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Am i a pathetic math major who just doesn't see it yet?

  1. Nov 24, 2009 #1
    what i feel a lot of the time about math is not exactly arrogance, but close... i just took my first sorta upper level course in lin. algebra, and i got a d on the first test, a hundred on the second, and now i am unsure about how i did on the final (maybe a b). the sort of arrogance comes from me going through this thought process: "i didn't get that right on the test, but i understood it pretty easily afterwards so i understand the concept"... am i just fooling myself into thinking i can study math successfully? i don't think the class was that hard, contrary to my grades, but still i don't figure out the answers a got wrong until thinking a lot about the problems after the test on my own. i guess i just feel like i have no real feedback and i just make things up in my head that i wanna hear. what do you think?
     
  2. jcsd
  3. Nov 24, 2009 #2
    maybe what i asked wasn't clear, but i'd like people to be honest. i need to get out of my own head for once. is figuring out and having the desire to figure things out on my own make up for my shortcomings on tests?
     
  4. Nov 24, 2009 #3
    Maybe its test taking skills? How do you do on problem sets?
     
  5. Nov 24, 2009 #4
    Mmm, probably not. It's great that you have the desire to figure things out, but you need to apply that desire to studying and doing the work so that you don't have shortcomings on tests. While grades are an indicator of how well you are doing in a class, it is not indicative of your understanding the material (I stress a lot on tests, so while I understand the material my test-taking abilities aren't the greatest)
    My suggestion is to keep on top of your suggested reading (ie. reading the material before the lecture) and doing more homework than assigned so that there are no shortcomings when you have your tests. It might seem like a drag to spend your weeknights not watching TV or hanging out with friends, but 5-10 years from now it'll be paying dividends.
     
  6. Nov 24, 2009 #5
    i don't do as much as i should.. i do a lot of calculation practice but when it comes to doing proofs i hesitate to do them for homework... i dunno, maybe because i am intimidated because if i can't do it then i'll feel like i just don't get any of it. i know this sounds stupid but i am really weird. i've done poorly on proofs on the test but understand them afterwards and brooding for a little while. i guess im just afraid of failing and having my failure right in front of me..
     
  7. Nov 24, 2009 #6
    so that's it.. study?
     
  8. Nov 25, 2009 #7
    Studying is important. Go over your notes to make sure that you understand everything, do extra problems from your textbook/online, ask your teacher for help on problems you cannot do, etc. Calculations are important but proofs are the main focus once you get past your first year. A lot of the time the hard part of proving something is knowing just where to start and practicing a lot before the test will help you in this area.
     
  9. Nov 25, 2009 #8

    Vanadium 50

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    I see that your writing is sloppy - poor capitalization, poor punctuation, etc. You might say "well, the reader can figure out what I meant", but this attitude will take you nowhere in mathematics. You simply must learn to be careful, and I believe developing a general attitude of care will be much more valuable than trying to switch it on and off.
     
  10. Nov 25, 2009 #9
    Initially, i thought you were just being a little derisive, but i think you have a very good point. I do have a particular comfort zone that i do not like to break out of, and I think you hit the nail right on the head. I will try and be more precise in the things i say and also in my math.
     
  11. Nov 25, 2009 #10
    dmatador,

    I know the feeling you are having all too well. I also used do badly on a test, or homework, and after a few minutes of looking at the solution decide I understood it all along and move on. You are right though, it is a kind of arrogance, and it has to be overcome if you want to be successful.

    It is not simply enough to "understand" something when you are staring at the solution. The hard truth is that if you made enough mistakes to do badly the first time, then you didn't really know the concept well enough to use it yourself, and you probably won't be able to use the concept later in real problems that don't already have solutions.

    It may seem boring to repeat problems on the same concept, but the repetition will help you remember it. It may seem frustrating to approach a problem like a proof with no ideas on how to start, but you wouldn't be assigned the problem if the instructor didn't think you were capable of doing it, so look over your notes and text and find a similar example.

    These are hard study habits to build, I often relapse into bad habits when I'm particularly tired or stressed, but if you build these habits you will learn the material in a more meaningful way.
     
  12. Nov 25, 2009 #11
    Calculation isn't all that important in math. Most computations we do follows easily when you understand the concepts. There are of course exceptions, but mostly we leave computations to computer scientists, physicists, engineers, statisticians, etc., or whoever applies the math.

    At my school the math department head held a speech for freshman math students on how to study math. He identified the single easiest trap to fall into as exactly yours, so don't feel bad about it; it happens to a lot of people. It's all too easy to read a proof or a section and convince yourself that you understand it and would be able to do it yourself, but in math you really need to do it yourself. You need to do the proofs, and do them again later; think about them, see if you can spot a general pattern, a clever strategy, an interesting use of some property, if someone could have been done differently, etc. Someone here said that for every page of math you read you should write three (I believe it was Mathwonk in his long thread, quoting someone else, and I'm not sure 3 was really the number).
     
  13. Nov 25, 2009 #12
    Dmatador, I just went through this same scenario with my first year. I have always been a good "mental calculator" so I walked into my college level courses thinking, piece of cake. Wrong, D first test, 25% on second test, which is where I came to the realization, that I needed to over power my brain and actually walk through all of the topics which I thought I understood. From then on I made a life change. Vanadium 50 made an excellent point which I ultilized on my own. I began first with an exercise routine. A Ferrari is only as fast as it's engine's capabillity. I also got into routines, of everyday errands/chores, and did them the long way, forced myself to slow down and not skip any steps. After adopting this regimen it naturally carried over into my study habbits. I began doing every problem assigned for homework and even the advanced applications portions to insure there would not be a scenario I would encounter where that could possibly derail my momentum. This has generated somewhat of a snow ball effect, because after the third exam I received a 100 as well as 90+ on remaining quizzes. With the high marks to which I am accustom, I gained confidence again, but not the arrogance. I am only starting my second year, but so far the method has proven to work for my situation. Along with all of the life changing, don't forget to study constantly! Math is not a memorization sport like some other subjects can be. It is very conceptual and until you try it, it wont be understood properly, unless you're Stephen Hawking and can proccess QM and other abstract maths in you're head. Good luck and I hope this helps you out. Always keep you're eye on that carrot 5-10 years down the road, that helps too.

    Joe
     
  14. Nov 25, 2009 #13

    Moonbear

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    This is an excellent point! I don't know how many people here ever experienced having their notebooks graded when in high school. If they did, they probably thought it was a stupid or futile exercise, or perhaps just easy points. However, there was good reason for it. The teacher was looking for things like neatness. And, indeed, one's care with writing on a forum is about the only indication we really have of someone's neatness or carefulness or attention to details. In math, this is immensely important. If your handwriting is sloppy, if you take shortcuts, if you're careless, you're going to end up with a jumbled mess that is hard to follow and prone to errors and next to impossible to proofread for errors.

    One thing that helped me in my math courses, and in other courses that required using math, was to take notes and do assignments on grid paper instead of regular lined paper. It helped me a lot to be able to align columns neatly with the aid of the grids.

    Just getting organized helped in a lot of other subjects too. Notes are useless if you can't follow them later.
     
  15. Nov 25, 2009 #14
    I went this route, instead of writing things down I try to do everything in my head. Then afterwards it feels trivial once you get a pen and paper on a test. This way when you are good at it you can practise by just looking at a problem, do a rough sketch in your head of how to solve it, see if it is correct or not and then learn from that.

    Being good at mental algebra is very important when studying mathematics and it correlates quite well with being good with mental arithmetics even though they aren't the same thing and arithmetics is a quite useless skill outside the basic operations on double digits. Practise doing stuff like linear algebra, tough integrals or similar in your head. Like, when the teacher is going to show you how to solve a problem, race with him on who can get it first!
     
  16. Nov 25, 2009 #15
    I second what Klockan3 said. I always look at a lemma or proposition and see if I can prove it mentally from what I have read; if I can't I look at the proof. If I can't just spot some little point I was missing when trying to do the proof myself I will go back and reread the section. I think that if you know the material up to the point of a proof, you should be able to do the proof yourself except in extreme cases (I think I would have had trouble proving Hilbert's nullstellensatz the first time I saw it even though it seemed intuitively true to me).

    On the other hand, you have to keep in mind that some of the properties are going to be very subtle as you go further along, so it is not always practical to come up with every proof yourself. That being said, in linear algebra I verified every proof either in my head or on paper and if we were only given a sketch of the proof or the proof was skipped I would prove it and have my professor check it to make sure I was doing it right (if he had time, which he usually did).
     
  17. Nov 25, 2009 #16

    chiro

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    I should point out that there is a difference between learning maths in say a undergraduate degree and "really" learning maths in a research context. When you learn in a research context its like your back grinding axes for a battle as compared to say "mowing down the enemy with AK47s".

    If you look at coursework you'll see that it is very very refined to a point where an enormous amount of information has been "synthesized" into short and concise theorems, lemmas, transforms, substitutions and everything else that discuss a particular subject by cramming so much stuff in that being able to succesfully digest, relate, compare and contrast, and get the "big" picture, is often very difficult.

    If you remember that we are cramming thousands of years of thought and discovery into a matter of years, it should help you realize that knowing something (and by that I mean "really knowing something" like Richard Feynmann said) takes a lot of time and a lot of effort and most likely will not just be from getting a GPA of 4.0.

    If you do go on to research, then depending on how far you want to go with research, you will find that you won't have the luxury of a nice refined infrastructure of knowledge to go on. I'm not saying that things don't build on each other, you may probably have to do course work to get "up to speed" but once you've done the "refined and engineered" work then the rest is going to likely be a lot more disorganized, full of holes, lots of little pieces but no big "picture" or "outline" and something that tests you in the way that helps you realize what these did to extend mathematics. It will with persistance more than likely lead to the kind of "systematic refinement" that you see in your coursework
    classes, however its the kind of thing that will teach you about math because in this
    way you are "making" math rather than simply "using" math.
     
  18. Nov 25, 2009 #17

    Vanadium 50

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    Moonbear, as former math instructor of mine used to say, "there's no such thing as a proof that's almost right".
     
  19. Nov 28, 2009 #18
    There is also in my class, a strong connection between mathematics and writing skills. This is an interesting observation, that I've never noticed before.
     
  20. Nov 29, 2009 #19
    I think Vanadium 50 has a very good point, but you will never convince me that the grading of my notebooks in high school was justified! :D

    When I take notes, I take notes in a way that is intelligible and useful for me and not for anybody else, and I don't want a teacher telling me what is and is not useful for me.

    When I write on a forum, write a paper, write a proof, do a problem set, or take a test, then I write in a style that is directed at aiding the understanding of others.
     
  21. Nov 29, 2009 #20
    Practice makes prefect. If you enjoy doing math then do enough so you get As on your tests. If you do not enjoy doing it enough to do enough to be successful than find something else to do. Of course it may be "civilization and its discontents" there is no job that is appealing 100% of the time.
     
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