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Schools University with most brutal math course?

  1. Nov 8, 2009 #1
    The difficulty of the courses is one of my major priorities in my selection of the universities I intend to apply to soon. I don't want any easy "plug-and-chug" crap as I would be bored easily and lose motivation to study. So I am asking you guys, which university has in your opinion the most brutal courses in math?
  2. jcsd
  3. Nov 8, 2009 #2


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    Are you sure this is really what you want to ask? "Difficult" and "worthwhile" don't always go hand in hand.
  4. Nov 8, 2009 #3
    Well, of course I would like them to be both difficult and worthwhile. I rather have the studies be hard because of the huge amount of materials needed to be learned and the high academic standards demanded by the professors, not because of a lack of facilities and a highly inconducive learning environment. I had that same particular kind of experience during my first undergraduate degree and I would not to repeat it again.
    Last edited: Nov 8, 2009
  5. Nov 9, 2009 #4
    probably any university. :)

    certainly more prestigious universities will have more motivated students that will make the professors assign more difficult homework, but you can't turn a algebra class into a plug-and-chug class.
  6. Nov 9, 2009 #5

    This is probably a good candidate. Here is the description from the Harvard website:

    This is probably the most difficult undergraduate math class in the country; a variety of advanced topics in mathematics are covered, and problem sets ask students to prove many fundamental theorems of analysis and linear algebra. Class meets three hours per week, plus one hour of section, and problem sets can take anywhere from 24 to 60 hours to complete. This class is usually small and taught by a well-established and prominent member of the faculty whose teaching ability can vary from year to year. A thorough knowledge of multivariable calculus and linear algebra is almost absolutely required, and any other prior knowledge can only help. Students who benefit the most from this class have taken substantial amounts of advanced mathematics and are fairly fluent in the writing of proofs. Due to the necessity of working in groups and the extensive amount of time spent working together, students usually meet some of their best friends in this class. The difficulty of this class varies with the professor, but the class often contains former members of the International Math Olympiad teams, and in any event, it is designed for people with some years of university level mathematical experience. In order to challenge all students in the class, the professor can opt to make the class very, very difficult.
  7. Nov 9, 2009 #6


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    Wow Monocles, sounds incredible.
  8. Nov 9, 2009 #7
    Wow, that sounds awesome! But too bad I have zero chance of getting into Harvard, especially since I am a foreign student and haven't had the fortune to be raised as an ultra-valedictorian. Sigh, life is so unfair....
  9. Nov 9, 2009 #8


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    Don't worry. Get yourself into a University and study hard.
  10. Nov 9, 2009 #9
    then go to Harvard for graduate school :)
  11. Nov 9, 2009 #10
    Hmmm, I'll take a stab at this question. This is the pset I turned in today:


    Compared to the other psets, this one was relatively easy. It also happens to be one of the few that doesn't have "two" problems that basically ask you to prove a dozen or so exercises in Paul Sally's textbook, which mostly involve recovering various theorems.

    On the pset given two weeks ago, we were asked to prove Tychonoff's theorem. Previously, we have been asked to prove Ostrowski's theorem (find all absolute values over the rationals), determine all the sets that can be formed by taking an arbitrary set in a metric space and composing it with boundary, closure, and interior operators, prove the unique completion of an arbitrary metric space, show that the nth harmonic number is not an integer for n > 1, prove theorems in field theory in relation to the reals, prove various fundamental theorems in general topology, and other nontrivial problems I am forgetting.

    But yeah, this is an honors real analysis course open to freshman and it is pretty fun if you're willing to devote a lot of time to it.
  12. Nov 10, 2009 #11
    Aside from the obvious (Harvard, Caltech, Cambridge), I believe the University of Toronto is supposed to have some very rigorous math courses.
  13. Nov 11, 2009 #12
    the most brutal math course would be one where the professor does a bad job of teaching his students
  14. Nov 11, 2009 #13
    However MIT and Harvard is interesting because the grades are so inflated that it's practically impossible to get a 'C' unless you just don't show up (and if you have trouble then you just drop the class and no one knows about it).

    So the classes at MIT and Harvard are "hard" in the sense of challenging, but I'd say that they aren't "brutal" since the grading and pass rates are much higher than in most "weed out" classes at state schools. You take the class, if you find you aren't an intellectual masochist, then you drop the class and take something else, and it's not the end of the world. If you find you are an intellectual masochist, then you find yourself in a room with other intellectual masochists, and what comes out is scary.

    If you really want to challenge yourself, just start ordering books from Amazon and learning stuff on your own. I don't know if Harvard has opened up its courses but MIT has so there's nothing keeping you from downloading problem sets and doing them yourself.

    Yes, it's hard to have the self-discipline to do something like this, but you wanted a challenge, didn't you?
    Last edited: Nov 11, 2009
  15. Nov 11, 2009 #14


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    Cambridge's graduate mathematics course (Part III) is also considered quite brutal.
  16. Nov 11, 2009 #15
    honestly taking higher level math classes at any established university will not be plug and chug and you have so many options each semester that you can just avoid those classes. if you find things to be too simple then you quickly finish your requirements and move on to taking graduate classes. most universities welcome their under grads to take graduate classes as long as they have the pre reqs from under grad. those courses won't be unreasonably difficult but will be a good challenge for any student.

    at my university to be a math major you had to have at least calc 2 done before your freshmen year and the first class you took was a two semester class that combined calc 3 dfq linear algebra and a bit of proofs. so you did 4 semester's work in 2 and you are expected to have most of your cores done by this point. second year is when you start taking your algebra and analysis classes and 3ed year is topo/set theory/complex... and a few other choices but you have to have 2-3 maths a semester. by your 4th year you are expected to be mostly done with you undergrad maths and start taking grad analysis and algebra.

    this curriculum is very intense and you blow by the easier topics... i personally took it upon myself to do some summer classes and start doing the grad classes starting the second semester of my junior year.

    what i am trying to say is that it's up to you... if you are motivated then you can take more classes and read out of multiple books to get more of a challenge.
  17. Nov 11, 2009 #16
    Also one thing that you do have to be prepared for is that you will reach a point at which you will hit your limits, and when that happens it's important that nothing seriously bad happens. It's always a bit shocking and painful when someone that is smart ends up in a room in which they realize that they are the dumbest person there, and one good thing about taking really hard classes in really hard universities is that you realize how dumb you really are, (and everyone is dumb about something).

    The other thing that you have to be careful about is that physics and math are extremely addictive and like any sort of addiction, it's possible to have bad things happen if you aren't careful about it.
  18. Nov 11, 2009 #17
    Kolmogorov and Fomin? Introductory Real Analysis? Ha!

    I remember that book. I picked it up as a freshman thinking I was going to learn about epsilons and deltas. Saying that I was confused would be a severe understatement.

    It blows my mind that there exist freshman (17-18 year olds) who can dive strait into that stuff. Makes me feel like a damn moron, really.
  19. Nov 11, 2009 #18
    there's grade inflation everywhere? i'm at a state university and i've had a huge ( like over 50% ) curve in every math and physics class since calc 3 ( i've taken almost every single class from both majors ).
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