Math 55 at Harvard: A Comprehensive Undergraduate Mathematics Experience

[bignum]

I actually want to know, is it like four years of undergraduate mathematics crammed into one? Are there actually people who get like 4.0 GPAs in that course?

 

[Landau]

I wouldn't exaggerate. It's basically analysis and linear algebra, but at an insane pace and covering some advanced stuff, but I think most math majors will see the material in their first two (or three) years. They are using Axler and Rudin plus additional notes. Note: this is based on an old webpage, I don't want to give the impression I followed this course :)

Most of your grade (about 2/3) will be based on weekly problem sets.
Doing mathematics is the only reliable way to learn it, and most of the ma-
terial in 55 cannot reasonably be done in the framework of a few-hour exam.(There may be one or two in-class quizzes that will test your recollection
of basic concepts; such a quiz will count for at most the equivalent of one
homework assignment.) A final take-home exam will account for most of the
remaining 1/3 of your grade, with class participation used mostly to decide
borderline cases. Math 55 is not “graded on a curve”; I would be most de-
lighted to find that every single student in the class has earned an A. (When
I have taught 55 previously, most but not all students did earn A or A−.)

 

[Anonymous217]

It's rare for people at Harvard to have 4.0 GPAs by the end of the senior year. If you were aiming for a perfect GPA, then I wouldn't recommend taking Math 55. By the way, I also wouldn't recommend it if you haven't taken Multivariable, Linear Algebra, and a few more classes. That class is filled mostly with highly competitive students from IMO, RSI, etc.
I've heard that Math 25 is still pretty hard by itself.

 

[deRham]

Anonymous is right.

Let me emphasize something - it's not so much the amount of material as the exceptional difficulty of the problems and the pace at which the course is conducted. Classes where the problem sets are insanely tough and long will invariably attract people who did competitive mathematics for the thrill.

 

[sentient 6]

I actually have notes for both 55a and 55b if anyone is interested. No I did not do 55, I am still in high school, but i found them online, I was curious to see what the course looks like... it seems very interesting! too bad I probably can't go to harvard XD

 

[zpconn]

Curtis McMullen taught it last.

http://www.math.harvard.edu/~ctm/courses.html

It seems a lot of the material for 55b is still up. It looks like it just covers algebra, real and complex analysis, and a tiny bit of calculus on manifolds. And that's over the course of a whole year. Certainly not easy, but certainly not four years of material.

 

[sentient 6]

yeah for sure, but it seems like before the class was more free to do what it wanted? I don't know I gather that from the articles I read about it. Now it seems like they want to keep it to what will be covered by other courses, or combinations of other courses but I think maybe that's a good thing... what's the point of rushing education?

 

[Mathnomalous]

They use books printed years ago, I like that. That's very smart, unlike us tools encouraged to buy new editions every year.

 

[deRham]

"Certainly not easy, but certainly not four years of material."

Like I said, I think the point of the class is to get students who have terrific training to exercise their skill with some real, tough mathematics.

I think 4 years of real material takes 4 years for almost any superstar student - just some students will absorb more from it than others.

 

[TMM]

I covered much of the same material (but much more algebra, galois theory, representation, etc, and less analysis) in two freshman level classes this year. On top of that I took some set theory and some chaos theory. In that sense it's less than a year's work, but certainly an absurd amount for a single class.