1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What subject in undergrad math is the hardest?

  1. May 15, 2010 #1
    I am not a math major. I studied cal I, II, III, ODE and almost finish PDE. I just want to gauge the difficulty of different math classes.

    To me ODE was the hardest even though you need that for the PDE. ODE have so many different topics it is hard to follow all the derivation. I had to restudy the whole ODE even I was the first in the class two years ago. PDE is hard, but it has a logical progression. You go through the same thing over and over just in different coordinates. Make it easier to understand even you might miss the first go around. The only difficult part of the PDE are the Bessel's function and Legendre function.

    How is complex analysis compare to ODE and PDE. that is another one I am interested in the future.
     
  2. jcsd
  3. May 15, 2010 #2

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Much easier I think. But I suppose it depends on would kind of class it is. The one I took was based on Saff & Snider, and one of the easiest math classes I've taken.
     
  4. May 15, 2010 #3
    How hard a course is has more to do with how the course is laid up rather than what subject it is. It also depends on your own preferences and how well you know the prerequisites.
     
  5. May 15, 2010 #4

    Landau

    User Avatar
    Science Advisor

    Indeed, it depends almost solely on the instructor, how the course is given, and what is expected of participants, rather than the subject iself. Any subject (even calculus) can be given at an extremely elementary or insanely advanced level.

    Personally, the hardest course in my bachelor's was probably smooth manifolds, which was partly because I lacked topological prequisites.
     
  6. May 15, 2010 #5

    lisab

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Based solely on the posts I've seen here on PF, the class that gives a lot of math students trouble is their first class that requires proofs.
     
  7. May 15, 2010 #6

    MathematicalPhysicist

    User Avatar
    Gold Member

    Do you refer to differentiable manifolds?

    Yes I also took a similar course (analysis on manifolds), not an easy course espcially Sard's theorem, perhaps the hardes theorem I met in my studies.
     
  8. May 15, 2010 #7
    Thanks for the respond. I am refering to what the college standard requirement of the class. The requirements are pretty standardized.

    What class manifolds is in?

    I am glad that Complex analysis is not hard.
     
  9. May 15, 2010 #8
    Can you give an example?
     
  10. May 15, 2010 #9

    thrill3rnit3

    User Avatar
    Gold Member

    Universities offer so-called "Introduction to Proofs" or "Introduction to Higher Mathematics" class which focuses on creating proofs.

    Or probably a linear algebra class that focuses on proofs rather than calculations.
     
  11. May 15, 2010 #10
    Was your ODE class concentrated on solution methods (integrating factors, variation of parameters, etc.) or did it have more to do with the analytical properties of ODEs (existence, uniqueness, Picard-Lindelöf Theorem, etc.), or both?

    Personally the first parts of real analysis have been the toughest so far (math major in third year), especially learning to work with epsilon-delta arguments. That stuff killed me freshman year in honors calc, but I think I've finally kinda gotten over that now in my analysis courses.

    I'll be taking complex analysis next year, but I expect it to be a lot like real analysis, so not exactly easy. I'd be really surprised if any "analysis" course would be really easy, for the average undergrad anyway.
     
  12. May 15, 2010 #11
    The ODE class I had contrate on solving the problem. Integrating factors, variation of parameters etc, they were easy to use, but it just have so many different method and I being into learning the derivation of those formulas, found my head spinning because there were so many of them. Also the hard part I feel was the Series method. That get so tedious.

    In contrast, PDE is much harder to understand, but it is not all over the place like ODE. You spend the time deriving the formulas and you learn and it get easier, everything make sense. Only the series stuff like in the Bessel equations get tedious. It is not like ODE that there are so many that I end up giving up and just remember the condition and apply the formulas. I took the class in Junior college, nothing like the ivy leaque college. But I did got the highest marks. All the students complained that they had to spend so much time compare to other classes like the multi variable calculus etc.

    I guess the most difficult part for me is that ODE was just so different from the previous calculus that it really took me a while to bend my brain over. PDE is just a continuation of ODE, so no brain bending involve because it's been bended by the ODE already.
     
    Last edited: May 15, 2010
  13. May 15, 2010 #12
    Well, I can tell your PDE course was not a good one. There is a LOT more in PDE's than just separation of variables.
     
  14. May 15, 2010 #13
    I did not mention, it has fourier series expansion, fourier transform, lagendre, bessel and a little strum liouville also. Other than bessel equations, none really stand out to be that difficult. I am studying on my own by following the San Jose State Univ. Class. I actually got the chapters and topics of the course covered and the homework problems from the professor. I use 5 or 6 books to cover the topics to make sure I don't skip anything.

    In fact I studied more than the school required. SJSU is not an ivy leaque college either. Their PDE class don't even require studying poisson's equations which I studied on my own. Also I've gone deeper into D'Alembert, Bessel's equations than the their book covered.

    Please let me know if I miss anything. Remember this is an undergrad class. I am not a math major, I am studying these for advanced study of Electromagnetics/Electrodynamics. That is the main reason I asked about complex analysis.
     
  15. May 15, 2010 #14

    Landau

    User Avatar
    Science Advisor

    Yes, smooth manifolds = differentiable manifolds. We used lecture notes which were very hard to understand; the books by Lee and Lang were recommended, but they didn't really went well with the course.
    Perhaps you're forgetting that not all people on this forum are from US.
     
  16. May 16, 2010 #15
    Well, if your complex analysis course will be anything like an upper level math course (which it should), then I would expect it to be relatively rigorous and proof-oriented rather than computational which you might be used to in your calc and ODE (and PDE?) classes. I think that if you're not used to proving things, complex analysis might be above you. Also your lack of background in real analysis might make it hard. Of course, check with whatever dept you're taking the class from... maybe they don't teach it very rigorously...
     
  17. May 16, 2010 #16
    At my university it's called Intermediate Analysis. My vector analysis professor calls it a "Baby Analysis" course and says it's not really an analysis course. However, there is an upper-level Introduction to Real Analysis course which he says is tough. Given my experience with him, if he says that, then it's a damn-hard class.
     
  18. May 16, 2010 #17
    I am looking at "Introduction to Analysis" also. I have two of those books, it does not look too complicated.
     
  19. May 16, 2010 #18

    thrill3rnit3

    User Avatar
    Gold Member

    no, I'm talking about something else. Some schools offer a class that is just dedicated to learning and doing proofs (completely different from an Analysis class).
     
  20. May 16, 2010 #19
    Hmm. Let me see if mine offers something similar. I don't think so, though.

    This is as close as it gets from what I can tell.
     
  21. May 16, 2010 #20

    thrill3rnit3

    User Avatar
    Gold Member

    this one
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook