In university/college, are you expected to self-learn?

-Dragoon-

Quote by Clever-Name

She offered 2 hours of office hours a week but they were scheduled during my lab, and there were no TAs for the course, and even when I did go to talk to her she was awful at explaining things. The only resources I had were my textbook, wikipedia, and my brain. It sucked. I didn't do that bad though, I managed to get through it.

Wow, I hope to not have a professor like that in my first year classes. The material is hard enough, and dealing with an incompetent professor to top it all of? I'd probably drop the class.

Quote by Clever-Name

No clue, there were students from all over (economics, some from psych, math, applied math, physics, etc.) So I have no idea how they got in there, I believe the person who made the most stupid remarks was in comp sci.

Lol, I find that to be ironic. Comp Sci is even more proof-y and "pure" mathematics wise than applied math, no?

Quote by Clever-Name

What degree are you going for? Straight Mathematics? If you're doing straight mathematics look at the outlines for both courses (calc and analysis), see which one might benefit you more in the long run depending on what future classes you have to take.

Originally, I was going to go for a math major. Now I am aiming for a math specialist, which requires analysis I and II and algebra I and II as well as foundations of physics I and II to declare as a major. I could also opt for a double major in math and physics, but the university will then force me to do more electives while the specialist program requires few electives. Though if I don't do as well as I'd hope in those classes, their easier counterparts are still good enough to satisfy the double major requirement and is my backup.

Either way, I want to learn how to write proofs as soon as possible. It looks very enjoyable and is a fresh change to the "plug-n-chug" that I'm used to. With the double-major, I wouldn't be allowed to take a proof-y class until my third year because the first and second year classes proof-y classes are all excluded from majors. To be frank, I don't want to wait until my third year to learn how to do proofs if I don't have to.

-Dragoon-

Quote by Stylish

I was able to get by the first few, more computational courses without putting in much effort outside of class, but you will probably need to learn to teach yourself in the upper level, more proof-based courses.

Of course, but the thing is, all my first year math courses will be proof-based.

Quote by Stylish

The thing is, you will learn more by practicing working through problems/proofs than simply attending lectures. Also, professors can only go over so much in one semester, so if you're really interested in math then you'll need to invest your own time to get the whole picture. And as mentioned above, not all professors are competent at teaching.

I see.

Quote by Stylish

As for trying to learn how to do proofs, maybe you could try getting some sort of introduction to proofs book, and look through the proofs in your textbooks so far.

I would recommend trying to prove some of the theorems on your own. Try to read some of the proofs at first, and really understand how they work. Maybe try and work through them yourself afterwards if you feel it will help. Then try and prove some theorems without looking at the proof, and if you get stuck, read the next step in the proof, and then try to finish it from there. This was a strategy that I did at first.

So far, I've been able to prove trivial things like why the square root of 2 is irrational by contradiction. But I mostly did it out of rote memorization, which can't exactly be considered proving it, I suppose.

Quote by Stylish

Do not worry if you are unable to prove much at first, it was the same with me. :) You'll get better with practice.

I sure hope so. Thanks.

Clever-Name

Quote by Retribution

Wow, I hope to not have a professor like that in my first year classes. The material is hard enough, and dealing with an incompetent professor to top it all of? I'd probably drop the class.

That's the thing about University though, you might not be able to drop the class. If it's a requirement to proceed in your degree then you HAVE to take it and suck it up if you get a bad prof, like I had to.

Lol, I find that to be ironic. Comp Sci is even more proof-y and "pure" mathematics wise than applied math, no?

Probably, but the guy was just stupid in general, I dunno how he even got the prereqs to be in that class.

Originally, I was going to go for a math major. Now I am aiming for a math specialist, which requires analysis I and II and algebra I and II as well as foundations of physics I and II to declare as a major. I could also opt for a double major in math and physics, but the university will then force me to do more electives while the specialist program requires few electives. Though if I don't do as well as I'd hope in those classes, their easier counterparts are still good enough to satisfy the double major requirement and is my backup.

Either way, I want to learn how to write proofs as soon as possible. It looks very enjoyable and is a fresh change to the "plug-n-chug" that I'm used to. With the double-major, I wouldn't be allowed to take a proof-y class until my third year because the first and second year classes proof-y classes are all excluded from majors. To be frank, I don't want to wait until my third year to learn how to do proofs if I don't have to.

If you can't take any classes then study up independantly. Find textbooks on proof writing, talk to profs in the math department, talk to people who are competent in writing proofs, etc.

ZenOne

Since you want to be a math major I take back everything I said.

-Dragoon-

Quote by Ryker

As someone who hadn't done proofs in high school, but took proof-based courses in his first year, I can tell you that they will not expect you to know how to prove stuff your first day. You'll be confronted with proofs from almost day one, and the learning curve is going to be very steep, but you'll be given the chance to get acquinated with proving stuff. So not having that background shouldn't be a detriment, it's up to you whether you'll be able to handle it or not. But I do recommend you take the course, just because it's way more fun and you also learn more. On the other hand, it's also a lot more work. For example, a friend of mine who first enrolled in the honors version of our linear algebra course, but dropped out and switched to regular, because she found it too difficult, said she then had to spend roughly two hours on her homeworks to get a 100%, whereas we spent upwards of 10 hours on each homework, and I don't remember there being a time where more than five people got that. Quite the opposite, lots of times no one got that mark.

But like micromass said, if you want to get into it, get into it now.

Coming into the class, Ryker, did you know how to prove anything? Do you feel that held you back relative to your other classmates? On average, how long did it take for you to finish the problem sets that are assigned daily or weekly? Aside from working hard, what else did you do to ensure that you did well in the class, Ryker?

-Dragoon-

Quote by Sankaku

Others have given good advice above, but I thought I would summarize a bit:

1) Yes, you have to learn to teach yourself. However, you have many tools at your disposal: Your textbook, supplemental books, video lectures on the internet, forums like this one, etc.

2) Use the lectures as an opportunity to ask questions. Many people are too shy and/or afraid of looking like a fool. As long as you really read the material before class, no question is a dumb question.

3) Use the teachers you have available: Professor office hours, TA times, etc. Many schools have a math support centre where you can come in and ask questions. Use it. Also, work with your friends - sometimes you learn best when having a relaxed discussion with your peers.

4) Look for an intro proof course. Most schools have them these days. Sometimes they are named in obscure ways, but an academic advisor will be able to tell you what to take.

5) Be prepared to put in some time. Proof courses are different, as Ryker said. It takes practise to get any good at it. Many people quit too early.

Have fun!

This is very helpful advice and answers many of my questions. Thank you, Sankaku.

Quote by bcrowell

Retribution, the answer to your questions is that it depends entirely on the professor. Some profs expect you to learn more on your own than others. I second Sankaku's advice to have fun. Just dive in and try to learn the material. You'll do fine!

Thank you, bcrowell.

Ryker

Quote by Retribution

Coming into the class, Ryker, did you know how to prove anything?

I'm not sure, perhaps something really easy, but I certainly wasn't aware of different proof techniques. I mean, I was six years removed from high school, and haven't done Maths since. Apart from going through my old notes over summer, that is.

Quote by Retribution

Do you feel that held you back relative to your other classmates?

No.

Quote by Retribution

On average, how long did it take for you to finish the problem sets that are assigned daily or weekly?

In Calculus, problem sets were assigned weekly and it took me ~10 hours, whereas in Linear Algebra they were assigned bi-weekly and it took me 8 - 18 hours (usually 10 - 12, but there were some harder assignments that took me 18 hours with thinking about problems for several days).

Quote by Retribution

Aside from working hard, what else did you do to ensure that you did well in the class, Ryker?

Lift heavy weights and eat beef.

thegreenlaser

I find that I learn best through a combination of lectures and self-teaching in university. I sit in the lecture to sort of get an introduction to a topic. The lecture gets me thinking about the main points of the topic so that I can really solidify it by reading and doing problems later. I actually find that this works better for me than reading the text book before the lecture because if I'm teaching myself, I can stop to ponder a specific point that's unclear to me or quickly move past stuff that makes sense. I do find lectures really useful though, as a 1 hour lecture by a good professor can easily make up for 2-3 hours of self-study time, if not more. It's just that for me, the lecture just works better as an introduction to a topic than as an in-depth study, so I tend to put the lecture before the self-studying.

mathwonk

yes you yourself are ultimately responsible for your own learning. however that is such a hard task that it then follows you should use every method available to you. if you do not go to every lecture you are foolish. but that does not mean that will suffice.

its not as if any one source is sufficient to learn something. you have been struggling to learn epsilon proofs by reading. good for you! now go to lecture also, and do homework, and discuss with friends and just MAYBE all those together will suffice for you to get it down well.

-Dragoon-

Quote by Ryker

I'm not sure, perhaps something really easy, but I certainly wasn't aware of different proof techniques. I mean, I was six years removed from high school, and haven't done Maths since. Apart from going through my old notes over summer, that is.No.In Calculus, problem sets were assigned weekly and it took me ~10 hours, whereas in Linear Algebra they were assigned bi-weekly and it took me 8 - 18 hours (usually 10 - 12, but there were some harder assignments that took me 18 hours with thinking about problems for several days).Lift heavy weights and eat beef.

I see. Thank you once again for your insightful posts, Ryker.

*Angry Citizen*

The only resources I had were my textbook, wikipedia, and my brain.

Well, now you have your textbook, wikipedia, PHYSICS FORUMS, and your brain! I personally think university exists for the sole purpose of teaching you how to learn on your own. Sometimes I wonder if those "awful professors" everyone talks about aren't intentionally trying to do you a favor.

Regarding proofs, whether you're in mathematics or in engineering, I think it's handy to know certain proofs. The integration by parts technique was just another formula to memorize until someone said, "Dude, it's the product rule. See for yourself."

-Dragoon-

Quote by thegreenlaser

I find that I learn best through a combination of lectures and self-teaching in university. I sit in the lecture to sort of get an introduction to a topic. The lecture gets me thinking about the main points of the topic so that I can really solidify it by reading and doing problems later. I actually find that this works better for me than reading the text book before the lecture because if I'm teaching myself, I can stop to ponder a specific point that's unclear to me or quickly move past stuff that makes sense. I do find lectures really useful though, as a 1 hour lecture by a good professor can easily make up for 2-3 hours of self-study time, if not more. It's just that for me, the lecture just works better as an introduction to a topic than as an in-depth study, so I tend to put the lecture before the self-studying.

Interesting. I'll definitely try this come Septembre. Great and insightful advice as always, thegreenlaser. Thanks.

-Dragoon-

Quote by mathwonk

yes you yourself are ultimately responsible for your own learning. however that is such a hard task that it then follows you should use every method available to you. if you do not go to every lecture you are foolish. but that does not mean that will suffice.

its not as if any one source is sufficient to learn something. you have been struggling to learn epsilon proofs by reading. good for you! now go to lecture also, and do homework, and discuss with friends and just MAYBE all those together will suffice for you to get it down well.

Yes, definitely. One method alone is not enough to learn the concept. But, I am not in university yet so I have no lecture to attend. I'm trying to learn the delta-epsilon proofs on my own so I can have a head start.

mathwonk

can you prove that if 1.5 < x < 2.5 then 2 < x^2 < 7?

what if 2-d < x < 2+d? then what can you prove about x^2?

in that latter case, if d-->0, what does x^2 do?

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mathwonk Recognitions: Homework Help Science Advisor	can you prove that if 1.5 < x < 2.5 then 2 < x^2 < 7? what if 2-d < x < 2+d? then what can you prove about x^2? in that latter case, if d-->0, what does x^2 do?