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What to think? doubting some math life choices

  • Thread starter dexdt
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Hi, this is probably just going to be a rant , so turn away if you don't care:
I'm taking math courses at my university right now, and I've been self studying math for about a year and a bit more now ( in highschool, I only took math up to grade 10.. and it was "essentials" math, I was a bad kid back then ). I've been doing well so far, taking a first year honours "calculus" spivak style course and I've been getting 100% on my problem sets, I got 89% on the midterm but only got 64% on another test because I suck at computing integrals ( although I did get perfect on the proof questions ).

I'm also taking second year algebra courses, I scored a 90% in my first linear algebra course, it's a theoretical one, not a matrix computational one and now I've come to some road blocks.. I'm in the second term of the linear algebra series, the course now is on spectral theory ( normal, unitary , self-adjoint operators et c ) and I love it, but I just took the midterm for that class and I think I bombed it.
The sad thing is that I thought I was ready for it, but a couple of questions came up and I just couldn't think of solutions in time and I just spaced out.. I couldn't come up with the "trick" needed to solve the question. I'll probably get a 50-60% on this midterm, which isn't so bad because the test is only worth 20%.. but I'm currently taking it as a slap in the face: I don't really know how far I can go to realistically become wanna-be prospective mathematican.
I love the material and I love mathematics ( especially algebra ), it's a big part of my life and I'm constantly thinking about definitions and trying to think about how things work together (when I'm at work , walking around.. et c ) .. but I'll be honest, I haven't spent much time at all just sitting down with a book and some paper to do problems ( especially how I have to hold a job ) . So, if I have any hope, I could possibly blame my shortcomings on bad habits.. But maybe it isn't that, I don't know what to think.. especially how people I've seen and read about always seem to have been good at this stuff from the getgo, where I'm getting a crappy 50-60% on my midterm.. Anybody want to share any "failure" stories? Zero to hero stories? Should I rethink some life choices?
Thank you for reading
 

Answers and Replies

  • #2
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Don't you think it's kind of silly to expect perfection from yourself?
 
  • #3
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Well, to be honest, calculus and linear algebra are the easiest math courses there are. Easy in the sense, that it's not that hard to become familiar with the theory, and that it is easy to learn the tricks of the trade.

However, the more advanced your classes are going to get, the harder it's going to be to grow familiarity. And it order to achieve this, you'll need to make a lot of exercises, and you'll need to know your theory very well.

In a lot of exams, they will ask questions that require some kind of trick. And the only way of knowing such tricks is by doing a lot of exercises! So if you want to do better on your exams, you'll need to work harder... I guarantee you that every professor and math graduates, have worked extremely hard for getting the material!!

Of course, it's also possible that analysis is not "your thing". Everybody has a field in which they're good at. Maybe analysis is nothing for you, and perhaps you'll like algebra way more...
 
  • #4
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Well, to be honest, calculus and linear algebra are the easiest math courses there are. Easy in the sense, that it's not that hard to become familiar with the theory, and that it is easy to learn the tricks of the trade.

However, the more advanced your classes are going to get, the harder it's going to be to grow familiarity. And it order to achieve this, you'll need to make a lot of exercises, and you'll need to know your theory very well.

In a lot of exams, they will ask questions that require some kind of trick. And the only way of knowing such tricks is by doing a lot of exercises! So if you want to do better on your exams, you'll need to work harder... I guarantee you that every professor and math graduates, have worked extremely hard for getting the material!!

Of course, it's also possible that analysis is not "your thing". Everybody has a field in which they're good at. Maybe analysis is nothing for you, and perhaps you'll like algebra way more...
that's my point, it's silly to expect perfection from myself, but (calculus kind ) analysis and linear algebra are supposed to be the easiest math courses there are.. I should at least be able to do reasonably well ( if I have some aptitude for it) in these courses without busting my butt or putting much time into it ( these are the "honours" courses in my school though )
 
  • #5
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Of course, it's also possible that analysis is not "your thing". Everybody has a field in which they're good at. Maybe analysis is nothing for you, and perhaps you'll like algebra way more...
Because when it gets hard, it's time to give up.
 
  • #6
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especially how people I've seen and read about always seem to have been good at this stuff from the getgo, where I'm getting a crappy 50-60% on my midterm..
"Don't try to be a great man; just be a man, and let history make its own judgments."
-- Best quotation from a Star Trek movie
 
  • #8
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Well, if you want a failure story, my husband nearly failed a Spivak-style first year math course, and he nearly lost his scholarship. He's a math prof, now. His trick? Do lots and lots more problems than you think you need to do. Live, eat, and sleep math.
 
  • #9
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Well, if you want a failure story, my husband nearly failed a Spivak-style first year math course, and he nearly lost his scholarship. He's a math prof, now. His trick? Do lots and lots more problems than you think you need to do. Live, eat, and sleep math.
I agree 100%. If you're not making good grades now, that doesn't mean you're stupid or anything. Don't think that! You've just hit a wall, but if you keep hitting it again, the wall will break, so do lots(!!!) of problems and work very hard. I guarantee that you will get through it...
 
  • #10
A. Neumaier
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I love it, but I just took the midterm for that class and I think I bombed it. [...] I don't really know how far I can go to realistically become wanna-be prospective mathematician.
So far, things look promising.

but I'll be honest, I haven't spent much time at all just sitting down with a book and some paper to do problems
This is the only root of your problems. In science, I used to be good at school - things were so easy that I hardly needed to prepare. But at university, things got harder and at some stage I needed to learn (through bad experience - being too careless in the beginning of a course and suddenly losing track of what's going on) that we all advance easily until we are at the level - different for each one of us - where further growth means consistent and serious work. Then we need to accept that and work! And to compete with the best, it takes much more than 40 hours a week.... Now I am professor and head of a large research group.

You need to think about quitting math only if you can no longer muster interest, or if the very best (!) of your efforts don't make you succeed.
 
  • #11
mathwonk
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I agree with the previous post. You don't need any advice, as you have completely understood your own problem, namely you haven't made a commitment to do the work required to master the material. You are still just wandering around thinking abstractly about the fun parts, and not doing the exercise needed to build up some muscles at computation. Believe me, I've been there. I suggest you get to work as soon as possible or you may be forced to make another choice of career. All careers require hard work however. It may be wisest to make that commitment to one that you actually enjoy.
 
  • #12
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thanks everybody for the encouragement; and it's true, I shouldn't give up just because I'm having trouble, I was just worried that if I'm having trouble now, how would it feel when I get into more advanced mathematics? well I'm hoping that I'll be more practised and mathematically mature by then.
And you're right mathwonk, I'm having a lot of fun thinking about the "abstract" stuff, but I'm only dabbling around until I practise enough to become a practical "mathematician". I'm going to work on setting myself on a rigorous study schedule, rather than just reading up on material whenever I feel like it, I'm 20 years old right now so I think that I have time to get my act together. I'm definitely not giving up, there isn't anything that I've encountered that is as awesome as mathematics ( and I think I've seen enough to say this on a non-superficial level )
 
  • #13
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Well, if you want a failure story, my husband nearly failed a Spivak-style first year math course, and he nearly lost his scholarship. He's a math prof, now. His trick? Do lots and lots more problems than you think you need to do. Live, eat, and sleep math.
thanks, another to look up to :)
 
  • #14
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Ive had a similar experience. Several times in math last year (when I first hit my first few rigorous math classes), going through the same thing this year in my junior level physics classes.

One practical thing you can try immediately is to budget your time better on tests. Sometimes I know that I look at a problem on a math midterm on the first read through I don't even understand what is being asked. Before I would get overly anxious because I didn't think I could do the problem, then I'd dwell on the problem (usually not even writing anything down, just sitting and thinking) wasting very valuable time. What this did was force me to rush through problems I would normally know how to do well and make mistakes on those (or freak out and completely forget how to do it). Its called the Test Death Spiral.

Avoid this. If you look at a math problem and you are not sure you even know how to solve it, read it once through, think about it for about 30 secs or 1 min and if nothing is clearing up...MOVE ON. Find a problem you can begin to do. This will do a few things for ya:

1. Now that youve seen this hard problem, and youve thought about it for a bit, your brain can think about it in the background. If you end up having some time to come back to it, chances are you will at the very least understand the question and can being to jot down some ideas on how to solve it.

2. You wont get more anxious

3. If you come across a fairly easy problem next, you will quickly forget about the anxiety brought on by the other problem and you can focus on your current problem. Because you didn't waste time on the hard problem, you don't have to rush through the other problems; you will be less likely to make mistakes on those.

4. By completing a few easier problems, you will gain confidence, lower anxiety and think more clearly. You might even be lucky and one of those problems may offer some insight on the problem you cannot do. Math really relies on itself, chances are you will be applying similar ideas and concepts over and over, but just in different situations. By recalling these ideas, you are likely to recall some important result that leads to a "Eureka" moment where that hard problem suddenly becomes very clear and very solvable.

Talking about not falling into the death spiral is one thing; being able to avoid is quite another, and if you typically suffer from test anxiety, then doing what I stated above can itself require a lot of practice. But I really feel that you can improve your test scores significantly by simply making sure you avoid the Death Spiral.

Of course, the best way to avoid text anxiety all together is to be well prepared. That being said, you gotta start figuring out how to study smarter. I typically can do all my homework just fine (I may take a long time to complete it, but I can do it), but usually struggle on tests, I've modified the way I study to try to improve. SO here are some things that work for me (you can try them and see if they work for you; everyone learns differently):

1.Try not to let too much time go between a lecture and the reading that covers the lecture. Optimally you will want to read (very gingerly) ahead, so that the lectures don't take you by complete surprise. But I know life is life and this is not always possible, so...

2. At the very least you will want to make sure you engage in ACTIVE READING. This means you do not want to just read something through (like a novel), but you want to take your time and TAKE NOTES on your reading. Read, think about what you just read and see if you can explain what the author just said in your own words, on paper. Does the author prove something, but you can't quite follow it? Don't move on until you are sure you know why the author is doing what he's doing and WRITE THIS DOWN in your own explanation, do the same thing for example problems. Basically, do not move on until you understand what is being said, and understand it enough to explain it clearly and write down your explanation.

Sometimes it takes me 20-30minutes or more to get through a page. I can spend a couple of days taking notes on just a couple of sections. But this really helps. Not only do you really digest the material well, when its time to study for your test you wont have to reference your text as much; you will have created your own cliff notes, that clearly explains the topics in your language , that address the concepts you had a hard time understanding. This makes for a very very effective study aid when you need to review.

3. After you go through a section you will probably want to do whatever homework problems relates to that. What this does is force your brain to APPLY what you have just learned immediately, not only are the concepts very fresh, but by applying the concepts you will ingrain in your brain a deeper understanding of the material.

4. Work in groups if at all possible. This works out very well in rigorous math classes where you work with concepts, definitions and theorems much much more than you do with calculation. You may read some theorem, and you can analyze it from your point of view, but when you work with a group, you will almost certainly find that other people have a different perspective on the topic. You may not be looking at it correctly, or your classmate might be wrong, or you both may be wrong, or you may both be right and add to your understanding. Either way, when you discuss problems verbally with other people you will be forced to consider things you may have not through of considering. If you need to correct someone else's thoughts, you will have to explain, verbalize, be clear about where the person may be going wrong. All of this deepens understanding of the material.

5. And of course, work as many problems as you can. Don't limit yourself to "just" the tough ones. Especially if its a hard concept to digest, you want to do as many "quick and dirty" exercises/calculations as you can so that you start getting an idea of how the theory is working mechanically.

6. If you have access to a solutions manual, NEVER EVER USE IT to shortcut your homework. I know time can get tight, and sometimes you just gotta get the assignment done, but realize that by resorting to the solutions manual too easily you will be seriously handicapping your chance at understanding the material.

Also, remember that solutions in a manual are usually very tight, clean and compact. Not only can you learn nothing from just glancing at the solution, but most professors, TAs, graders will know that your solution is something that is expected from grad student, that can be immediately understood only by a grad student (chances are they know what the Solutions of the manual are anyway).

7. That being said, you can use the solutions manual as yet another resource to learn from. For example, suppose you want to work on extra problems not assigned in class (and thus probably no solutions provided or worked out by the Prof/TA). This give you a chance to check your work, and when stuck a chance to get some ideas. If a problem completely stumps you but you really want to know how to solve, look at those super tidy, super clean and compact solutions from the manual and ACTIVELY take notes on the solution. Make sure you can verbalize the solution, make sure you can explain why the author solved it and WRITE IT DOWN. This is a chance to turn a very tight proof into a nice little exposition that you can then reference later on.

Those are just some of things Ive began doing to help myself out. Of course doing this type of studying eats up lots of time, but it is possible to do this for every class, especially if you stay on top of it and don't slack. But if you study smarter, you will get a lot more bang for your study time.
 
  • #15
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great post, thanks for putting your time into it :)
 

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