Source
r/Harvard•
JS0D

Can anyone talk a bit about Math 55?

I will be a freshman next fall and I’m interested in majoring in some kind of math or science. I’m taking BC calculus right now and I thought I would just go on to multivariable next year, but now I am curious about math 55. Has anyone taken it/is currently taking it who could talk a little bit about what the class is like? I’d also be interested in any kind of reading I could do to get a sense of the topics.

I’ve also never taken a computer science course and I’m wondering if there is any gateway into that field at Harvard for someone like me.

Thank you!

Posted Jan 21, 2019, 5:50 PM UTC

718
SamStringTheory•

Have you done competition math before (e.g., USAMO/IMO)? If not, you're probably going to be in for a rough time. There's also Math 23/25 which are both proof based, but lighter than Math 55. There will be an information session during orientation that tells you about each of the course.

CS50 is the typical intro CS course that everybody takes, including those without CS experience. I think there's also CS1, but I've never heard of anyone taking it.

Honestly, don't worry about any of this stuff until you get to school. You will have plenty of time during orientation to talk to your advisor and work out a good schedule for you. Enjoy the rest of your senior year!

13
user1636•

Competition math is not necessary. What is needed is familiarity with writing proofs. Someone who went to PROMYS or the Ross program but has had little success (or interest) in contest math would have the right skill set to consider Math 55.

4
SamStringTheory•

That's fair. I'm not familiar with PROMYS/Ross. I just use USAMO/IMO as examples because it's the most popular math competition and is proof-based.

2
bgnwpm8•

From looking at previous years' notes it seems pretty clear that multivariable calc, linear algebra, and real analysis experience are expected. Of course, Math 55 has become standardized and easier than when Elkies and Gaitsgory used to teach it but someone in BC calc is definitely not ready.

2
bgnwpm8•

If you're only taking BC Calc you're absolutely not ready to take Math 25, and maybe not even Math 25, but if you're a hard worker and smart then I think 25 would be okay.

5
JS0DOP•

Okay. I sort of wish I had gone to a school where it was possible to move into multivariable and linear algebra in high school but I think I’ll probably try to take on 25 next fall. Thank you

1
bgnwpm8•

25 is still an amazing class to get started with "real" math. You'll be ready for abstract algebra, complex/functional analysis, and a lot more. Math 55 is difficult just to be difficult and isn't a good use of your time in your first year when you should be making friends, not working on psets 30 hours a week.

2
imoverthese•

CS50 is the quintessential intro CS course. I didn't take 55, but I did take BC calc in senior year. Most students who go into 55 have a lot more math background than that, from my understanding. Definitely seek out info from people who did take it tho! Edit to say: if you want to learn multi but take a more challenging class than the 21 series, you could look into math 23/25 which are more proof based multivariate.

3
lazimsiz•

I have a roommate and a circle of friends enrolled in Math 55 kids, so I feel qualified to answer this question. IMO or any other competition is not necessary at all, and there are many (30%) who didn't win any competition at all. You are expected to know Calc, Multivariable, Linear Algebra on the college level and have a good background in proof-writing. There are kids who took 6-7 college-level math classes at high school, and there are kids who took none but self-studied nevertheless. The class is a grind, though. You have to work, but if you are into (overly-)theoretical math, you will enjoy it. There is also the option of downgrading to 25 or any other lower-level math class until almost halfway through the semester.

Also, math department and community here is really amazing. Advising is life-changing too.

3
gdavtor'16•

I took BC followed by 25. It's a fair amount of work, but definitely doable

2
JS0DOP•

Is 25 mostly multivariable calc? Some have also said that these courses tend to involve more proofs. What does that actually look like in a math course? What exactly might you have to prove and what does that entail compared to solving problems as I always have? Sorry that was a lot of questions and thanks

1
gdavtor'16•

Math 25 is proof-based multivariable calculus and linear algebra. It starts with set theory and the basics of proofs, and then does intro level material in analysis, topology, and linear algebra. All of these subjects are approached from a proof based perspective rather than a problem solving perspective like BC calc. Highlights of things you usually prove are: fundamental theorem of calculus (and Stokes's theorem), Fubini's theorem, Rank Nullity, spectral theorem, Bolzano-Weirstrass theorem (give or take some).

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JS0DOP•

That is something I will probably go for. It sounds like I don’t have the background for 55 but I’m up for a decent workload as long as it doesn’t take over my life. Final question: how would you recommend I introduce myself to set theory and proofs so that it won’t come as a shock when I start next fall? I’d be really interested to begin working on things on my own to preview what’s ahead. Were there any specific texts you used for class or things you found useful?

1
gdavtor'16•

I'd pick up a copy of Axler's "Linear Algebra Done Right" if you want a gentle introduction to proofs and linear algebra. I'm not sure if there are any books that do just set theory. But you could try the first chapter of Munkres's "Topology." It's a somewhat advanced book for someone in your shoes, but the first chapter does all the set theory that will be covered in Math 25.

2
hyy1237•

As a freshman who took the BC Calc exam, got a 5 on it, and then is currently in the 21a/b series, let me recommend that you go higher than the 21 series. While it teaches you a lot, it's not too dissimilar from high school mathematics and does not feel particularly intellectually challenging. Also, taking 22/23/25/55 will allow you to be introduced to proofs earlier and circumvent some classes later on.

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JS0DOP•

Do you think I should probably go for 25 then?

1
hyy1237•

All of the higher-level intro classes (22/23/25/55) are drastically different from one another, so I'd recommend (once you get on campus next fall) going to the open math advising office hours they have during opening days to talk about what you'd most be interested in. Don't stress too much about this stuff now—plenty of time to figure it out!

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