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First Year Math graduate school - Full of possibility!

  1. Jul 25, 2014 #1
    ah, but which ones?

    There's some personal stuff mixed in here, which I hope you don't mind reading, but which is relevant.

    Some background (for those that don't know me here) I'm 37, just completed my bachelor's (BA in mathematics). I am married, no kids, but with a supportive wife (wouldn't have gone back to school without her encouragement). I'm a little A.D.D., not naturally a math whiz, just an extremely hard worker.

    I got a TAship, which I am very excited about. Though this also means I need to adjust my course load accordingly.

    I am also doing a bit of research (off site internship) with a mathematical oncology group, which has been great experience, and has re-peaked my interest in doing more applied stuff. (I had fallen into the rabbit hole of "I want to do pure math" for awhile, but now I am coming back to what some call reality.)

    My academic advisor is not reachable at the moment so I've been hitting up a bunch of professors for advice, which has been interesting. I though I'd ask here.


    The first professor advised me that since I was going to be a TA, I shouldn't take the usual qualifier heavy sequence, which is:

    First semester:
    Analysis (Lebesgue stuff)
    Algebra I
    Elementary Abstract Algebra

    Second Semester
    Analysis II
    Algebra II
    Some elective

    but he suggested rather I take a graduate seminar elective in the first semester (if not the second), which is pass/fail, gives you a little bit of experience looking at mathematics research, and otherwise ensures you are full time and get the benefits of a TAship. I kind of liked the idea until someone said:

    "Well of course he said that. It's his seminar!"

    Nevertheless I like the idea as I am pretty sure I will be overwhelmed by grad school when I start. That leaves the question of which course to drop?

    Which takes me back to my mathematical oncology stuff, and applied mathematics.

    I'm a little confused on this. Much of applied mathematics is differential equations, which is closer to analysis than it is to Algebra. But Algebra, in particular linear algebra, is more directly suited towards doing applied mathematics. I would like to be able to come back to my internship next semester with more tools to do my research.

    Other possibilities for a "third class" (dropping a core class) are Dynamical Systems, and a class called "Methods in Applied Mathematics" which no-one seems to know about, and may be a smorgasboard of topics. The Dynamical systems class does not have tests, and the grade is project based, which I really like. (I do better with projects and research than tests and homework, which is also why the graduate seminar is attractive).

    Oh, did I mention we are also buying a house? We are closing the weekend after I start classes. So, I have to keep in mind these personal considerations.

    One more question:
    I didn't do as well in Intro to Real Analysis in undergrad as I would have liked, mostly for personal reasons. I had two deaths in the family(father and grandfather), my wife had a miscarriage, and I was serving as math club president, which took a lot of time. There was much understanding by the faculty in this matter. But I felt that I didn't get what I needed out of the class - the sort of "rigorization" of the brain that happens. I got a C+

    I can take it again, sort of. Same class, but the graduate version, in the fall. I'm not sure if this kind of thing is frowned upon. Basically I would focus on algebra this year, take that qualifier, and then start again with Analysis.

    I am sorry if this is confusing, but i'd appreciate any advice or discussion, or thoughts, or shared experiences, even if they do not directly answer my question. Anything helps.

    -Dave K
     
  2. jcsd
  3. Jul 25, 2014 #2
    BTW, it goes without saying probably that Qualifiers are a Big Deal.

    Other advice I've heard was "don't study for classes. Study for the qualifiers."
     
  4. Jul 25, 2014 #3
    I don't understand why there are two different algebra classes.

    I think that would depend more on what kind of applied math you are talking about, but generally, I don't associate it much with abstract algebra. I could believe that linear algebra would be more useful in your case, but that's a relatively small part of abstract algebra. The breakthrough for me when I finally understood linear algebra well was when I studied 2nd semester intro to real analysis, actually, although in algebra, you do get some practice.

    I knew a lot of people who took intro to real analysis again in grad school, but in our program, that made more sense because the first two exams were based on undergraduate analysis and algebra (though at a somewhat higher level than what most of us had studied, and with difficult problems). I don't think it's frowned upon if you are in need of it.

    My problem with the "don't study for classes" advice was that I was never sure what I could get away with in terms of slacking off in classes. One time, I did really, really badly in a PDE class and managed to squeak out of it with a B-, which was the worst grade I had in grad school. I would have failed it, if it had been graded by undergraduate standards (granted, the material was a zillion times harder than undergraduate material). So, apparently, you can do pretty badly, but the problem is that it's a little bit uncertain, so to play it safe, I think you have to at least try to follow the class somewhat. It is possible to fail the classes if you turn in only 2 assignments or something, so you can't ignore them completely.
     
  5. Jul 25, 2014 #4
    Sorry, it's Algebra I and advanced Linear algebra. Typo.

    I feel like I was barely mentally engaged in the class, and getting by gradewise. I managed with all the rote definition/theorems type stuff, and actually did OK on tests because of this. But the homework, which required some deep thought, and serious time, was more or less a failure.

    To be a little more specific, the advise was something like "use your classes to prepare for your qualifiers." So it wasn't so much about ignoring the classes, but an attitude that the purpose of the classes was to answer questions you already had about qualifiers, based on studying previous qualifiers.


    Hopefully now that I've made the correction with regards to Linear Algebra, my question makes more sense.

    I just made my first attempt at a schedule with Algebra I, Linear Algebra, and a Dynamical Systems class (which would be great for the research I'm doing) and it results in a 2 day per week schedule with the classes right in a row for those two days. Having 5 straight hours of graduate math classes does not seem very wise... (and in my case, going that long without a solid meal is not very healthy!)

    -Dave K
     
  6. Aug 2, 2014 #5

    mathwonk

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    Hi DK. I read some of this, haven't absorbed it all but will make a comment or two.

    RE: don't study for classes, be skeptical of cynics. not studying for classes alienates the people you will need to votw to keep you, and agree to advise you, so is ["stupid"].

    As one of my most brilliant teachers (Maurice Auslander) put it: at some point someone has to agree to advise you in writing a thesis so you have to impress someone that this is feasible. Now if after several classes you have not impressed anyone, then you can still pass the quals and say, well you have to take me, I passed.

    So he thought of the quals as a safety mechanism for a weak student.

    Did I tell you my quals story at Utah where I graduated? It was my second or 3rd quals experience, having gone to Brandeis, and also having just waltzed over to U of Washington and taken their quals off the street,

    so when I arived at Utah the first day conversation went somewhat like this:

    me: where do I go to sign up for the qualifiying exam?

    them: Say, usually the students are terrified of those, why are you so anxious to take them?

    me: well I want to be a professional mathematician and these measure my ability to do so, so I figure if I can't pass them I need to seek another field of activity, so I should take them right away.

    them: whooooaaaa... wait a minute, have you ever taken them before?

    me: sure, I passed them at Brandeis and also at UW.

    them: well that's all there is to it, you obviously don't need to take them again. here's your exemption.

    me: oh, thank you.
     
  7. Aug 2, 2014 #6
    Well, as long as you do pretty well in a couple classes/reading courses, it should be fine. Not studying at all is extreme, but there are a lot of things you can choose to put your time into in grad school, so I don't think classes are the number one priority, particularly ones that you might not be making too much use of. Personally, I think I would have been better off if I had put more time into my teaching/grading duties to make sure no one had anything to complain about there. Basically, grad school is going to demand about 10 times more from you than you can actually do, so you're going to fall short somewhere. The question is where to cut the corners because they don't really give you any choice, unless you are superman or something.
     
  8. Aug 3, 2014 #7
    I'm starting to regret posting the comment, or perhaps I didn't say it well.

    The point was that you should use qualifier classes to study for your qualifier. You are still studying for your class, but the point is that you've been looking at past qualifying exams and you have an idea what's on them, so you're coming to class with questions about that. You're still studying for the class and expecting to do well, of course, but the qualifiers are really the priority.

    The impression I get is that they care about qualifiers a lot, and I've been told by one professor that the graduate committee is "tightening up" on this. I think some students were taking too long to get them done or something.

    Well, as far as the schedule, I went with taking the graduate seminar as my third class. I'll focus on algebra this year, analysis next year. Aside from the two algebra classes and TA duties, my wife and I are in the middle of buying a house (something we hoped to have done by the start of the semester, but which is dragging on). So that should be enough of a load. In the spring I can take Algebra II and two electives. But I might actually take (as one of the electives) the same Analysis class I took as an undergraduate, because I wasn't able to devote real time to it in my senior year. It will cover the same material but with a graduate student level expectation, and get me started on the next qualifier.

    -Dave K
     
  9. Aug 4, 2014 #8

    IGU

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    This is the sort of classic view you get from people who still don't get it. Qualifiers are not the priority, they are merely a means of weeding out the unsuitable. Your goal should not be to prove that you are suitable, but to get yourself firmly on the path to being a mathematician. That means understanding mathematics at a deeper level, figuring out what you really like and narrowing in on your preferred area of research, and getting to know the faculty and figuring out who you want as a thesis advisor. If you are not serious about becoming a mathematician you are wasting everybody's time and energy, especially your own. By the time you take your quals they should be straightforward because you understand and appreciate the math, not because you studied for the test.

    Just like going from high school to college involved a change of mindset, this is the next step and will require another change of mindset if you are to do well. If you think it's all about studying for the next big test, you are missing the point.
     
  10. Aug 4, 2014 #9
    Alternatively, one might take the point of view that the test is something to be gotten out of the way so that you can focus on those other, more important things. The fact remains that qualifiers are probably the thing that "weeds out" the most people, so if you have your heart set on the PhD, they are a big deal. So, one way to look it at is that by making it an initial priority, you are actually making it less of a priority in the long run because you won't have to worry about it once you pass. Personally, the qualifying exams were the least of my worries in grad school, since I got them out of the way pretty quickly.

    One possible philosophy you could take is to just focus on what you are interested in, in classes. If I had tried to learn less, I probably would have learned more because I would have learned it better and be less stressed out and overwhelmed. A philosophy grad student commented that the purpose of grad school was to learn to say no, by which he meant, you can't expect to be on top of everything, so you have to pick and choose what to be on top of, in order to avoid being overwhelmed. Being overwhelmed leads to worse performance than cutting corners does in the end, anyway. I don't think anyone is saying that you should completely ignore classes.

    The end goal of a PhD is ultimately writing a dissertation, so that's really the priority, around which everything else ought to revolve. I was all about exploration and finding my interests in grad school for too long and the result was that it took for ever for the dissertation to get done, and then it turned out, I ended up not even liking the subject after all that. And I know of worse cases than myself. So, I think it is true that you should start worrying about it from day one, at least in the back of your mind, because that's the real killer. If you fail quals, you just apply to a different grad school or get a job and move on. But if you fail to finish your thesis, that can be dragged out and be pretty painful. I finished mine, but it looked like a close call for a while, and it was no fun--all the other people in that boat who I know would agree with me on that. So, it's true that passing quals won't do you much good if you aren't ready for what's coming. But that's another reason to not take classes TOO seriously, except to the extent that they contribute to the thesis in some way, even indirectly, in terms of helping you find what you like or whatever. Perhaps, I over-emphasize not taking them too seriously because I think I personally could have profited from, let's not quite say taking them less seriously, but just being more selective about which classes and which topics to be serious about, rather than over-extending myself by trying to learn all of it. Some programs have less credits required (or no credit system at all), less breadth requirements, etc., so this can contribute a bit to different perspectives you'll get from people who went through different programs.

    Unfortunately, the way academia is set up, if you don't "prove" that you are suitable, it's game over, whether or not you are serious about becoming a mathematician.
     
  11. Aug 5, 2014 #10

    IGU

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    What?!?! Absurd. Writing a dissertation is just something you do on the way to getting a PhD. The end goal is to be a mathematician (or whatever else your actual end goal might be). Confusing the process for the goal will often lead to misplaced effort and failure.

    As one obvious example, if the goal is not attractive to you then you should find a new goal. If the process is not attractive to you then you should figure out how to get past it more quickly and easily and get help to make that happen.
     
  12. Aug 5, 2014 #11
    How is that absurd? It's sort of the definition of getting a PhD. I think you just might be equivocating on the word "goal". Your goal in GETTING the PhD may be to become a mathematician, but I was just saying the dissertation is the basic requirement. Actually, in my case, I sort of blew off the thesis and just wanted to learn math. Unfortunately, that does not lead to either a PhD or becoming a mathematician. The idea that you can just pursue your intellectual interests and that's all there is to it is very likely to lead you down my path, which is to either drop out towards the end or finish unhappy. These are the incentives that the system has put in place. I am a prime example of following EXACTLY what you are saying and trying to just become a mathematician without worrying about all the requirements. The result was failure and not being productive, as judged by the system (i.e. no publications, took 7 years to finish, etc). So, your advice only works if your intellectual interests just happen to lead you in the direction of what gets rewarded by the system. I got burned for not making my thesis a priority. Now, of course, you could conclude the moral of the story is to make sure you choose something you like (not so simple--I initially thought I liked it), rather than to be terrified of the dissertation, but what I've been saying does not at all preclude the possibility that PART of preparing for it may be to find something you like. I do think some level of terror is in order, though. If you just fumble around, studying what you like, you may never write a dissertation or get a PhD or become a mathematician or any of that.

    It's not that simple. If you think you are 3/4 of the way to the goal by the time you realize you don't like the goal, it's not so easy to just find another goal. It's easier to just suffer and get to the end of it than start over again.
     
  13. Aug 5, 2014 #12
    Here's a bit of advice a math prof gave me, just before I left for grad school. He said, you have to just do what your adviser tells you. I didn't really understand at the time, not because I didn't know what it meant to do what your adviser says, but because it seems like it would be no big deal. He also illustrated it with the comment "This won't win me the Fields medal," as an example of what the objection might be, which didn't seem like a thought that I would have. My reaction, which I kept to myself, was, "Why wouldn't I do what my adviser says?"

    Now, I know exactly what he meant, except I don't care about Fields medals. I did want to pursue something a little more grand than my thesis. But you could come away with a different conclusion than that I should have done what my adviser said. Honestly, I probably chose the wrong adviser. So, that's something to watch out for, too. You might conclude that rather than doing what your adviser says, you should make sure you like what he says by choosing the right adviser.

    It's not a perfect world, though, sometimes, so it may be some combination of the two.
     
  14. Aug 5, 2014 #13
    I had no problem understanding what he meant here. If you're not a mathematician, you can't write a good dissertation. Is that incorrect?

    Perhaps we (and people in general) just view goals/process differently. By way of analogy, I have always trained for races (half marathons, marathons etc.) because I knew that in order to finish a half marathon or marathon I would have to become a person capable of running that type of distance, that is, a fit person. I would have to sacrifice certain things, eat a certain way, and I would have to run a whole hell of a lot.

    I don't know [bleep] about grad school as I haven't started. But I know that I tend to do well with this sort of end goal/backwards planning sort of thing.


    I disagree. If the process is not attractive then there are other things you can do, including realize that it's a labor of love and that some difficult things must be done in order to accomplish your goal.

    -Dave K
     
  15. Aug 5, 2014 #14
    I think I might get what you're saying, though I might not. It sounds a bit like "don't aim too high" but less cynical than that. If I don't understand what your saying, I might just not be meant to understand it yet. I really have to admit I don't know how grad school works at all, and I get the sense that it's something that no person can convey to another.

    -Dave K
     
  16. Aug 5, 2014 #15
    I don't see how that disagrees with making the thesis a priority. Saying the thesis is top priority doesn't say anything about what you should do to get there. If that means you have to concentrate on becoming a mathematician, that's fine. My point is that it is the biggest danger, and denying that is merely being oblivious to reality. It is the hardest part.

    Also, for me, it makes more sense to say that because it wouldn't have been unnatural or anything for me to get going on the thesis earlier on and the fact is that my life would have been a lot easier, had I done that. So, what I'm doing is pointing out a very easy way that I could have avoided a lot of hardship from getting behind on my thesis. I know other people who had the exact same thing happen to them, too. A lot of my difficulties stemmed from underestimating the difficulty. The result was that even though I took 7 years to finish, perhaps 90% of the work had to be done in the last two years. It would have been MUCH easier if I had gotten a better start on it earlier on, rather than just studying whatever I was interested in because I really didn't need all that stuff for the problem that I was working on. There's not that much shame in taking 7 years--lots of people did in my program, but at some point, you are going to feel the pressure because your funding will run out and so on, so it gets to be very stressful if your thesis is still hanging in the balance at that point.


    Well, it means do what your adviser says. Not so much emphasis on not aiming high. I never aimed high in terms of publishable results, but I aimed high in terms of understanding. I really wanted to understand all the connections of my field with physics, but I just didn't have time for that in 7 years and my thesis was only tangentially relevant to that, so the thesis became the side project, rather than the other way around. If you do that, it will be hard to finish.
     
  17. Aug 6, 2014 #16
    OK, I have heard this as well.

    Do you have any advice for honing in on your thesis work early on? I'm already thinking about it, somewhat constantly. But when I look at thesis topics (of past theses), they are so specialized. I don't understand what any of them are even about. How could I get a jump on this early on?

    I have maybe a very general idea of what I'd like to do. Very very general. (In fact I even am pretty sure I know which advisor I would go with. ) I would very much like to avoid the "getting stuck at the thesis" scenario that I've heard of so often.

    Note my comment about advisor above. The only advisor I've been assigned right now is a general advisor in terms of what classes to take and such. He has always been a helpful guide for me and a great professor. Unfortunately he isn't available now, in this intervening summer between undergrad and graduate school.

    -Dave K
     
  18. Aug 6, 2014 #17
    Well, it may take a while to get to the point where you can decide on a thesis topic, so you don't have to narrow it down that much--just beginning to narrow it down is good enough. You want to start as soon as you can, but not sooner. If you decide on something too soon, maybe you won't be sure you like it yet and so on. But you can work on skills that will apply to any thesis, like LaTeX, so you have just one less thing to learn, if you haven't learned it already. If you are going to need any diagrams, you may want to get some practice with that, using Inkscape or Adobe Illustrator. Also, you might try to write up some expository articles or start a blog or something, so that you practice mathematical writing. Krantz wrote a book about mathematical writing, so you could read that and practice writing articles or something. You can also do your homework in TeX. Some people don't find it to be that big of deal, but for me, I was very surprised at how difficult the writing aspects of my work was. To give you an idea, I think my adviser was still marking up page 1 of my thesis for years, making minor changes. My adviser says he spends half his time just reading what he has written. If you really concentrate on being clear and precise and spelling everything out the first time you write, you might have to do less editing. That was one of the things that I really didn't enjoy too much. I think writing in topology might be more difficult than in some other fields, though, so I think that is part of why I suffered so much (a related issue in topology is deciding how rigorous you should be).


    Sounds like a good start.

    That sort of adviser is a little more straight-forward to work with. The final adviser is very important. They will be your guide, so you have to choose carefully. Talk to any of their current students to find out what it's like to work with them. When people asked me about my adviser, though, I'll tell you the difficulty there in terms of giving people advise about it. The thing is, I only had one adviser. So, it's hard to effectively talk about what the pluses and minuses of that person are because it's hard to know if their approach is standard or what.

    I had a friend who started working with one guy and had a communication problem with him, and he just didn't know what he was supposed to be doing, so he switched to another adviser and it worked much better. Yet, the most successful classmate I had worked with that first adviser and when asked what his secret to success was, he just said he did what his adviser told him and it worked. So, it's a tricky business. When I chose my adviser, it was based primarily on subject matter, but in retrospect, that's probably not the most important thing (plus, it turned out the subject matter wasn't quite right for me, anyway). Sacrificing interesting subject matter may be worthwhile to get someone who is better suited to help you get the job done.
     
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