Math 55: The Hardest Freshman Course in the Country

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.



  1. Dear Friends,

    So often we tend to measure our mathematical abilities too harshly. My own expieience includes my inability to prove Pascal’s Rule found very early in all texbooks that deal with permujtations and combination. I picked a copy of George E Andrews’ “Number Theory” and staered at the problem 0n page 34″Ising the definition of (n/r), give a combinatorial proof that (n/r)=(n-1/r)+(n-1)/(r-1).
    The algebraic proof is easy, but how was I do use combinatorics, which Andrews introduced a few pages earlier. I was stumped, dead in the water! Try as I did, so many times, i t was beyond me and I went thru that”boy I thought I was good but….”period until I finally had an opportunity to visit The University of North Carolina at Chapel Hill last summer and sit in on an elementary Analysis class taught by a professor, not an assitant professor,.nor associate professor but a professor! I thanksed him for permittiong me to sit in and asked if he could show me how to do the proof. He stared at it for a bit then went threw some hand waving admitted that he wasn’t really prepared too give a “rigorous proof.” I would have be happy if he simply led me in a correct direction. Amazed his inability, I went down the hall,passing mmay closed doors. It was summer,pof cours. I finally found a very genial professor who could, at least discuss a proof, but could not truly do the job. He apologfizedc and mentioned that they “used to have a fellow here who was a combinatorics specialt!” Wow , i was feeling less bum very quickly. I recently found a proof on the web and I think all math majors should look it over. My point is that mathematics can be very difficult, even at the early stages of many topics. I had the same sort of expierience at Duke many years earlier with a problem a text titled “Topic’s in Algebera” text concerning Equivalence properties.I askd a group of grad students enjoy a break for some help and none hand any idea!
    Trust your own abilities. Just because you can’t prove a partucular theorem should serve you a starting point in the quest. Good luck. JMT

  2. I remember 18.100B. The year I took it (Spring 1980?) they added a writing requirement. A biography of Gauss was the easiest part of the course.

  3. >Basically it’s just C(n-1,k) combinations that do not use the new element plus C(n-1,k-1) that do.

    I remember a prof. showing us that proof in one of the undergrad math classes I took. I’d say it was my favorite “short proof,” of those that I encountered.

  4. I’ve picked up a little information about harvard math 55 on all these
    internet postings. my guess and comments about the course is as follows:

    A) The course makes you discovers all the theories by set forth by famous

    B) Alot of abstract math, hence IMO winners do not do well because they
    are use to solving tangible problems.

    C) Kindof like Newton when he invented Calculus.

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