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Things math majors should know

  1. Mar 31, 2012 #1
    Those of you in your upper level classes, graduate school, docs and post docs - what is it you wish you had known when you were an undergrad in mathematics? Things that nobody told you - but you wish they would have?

    I have all sorts of silly questions sometimes on things ranging from what classes to take to what kind of pen and paper I should use sometimes. Perhaps you can help me and others out here by using the question above as a guideline.

    -Dave K
     
  2. jcsd
  3. Mar 31, 2012 #2
    Personally, I think that I did myself a disservice by not taking a topology class. I know some basic stuff from analysis, but not enough. So, I think that everyone should take topology (especially those who are going to grad school.)
     
  4. Mar 31, 2012 #3
    If you can, you should audit at least one or two classes per semester. That way you can learn a lot more without it being too much of a time sink. You can do the homework of those classes when you have time or just ignore those classes when you need to prepare for tests in your real classes.
     
  5. Mar 31, 2012 #4
    I mind not having had differential geometry in my undergrad, but the university didn't offer it is an undergrad course, and couldn't take a grad course in it, mostly due to there being too many course requirements already. Differential geometry seems really useful as I want to become a theoretical physicist and now I'll probably have to start learning general relativity without knowing differential geometry, which is presumably worse than studying quantum mechanics without knowing hilbert spaces, and I already deemed the latter as unacceptable...

    EDIT:
    Although that is a good idea, some people don't even have time for that.
     
  6. Mar 31, 2012 #5
    I've thought about that transphenomen. I'm afraid I'm not too clear on my universities policy on auditing and it's been hard to find info on it. Does that usually cost something? Or can you just ask a professor if it's ok to sit in and do it unofficially?

    Robert - I'm glad you said that. I was pretty sure I was going to take topology just out of interest, but it's seeming more indispensable now.
     
  7. Mar 31, 2012 #6
    Does anybody wish they had taken a lighter course load and spent more time understanding the material? Or is the fast pace just "how it is" in undergrad years? (And then you can delve more deeply into your interests in grad school.)

    I'm seriously thinking of limiting my course load, even if it takes me a year longer. I don't have any course requirements other than math right now.
     
  8. Mar 31, 2012 #7
    At my college auditing is free. However, you obviously don't get a grade and you don't turn in homework or tests since they won't get graded. You just go there to sit for lectures. Finding information on auditing was very hard for me; there was only a vague paragraph about auditing in my 600+ page catalog. You best bet is to just email the teacher of the class you want to audit and ask if it is ok to audit his class. You don't even need the prerequisites to audit the class. For example, I will be auditing a graduate level general relativity class. When I emailed the teacher, he said he would assume the class knows Lagrangians and tensors. I don't know either, but I am studying up on them and find the probable challenge of the class exciting.

    Also, even if you have time constraints, you can do your homework from other classes while auditing a class and just listen if something interesting happens.
     
  9. Mar 31, 2012 #8
    Yes, I'm finding the same thing WRT to the search for information about auditing. It is a bit late in this semester anyway, but I'll consider next semester auditing linear algebra or something, which I'll take the semester after.
     
  10. Mar 31, 2012 #9
    That's a good idea. There are two versions of real analysis and abstract algebra. One for applied and theoretical where the theoretical is harder. I am auditing the applied so I can ace the theoretical later.

    Also, you can audit at anytime you want, even start in the middle of a semester. I did that with one class and I had a hard time catching up, but I learned enough to not need to try too hard when I take it for real later. For linear algebra, the first few weeks are just matrix multiplication, vectors, Gaussian elimination, and other things you should have known in a high school intermediate algebra class. If you start auditing it now, you should be able to keep up.
     
  11. Mar 31, 2012 #10
    I really wish I could do that. At my school, auditing a class costs the same as taking the class for full credit. It's silly.
     
  12. Apr 1, 2012 #11
    I suspect it's the same at my university, but i'm double checking.
     
  13. Apr 1, 2012 #12
    If this is possible for you, I highly recommend doing it. Many people are constrained by financial considerations that make it difficult to take extra time for their degree. However, if you can take fewer classes you will learn the material much better (and get better grades as well).
     
  14. Apr 1, 2012 #13
    Same at my school
     
  15. Apr 1, 2012 #14
    Yeah, whenever I mention it to people at my school they start talking about their scholarships and such, having to maintain a certain amount of credits, etc. I really don't have that issue. It will make things a bit more expensive as there are costs to every semester outside of just credits, but I'm ok with that.
     
  16. Apr 18, 2012 #15
    Ok, here come some of the really silly questions I warned you about:

    Paper and pencils.

    Seriously - I can't seem to find out what my optimum tools are. I go through notebooks like crazy, and I can't seem to keep organized between class notes and homework. Now I'm even starting to wonder if I should just stop using notebooks and use *blank* paper, since this is what professors seem to use on overheads and this is how we are tested. Makes sense to do my homework the same way, right?

    I haven't found the right writing utensil either. I keep getting mechanical pencils whose lead just falls out all the time. I end up having to carry a bunch of them around so I always have "backup."

    Becoming more visual: Are there "equation people" and "geometric people?"

    I tend to think I'm the former, but it seems that there's a lot of mathematics that depends on some kind of visualization, which I'm not that great at. Some teachers de-emphasize this, some teachers put a lot of emphasis on it. (Perhaps they themselves are in these two groups). Should I make a conscious effort to be more visual or just go with what I'm better at? I mean - knowing the shapes of different graphs, being able to work in three dimensional coordinate planes, etc.

    -DaveK
     
  17. Apr 18, 2012 #16
    Honestly, I think those are the type of thingsyou just need to figure out what works best for you. I don't see any general trends in my classes, some use pens, some use pencils, some use notepads, some use notebooks...I use blank paper and binders. The only thing I would recommend is either use a mechanical pencil or a pen so you don't have to sharpen the tip constantly.

    As far as equation people vs geometric people, I think this is true to a degree. But again, you just need to do what works best for you.
     
  18. Apr 22, 2012 #17
    Personally, I use recycled paper for my homework and take my notes in a notebook. My school collects computer paper that is printed on one side only to reuse in a recycle printer, so I just take paper from the collection bins and do my homework on the blank side. I like Pilot pens, but then I end up having to rewrite from the beginning if I screw up. My homework buddy turns in his work on gridded yellow paper and writes in mechanical pencil.

    A topologist told me that he didn't really like algebra because it felt like symbolic manipulation to him and he couldn't visualize it very well, so I guess some people do prefer equations over geometry or vice versa.
     
  19. Apr 23, 2012 #18
    I take notes on lined paper with a Pentel Kerry mechanical pencil using 0.5mm HB lead. Everyone has to find their own groove, though.

    I submit any of my work in Latex. However, this is a time investment to learn properly so don't do it unless you are serious about carrying on in mathematics.

    Strangely, I have a slight aversion to Point-Set topology because (to me) it seems like a mess of arbitrary unintuitive spaces with more counterexamples than anything resembling structure. Algebraic Topology is a bit of a different beast, though.

    On the other hand Algebra is the most beautiful thing I have encountered in mathematics. I am deeply visual so I have found (admittedly strange) ways to visualize all the structures I have met in Algebra. Whatever way you build intuition is up to you. You will need intuition of some kind, though. If you rely on just cranking through equations there is a ceiling waiting for you...
     
  20. Apr 23, 2012 #19

    chiro

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    I don't know if this is useful, but I would recommend that you know enough about other areas so that you understand why the other area is useful.

    In other words know what a specific area is about in a few sentences but not the actual specifics of the proofs, identities, formulas and so on: just enough so that you know that if you have to figure out something out and you remember what a particular area is all about, then you go to the area later on and use what is already out there for your problem. It's also useful in advising other people who you work with directly or indirectly in your own field since the nature of mathematics is that it's connected and often a different perspective can end up solving a problem (which has happened countless times)

    So if you a pure mathematician, know a bit about probability and statistics in terms of how to make a good inference. If you are a statistician, know about analysis in terms of convergence, continuity.

    The thing is that this is becoming necessary anyway with number theorists using probabilistic primality testing and other examples of this.
     
  21. Apr 23, 2012 #20
    Hey, that's pretty cool. Now do you actually do your work in Latex or do you do it on paper and then re-type into Latex? Seems like I'd have a hard time working without physical paper and pencil. What editor specifically?

    I feel sometimes that I am just plugging through formulas, however I'm only in Calc III. I find that it's hard to get a very deep understanding of anything given the pace of the classes. I feel that if and when I go and review the material on my own time I can get a more intuitive/visual grasp of it.

    -DaveK
     
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