from me was simply: “Welcome to Hungary.” (:

For example, in Abstract Algebra, we’re studying and doing problem sets on the symmetires of graphs.

Every single bioinformatics model I’m studying is a type of graph.

The matrices I am researching are bipartite directed multigraphs.

Our game theoretic models are…yes…graphs.

I knew that Hungarians were famous for their teaching of combinatorics, but I couldn’t have anticipated the extent to which graph theory is utalized as a mathematical tool here in Hungary.

I’m finding myself doing proofs in which I need to interpret the problem as a graph, then use graph theoretic theorems to solve it! I learned how to do this in discrete math; I would really be struggling if I hadn’t taken that class. And discrete is actually not even a direct requirement for my math major back home.

Some other discrete math topics I’m so grateful to know:

    • Counting, counting, counting: I use a lot of combinatorics counting arguments in abstract algebra. For example, last week we needed them to answer the question that there were, of course, 7 choose 3 divided by three times 4 choose three divided by 3 all divided by 2 unique cycle permutations in some group. I found the counting argument much more difficult than the algebra part of that problem!
    • Modular Arithmetic: Many of the groups we use as examples in Abstract Algebra utilize modular arithmetic in some way. We did a short lesson on it in the beginning of the abstract course, but it was incredibly helpful to already have an understanding of the properties of the operation and to have practice adding, multiplying, finding “fractions” and using inverses in modular sets. Even though we did a small unit on modular arithmetic during this course, our homework sets require a more through understanding of modular arithmetic than was covered in class and one that I only have thanks to my discrete math course back home.
    • Set Theory: In Game Theory, we are constantly using power sets, and everything is turned into a set of actions, a set of player payoffs, etc.
    • Probability: My bio research professor told me that many American students he meets seem to fear probability. “It’s just some value between 0 and 1. That’s it.” In my research group we’re working with uniform probabilities– we are using lots and lots of Markov Chain Monte Carlo processes, and I wish my probability background was stronger than it is.
  • LaTeX: It’s actually just coincidence that I learned to use Tex in discrete math, but I’m going to include it on this list anyway. (: I TeX all of my problem sets for Game Theory. It’s by far not required, yet by far the preferred method of receiving problem sets by my professor.
    Additionally, there is this social hierarchy that exists in the math community surrounding the use of LaTeX (just see #1 on “Ten Signs a Claimed Mathematical Breakthrough is Wrong” for proof). For us, it’s an unspoken understanding that the students who regularly turn their problem sets in using TeX are the ones you’re trying to measure up to. The math world is a learn to typeset in LaTeX or be an outsider kind of place.

I am using all of my previous math knowledge in some way this semester: sequences and series sometimes come up, properties of the real numbers are important, I might (rarely…) take a derivative, matrices are great, but, I am currently thanking the math gods that I’ve had a semester of discrete mathematics.


I am still updating my BSM Tips page! Don’t forget to check it out if you’re considering spending a semester or two at BSM.

A RES Experience

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On a whim, I joined a RES group here at BSM. I wasn’t planning to be in a research class– I considered it but was entirely daunted by the task. Yet somehow I ended up in the bioinformatics research group for the term…

And, although I absolutely love it, the RES class is definitely daunting. Our first real assignment was due last Thursday; we were told to give a fifteen minute presentation explaining the research question and goals in place of that week’s colloquium. Cue a lecture hall including the students who are giving presentations, the professors whose research topics are being presented by well-intentioned students, and a few extras who wanted to watch it all happen. Throw in some Hungarian cheesy biscuits, chocolate cookies, and fizzy water at the front of the room to snack on and you have the idea.

The presentation was essentially asking us in our small groups to give a fifteen minute presentation on an open mathematical question, on a subject we had known nothing about two weeks before, to a room-full of people, in front of the professor who came up with the question and could give the presentation better with his eyes closed. It was terrifying. My research partner and I were told afterward that we did “OK-ish” and I was fully satisfied with that result.

The event was really intense, but also totally fascinating to me. Interruptions from professors in the middle of presentations may or may not have (hint: they did) included things like:

–I can’t hear you because you are talking into the wall. I also can’t read your handwriting. Therefore I have no idea what you are saying.

–I do not know what g is. You did not label g. What is g? Is it a set, a polynomial, an integer, what?

–Can you put the title on the board? I do not know what you are talking about. You’re mumbling.

–You should have practiced with the Powerpoint clicker first. That is very distracting.

Whenever a mistake was made, professors in the back would have side conversations to clarify for each other. Students would make mistakes on the board because they were trying to give equations from memory, then their research professor would correct it for them from the back. You could tell each RES professor wanted their student to do well and get it right, in part because they were being judged by how well we were doing. The research questions were being introduced to some of the other professors for the first time by us, their students. So their ideas were being judged in whatever form we were presenting them. It had to be right.

During the Q&A for me and my partner, we were asked what results we expected by the end of the semester. My honest idea was I don’t know!! Ask my professor what he thinks we will find at the end of the semester! I gave my best shot at an answer, watching my bio professor’s face the entire time for any signal of agreement or disagreement.

The colloquium was somewhat painful to watch. Part of the assignment was to sit in the audience and observe each other flounder at the board. We wanted each other to succeed!

It was rough going.
Thankfully, there were cookies.

Mi furcsa Magyarországon? What is peculiar in Hungary?

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I have been living in Budapest for three weeks now, and really it’s been a lovely city to be living in. It’s easy to get around, beautiful, safe, and a fun place to live. I’m enjoying it a lot despite the difficulties of living in a city where you do not know the language.

Here are a few of the things I have encountered in Budapest that were culturally so different and surprising that I stopped to take a photo:

1. Okmánybélyeg

 

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These pictured are 18000 Forints worth of… postage stamps! Somewhere around 80 USD! In tiny pieces of paper!

In order to apply for your residency permit in Hungary, you must pay for it in the form of okmánybélyeg. You need to go to a post office and purchase them, then bring them with you to the immigration office. At immigration, you give the officer the payment who then pulls a glue stick out of the desk and pastes one by one them to your application.

In Hungarian class, we did an exercise in which the prompt was ,,Mi furcsa Magyarországon?”/”What is pecular in Hungary?” My response was the okmánybélyeg. My teacher said they were kind of a strange thing for Hungarians, too. :)

 

2. So. Many. Puppies!

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I thought this puppy was absolutely adorable. :) I walked past him downtown waiting for his owner at a restaurant. Budapest is known to be a “dog city” rather than a cat city. There are always people on the streets or in the park walking dogs and it’s not uncommon for them to be tied up outside grocery stores or restaurants. Dogs are let off their leash a lot more than I’m used to in the States, too.

3. “British” Secondhand Stores 

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I think this is just something that I personally haven’t figured out yet. Almost every secondhand store in the city is marked by a British flag and the designation ,,Angol.” I have no idea why secondhand stores must also be British. But it was helpful when I was trying to find one last weekend! Look for the British flag!

4. Light Switches

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The very first day I was in Hungary I was confused by the light switches. They’re so square and enormous compared to the ones I’m used to in the U.S. I kind of like them now, though. There’s a bigger surface area to hit when you’re trying to find the switch in the dark. :)

5. Eggs

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Two things about eggs: one, they’re not refrigerated in the store. I walked up and down and up and down the refrigerated dairy section in Spar before I understood they weren’t there. Two, you might find some feathers in your carton of eggs!

6. Parking on the Sidewalks

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A lot of the parking in the city involves parking half of your car on the sidewalk and half in the street. When I was dropped off at my apartment the day I arrived in Budapest, I thought the driver was just confused and had hit the curb. But, no, he was actually just pulling all the way into the parking space. :o

 

 


Ma volt az első nap az egyetemen tanulni mateket. Volt jól. Az tánarok nagyon kedves vannak. Most ismerem sok diák.
Today was the first day at the university to study math. It was good. The teachers are very nice. Now I know many students. (I need to learn a lot more Hungarian! Thankfully I am planning to take Hungarian II this semester) 

The first day of math was exhausting, but really good. I am excited to be back in the math classroom with a lot of really great students and professors who are very passionate about mathematics.