More Math-y Adventures

Standard

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.

Back to the Liberal Arts Version of Math

Standard

My professor goes through a proof during lecture that requires the definition of a convex combination.


Situation A: BSM, Game Theory Classroom:

He sees our blank stares and says, “What? Weren’t you required to take matrix algebras before you came here? Don’t you know what a convex set is?”

A number of students pull out theirs phones to look the term up as he proceeds with the lecture. We all receive an email later that day with the subject title “READ” and a link to an explanation of convex combinations that everyone will know before the next lecture.


Situation B: Smith College: Optimization Class:

She sees our blank stares and asks if anyone knows what a convex combination is. I’m the only one who raises her hand (thank you, Game Theory Professor).

The lecture stops and a full-out definition of convex combinations begins, complete with diagrams of geometric convex sets and explanations of the necessary set notations. We don’t finish the planned lecture for the day.


imagesI find the two versions of this situation quite representative of the difference between my Hungarian mathematics experience and my liberal arts mathematics experience. Honestly, I’m not sure which I prefer anymore.

On the one hand, it was very easy to get lost in lecture at BSM (e.g.: you just missed everything that was happening when you looked up the definition of convex combinations on your phone), but my current math lectures are so slow in comparison. People ask SO. MANY. QUESTIONS. Like, people ask questions about other people’s questions.

In Hungary, the professor might actually tell you that your question is too basic and needs to be talked about after lecture. And we covered so much more ground because of it. But… we covered so much more ground because you never fully understand everything that was being taught.

I can’t say that one mathematics experience is BETTER than another; they serve different purposes.

Although I’m definitely missing my Hungarian mathematics very much right now.

IMG_0121

Also, snow. So much snow. :o

Reblog: Parable of the Polygons

Link

Screen Shot 2014-12-12 at 19.10.12

If you haven’t seen it yet, you should stop reading this blog right now and go check out Parable of the Polygons!

It’s a project created by Vi Hart and Nicky Case called a “playable blog post.” It’s a sort-of game, sort-of blog post, sort-of math modelling presentation, sort-of social comment.

The interactive post focuses on the issues and segregation that occur when even just a small amount of “shapism” exists in society. The post is incredibly relevant to the current events regarding racism in the States, but also successfully comments on any sexism/size-ism/homophobia/etc.

The thing about the Parable of the Polygons that I think is really amazing is how universal the game is. It’s very appropriate for kids and schools, yet the “cuteness” of the shapes and demos does not make it too young for adults. It’s interesting for mathematicians and scientists since it takes a data-driven look at society, yet is no where near too dense for non-STEM individuals. And, although the post has been public for less than a week, it has already been translated into five languages by volunteers!

I also love that it brings together mathematics and humanities, something that is a relatively new and exciting interdisciplinary frontier. The interactive blog post is a good example of how powerful mathematics can be when applied to a topic you won’t think it apt. Vi Hart says:

[I]f there’s two subjects that get a really defensive and hateful reaction, it’s mathematics and social justice, so we figured we’d do them both at once.
(Vi Hart on her blog)

Go check it out! What do you think?

A Few Other News/Blog Posts on the Parable of the Polygons (because it is getting a lot of attention!):

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

Standard

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?

Standard

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.)

Mathematical Modelling: A Tool for the Indecisive (aka me)

Standard

It’s time to apply for next semester’s housing back on my home campus.

My friend who’s also abroad and I were stressed about filling out the forms with our housing preferences. We both want to be living in singles, but we want to be in the same dorm. So much is riding on the results of this form!

Our conversations went something like:

–I’d love to live in Safford.

–But so would everyone else! So we probably won’t both get into Safford.

–What about 18? No one wants to live in 18. We should both get in there.

–Yuck. There is no way I want to live there.

–What do we do?!!

So I did what any normal person would do… I created a mathematical model to rank the dorms for us!

(I think I have officially reached a new level of geekiness.)

I made a very simple Excel model which took into account:

  1. How much we like a given dorm (on a scale of 0-5)
  2. The ratio of Single Rooms : Total Students Housed in the Dorm (as a percent, then normalized also on a scale of 0-5), and
  3. The popularity of a given dorm (Very popular = 0 points, sort of popular = 1 point, not popular = 2 points).

Add the values up, and voilà! All the dorms on campus are ranked for us with scores between 0 and 12.

The thing that was very cool about it is that the model actually put the dorms we were thinking we might apply for on top of the rankings. So we did!

And there were no more stressed-out conversations. You can’t argue with math. :)

The Secret Pre-rec to BSM

Standard

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.