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Courses How would you rank these math courses in terms of difficulty?

  1. Oct 23, 2012 #1
    I'm trying to keep a balance in difficulty next quarter and would appreciate some feedback as to the difficulty of these classes. The four I'm choosing between are Linear Algebra (upper division), Linear and Nonlinear Systems of Differential Equations, Ordinary Differential Equations, and Partial Differential Equations; these are all the math classes I plan to take that I will meet the prerequisites for in the winter. How difficult are these classes compared to each other and compared to lower division math classes (single variable calc, multivariable calc, DE, LA)?
     
  2. jcsd
  3. Oct 24, 2012 #2
    For linear algebra, upper division as it means mainly module thoery? Or is it gonna be about inner product space, spectral formula, bilinear & quadratic forms, symplectic forms, tensor products? This needs to be clarified, because what you call it upper division might be freshmen course in other institutes.
     
  4. Oct 24, 2012 #3

    mathwonk

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    difficulty is relative to your preparation and the demands of the course. so only you in consultation with the professor can determine this. but abstractly ode is easier than pde.

    as you go higher in the series courses obviously get more demanding in terms of prerequisites, but some are more lax in terms of demands for performance.

    TALK TO THE PROF> WE DO NOT KNOW THE ANSWER TO THIS.
     
  5. Oct 24, 2012 #4
    It might help people answer if you included the official course descriptions (including pre-reqs).
     
  6. Oct 24, 2012 #5
    I'm really just what others considered difficult if/when they took any of these courses. And here are the course descriptions, sorry about that:
    http://www.math.ucla.edu/ugrad/courses/index.shtml (115A, 134, 135, 136)
     
  7. Oct 24, 2012 #6
    No worries, here's my reactions, though take them with a grain of salt as these are personal experiences and at a different school, and I have not taken all of these courses as they are described for your school:

    Linear Algebra - This sounds very similar to my LA course, which ended up being significantly easier than I had anticipated. It looks like, similar my course, the last month or so will be more difficult material, but the majority of the course shouldn't be as crazy as it sounds. "linear independence, bases, orthogonality, the Gram-Schmidt process, linear transformations, eigenvalues and eigenvectors, and diagonalization of matrices" -- these topics were (at least IMHO) relatively straightforward, even compared to the intro calc sequence. I got a B on the final, which was heavily focused on the last few topics, and still ended up with an A- in the course from doing so well on the earlier material.

    Linear and Non-Linear Systems - I haven't taken any courses similar to this one, but it looks like the most difficult course of those you listed.

    Ordinary DE's - Doesn't look too crazy, especially if you've already taken a DE course. Laplace transforms are pretty cool and not very difficult to use. If you can integrate by parts you can pretty much do Fourier Series. As with LA, some of the later topics will be more challenging, but nothing absolutely mind blowing.

    Partial DE's - Looks to be about on par with Ordinary, some straightforward topics, some more confusing. The general rule of thumb is that Partial DE's are more difficult than Ordinary.

    Again, I haven't taken all of these courses as they are described here, so it's difficult to say whether the level of difficulty will be greater or less for a given topic. My last piece of advice is, if you haven't before, check out https://www.myedu.com. They have professor and course recommendations and often, especially for public universities, grade distribution data, which can usually indicate the level of difficulty of a course, and what kind of a grade you might expect.

    Hope that helps!
     
  8. Oct 24, 2012 #7
    As long as you know lower division linear algebra, the first two DE courses shouldn't be too bad if you've done your calculus. Upper division linear algebra is the only proof based course mentioned (it may include a small bit of computational). That depends entirely on how you feel about writing proofs, knowing how to use definitions, etc.

    PDE's should be taken after ODE since some techniques will break a PDE into two or more ODE's. That and ODE's gives you some idea of what to do in one variable.
     
  9. Oct 24, 2012 #8
    I agree with the above statements, it really all boils down to how hard the professor wishes to make the class.
     
  10. Oct 24, 2012 #9
    Okay. I was just looking for a very general idea, which I now have, so thank you, everyone.

    And Mdhiggenz, I couldn't agree more. Of the four courses I'm currently taking (DE, LA, Calc 3, and Biochem), I'd consider DE to be either the hardest or second hardest, but the test was very straightforward and simple. Calc 3, on the other hand, which I wouldn't (so far) consider to be very difficult, had one of the most challenging tests I've ever taken (in part, though, due to time constraints).
     
  11. Oct 24, 2012 #10
    Haha same boat I am in actually. Currently my differentials class is super easy, even though I have taken practice exams from other professors than can make a grown man cry. While my calc 3 exams are so hard!
     
  12. Oct 24, 2012 #11
    You're taking Calc 3 and DE concurrently, too? My main problem is that a fair amount of material comes up from calc 3 or LA that I haven't learned yet so I have to go home and teach it to myself before I can understand what's going on, for example, when we started going over exact equations and I had never seen a partial derivative before. Other than that, I wouldn't consider the content, itself, to be all that difficult (although, again, it would probably be much easier had I already taken LA and calc 3), but by comparison to my other courses, I'd say it's fairly harder than calc or LA.

    Back to calc, our first test didn't even have any calculus on it, since we had only gone over vectors and parameterization (which I pretty much already knew from physics), but there were just so many problems (and we only had 50 minutes), one of which was something like find a vector u where u - v is perpendicular to w and u = kw and u dot v is parallel to w and illustrate with a graph. Maybe not that difficult given enough time, but fairly complicated and time consuming (like puzzles- the concepts aren't hard but solving them can be difficult and take a very long time).

    Anyway, that post was a little long, but I needed to vent a little.
     
  13. Oct 24, 2012 #12
    Yea I completely understand, what my diffQ professor did was taught us partials and gave us a hand out to do, then I learned it again a few weeks later in calc 3. That really sucks though I hate professors that gave insufficient time for exams, my calc3 professor gives 10 questions 1 hour and 48 min.

    The exam really only takes about 30-45 min if you really know your stuff. What drives me crazy is his exams will be covered for example ch11.4-12.5 which require skill so pretty much the majority of the exam. Then the lectures he has up to that exam will also be on the exam but will not require skill and we wont need to study. Me being gullible did not study the non skilled section, and he put a 10 point problem on our exam, and 4 t/f questions from section which I of course got wrong. It drives me crazy because I scored flawless on the material that was the actual exam, but lost my A =[

    There is my vent session haha
     
  14. Oct 24, 2012 #13
    Sorry to hear that. It's those topics that seem so simply that they don't really need to be studied that end up hurting you the most. Fortunately, now that I've realized that, hopefully I can work on resolving that issue. My professor gives us the option of dropping our lowest exam and having our final and second midterm count more if it will help our grade, so at least for me this test probably won't count for anything.
     
  15. Oct 24, 2012 #14
    So true, if you want I can PM you a website of a professors test bank from my university who was notoriously difficult I use it as a guide for calc 3 and diffQ. He also has some of the classes you are contemplating taking next semester I believe.
     
  16. Oct 24, 2012 #15
    Sure, sounds great. If you plan on ever taking biochemistry, my professor's website has all his powerpoints, study guides, old exams, review topics, and podcast lectures.
     
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