Harvard apparently has this notoriously difficult math course that the really advanced frosh students take. Like, the ones who have already taken advanced classes (and I’m not talking about the more fundamental multivariable calc, differential equations, and linear algebra). It has a whole “mystique” surrounding it. It’s called “Math 55.” Apparently you’re supposed to “oohhhh” and swoon when you hear that, or at least go “Oh my god! Isn’t that insane?” And then make some comment about it being the hardest freshman course in the country. At least, that’s what the Harvard math department touts it as on their webpage.

I’m surprised I had never heard of it. I only first heard about it by reading this article recently, excerpt below:

Later that first night, the first problem set is released online: 13 questions, each consisting of multiple sections to make a total of 47 parts. While nearly everyone is alarmed by the amount of work, Litt says he’s not too concerned. The class can’t stay this hard for this long, right?

“I figure he’s just trying to get people to drop the class,” Litt says.

He figured wrong. As class attendance steadily thins, the workload does not. The first few problem sets each take about 40 hours to complete. The work burden is reason enough for many extraordinarily gifted students to drop.

Case in point: Ameya A. Velingker ’10 took Advanced Placement calculus his freshman year and ranked in the top 12 for the USA Math Olympiad the year after that. “It was a tough decision to drop,” Velingker says. “You’re around all these people who are beasts at math. But I realized it was not going to work out.”

I don’t doubt that it’s insane.

I can’t help but be struck by the cult that’s grown up around it. The article analogizes it to be like a fraternity. (Of math geeks.) There’s also a lot of working together, burning the midnight oil.

It harks back my own “tough freshman math class.” I certainly was not Math 55 caliber. But freshman year I took 18.100B, the theoretical version of real analysis. We used a slim, blue, and terse book. Yup. The slim, blue, and terse book. And from my perspective, that book had been forged in the depths of hell. And given a $150+ price tag. [see update below]

I didn’t struggle in high school math. But let me tell you, putting myself in a class freshman year where I wasn’t yet mathematically sophisticated was not wise. Everything in class made sense. Well, everything in the first five minutes. Then came a bunch of notes and symbols, discussion about compactness and limit points, and then I left dazed, bumping into random people and pillars on my way to the library to curl up with the book, struggle, and be frustrated at my brain for not being able to “see” “it”.

We had weekly quizzes. I think I usually got a 0, 1, 2, or 3 points on them. Out of 10. My mind didn’t work that way. But I endeavored. I don’t know why. Pride? The belief that I could do it? Not wanting to admit that I couldn’t? And at my school, I thought it was rare that anyone went to talk with the Great Professors and ask for help. I was a freshman. I didn’t know anything.

And so I continued studying like no one’s business. And when the final came around (worth 40% or 100% of my course grade, whichever is more beneficial) I literally lived and breathed that blue book for days before. The final was hard — I think only 4 or 5 questions — and I left depressed. But I nailed it.

I don’t know what the point of this post was, except to recall one of two math courses which kicked my butt. Many of my students go through that struggle and frustration in high school. They study a long time and they still don’t get the grades they want. But I can identify with their frustration. It just came later for me. [1]

For those who want more information, besides the article above:

1. A forum talking about the course.

2. The Harvard math department website discussing Math 55. (Scroll down to Math 55.)

3. A few Math 55 course webpages throughout the ages: Fall 2005, Fall 2002.

[1] I know two main differences though. My students think that somehow their grade should be based on effort, and not merit. That didn’t cross my mind in college. I thought you should get grades based on whether you could work the problems or not. The second difference is that many of my students believe that there is a magic bullet that will help them, like meeting with me on the day before a test. I also knew at that point that there is no royal road to mathematics, no panacea that will force understanding.

Update: A funny comic about that dang book here.

I just watched this short film (4’56”) with scientists describing different types of magnetic interactions (e.g. on the sun, on Mars, in a regular situation). The filmmaker CGI-ed in visualizations of the various types of magnetic fields that come up. The still above is from the short.

My first reaction: hmmmm, applying this in the classroom somehow? naaaaah.

My second reaction:

It reminded me of working on my dissertation topic in grad school — on the rise of laboratory physics in American universities at the turn of the century. One of the things that happened was that American universities built teaching laboratories for students to actually do experiments in, as part of their undergraduate and graduate training. And building plans had to be quite elaborate because of the sensitive magnetic work that needed to be done — no ferromagnetic materials were allowed in the building of certain sections of the laboratories (research sections). Harvard’s Jefferson Physical Laboratory was one of the first built. And one of my favorite images from my in depth dissertation research was the following [1]:

This picture represents part of the JPL and the strength of the magnetic fields within it.  Clearly you see why the movie brought back this image to me.

And for those who are interested, my favorite quotation from this era dealing with laboratory teaching was:

The multiplication and enlargement of laboratories depended chiefly upon the growing recognition of the truth that firsthand knowledge is the only real knowledge. The student must see, and not rest satisfied with being told. Translated into a pedagogic law, it reads, ‘To teach science, have a laboratory; to learn a science, go to a laboratory.’ (1884) [2]

I love that an argument had to be made for laboratory teaching (not everyone agreed), and then there were battles over what kind of teaching should happen in the laboratory itself.

Sometimes looking back on this project makes me think: wow, that’s such an interesting dissertation you abandoned.

[1] Picture taken from R.W. Willson, “The magnetic field in the Jefferson Physical Laboratory,” The American journal of science 39 (February 1890): 87-93.

[2] On 174 in “The laboratory in modern science,” Science 3 (15 February 1884): 172-174.

I recently re-stumbled upon The Science Creative Quarterly. I find it every so often, read through a few articles in the archives, and then forget about it until some link or another drags me back there, where I repeat this process. Indefinitely.

This time, I (re?) discovered a great article on superstring theory. An excerpt to get you interested:

The idea is that all the particles and forces in the universe are different notes on appallingly tiny strings. A key tenet of this theory is that there are at least ten dimensions, that’s six more than the four we can access, but that the others can’t be measured or in any way observed because they’re too small. Seriously, that’s the entire argument. And an invisible and untouchable dog ate their homework. Also, the dog cannot be smelled.

The rest of the article is here, hilarious and full of things we’ve all thought but we’d never say, because we have that much faith in physicists.