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

  1. Jun 22, 2011 #1
    Most of the concepts? I do understand that the teaching dynamics in university are much different than in high school, as the professor won't be holding my hand and guiding me as a high school teacher would. But, seeing as professors aren't required to have any educational qualifications and most are there to research and teach on the side as a requirement.

    With that said, are most students generally required to learn most of the concepts by themselves and only go to the lecture to solidify that knowledge and ask questions from the text? Or is the lecture very vital to the learning process and the professors do teach the concepts from the book?

    I've been trying to self-learn the delta-epsilon proofs out of a textbook and it has been quite frustrating, actually. I was wondering if it was like this in university. Thanks in advance.
  2. jcsd
  3. Jun 22, 2011 #2
    Both of your questions are true. You are DEFINITELY expected to have read the material prior to lecture, but lecture is also imperative to your learning because the prof will take the material from the text and expand on it a bit and provide valuable examples. Learning in University is drastically different than in high school (in my opinion anyway). You will be much better off having some prior knowledge of the concept that you're about to attend a lecture about before attending said lecture.

    Self-learning is an imperative skill in University because as you said the prof will not hold your hand and guide you though every problem. However, with that being said, most profs are open to questions via email if there are no tutorial classes or TAs to contact. Your first line of attack if you're confused is to contact the TA for the course, or to hold out and go to the tutorial (if offered) for the course. If all else fails I guarantee your prof will have office hours and you would be able to go discuss your question during that time.

    With all that being said though I would advise AGAINST jumping straight to a TA or prof for help. Find study groups, find new reading material, teach yourself the concept you're struggling with. No prof is going to review the quadratic formula or how to manipulate vectors or simple math from highschool or first year, or... etc. If you are struggling with these concepts then find a textbook and relearn it.

    As for your comment about learning proofs yourself... I have to say yes, University is very much like this from my experience.
  4. Jun 22, 2011 #3
    Reading is one thing, but in math classes, are you also expected to self-teach concepts that haven't been covered in class yet and do the practice problems as well?

    I will definitely take advantage of office hours as much as I can, but, what I worry about is that won't be enough to cover all the questions that confuse me on a given lecture.

    Lol, asking the prof to review the quadratic formula? I can consider myself quite competent in mathematics at the high-school but I did struggle with optimization in calculus a bit and perfecting it over the summer.

    Interesting. What tips would you give to any students to help them transition from computational mathematics to proof-y mathematics? There is also a first year analysis course offered to math and science students instead of regular calculus. Would you recommend it or advise against it for a first-year math/physics student who isn't used to doing any proofs?
  5. Jun 22, 2011 #4
    Yep, some profs are terrible at teaching and you're going to have to learn how to deal with that. I had a prof in 2nd year Calculus who was in the Math department (this calc was applied math, not proof based) and all of her lectures were 50 minutes of proving some concept. There was no examples, no guidance as to how this new concept applies to anything, and yet we're expected to go complete a 25 problem assignment applying this topic. It was hell at times, but the textbook is your friend in these situations, the prof was just awful.

    Odds are the textbook will be able to answer most of your questions. Don't expect to be having dozens of questions, profs aren't THAT incompetent when it comes to teaching (through my experience anyway). Always try and find the answer in the text first, your prof will make you look like an idiot if he/she pulls out the text and shows you the answer in 2 seconds

    Re-reading your notes and working through a proof/example side-by-side with your notes can really help to clarify things when you're confused.

    Hey I've seen worse than quadratic formula questions. I've had some people ask some really stupid questions before. For example: Prof: *does a 25 minute example* "And so as you can see, using this method we can minimize our function" Kid: "Wait... I don't understand, how would we minimize x^2??" Ok maybe that's a bad example.. but you get the idea.

    You'll see some really idiotic people in your classes. You'll feel like a genius after some of the questions you'll hear.

    While I haven't myself taken any proof-y math courses (my experience comes from applied math and physics). I can only say that 99% of the people entering University haven't seen proof-based math (real analysis for example) until they take that first year analysis course. There's nothing much you can do other than take that course and hope for the best, I don't have any other advice on top of that because I personally haven't taken a proofy analysis course
  6. Jun 22, 2011 #5
    If you've never done proofy things before then it's essential to start as early as possible. You don't want to start doing proofs when they're already difficult.

    It starts in calculus. Do all the proofs in your calculus book. Your book doesn't contain proofs? Find one that does. The proofs in a basic calculus book are often quite easy, so it's a perfect way to start. Furthermore, proofs really help you understand the material.

    Take a class that learns you how to prove. And do a lot of proofs!

    Take some other proof based classes like linear algebra or discrete mathematics. These are difficult classes, but they usually don't have prerequisites. And they're proof heavy, so you'll learn the proofs by doing them.
  7. Jun 22, 2011 #6
    You should expect to do most of the learning on your own. In fact, you should expect some part of your exams to contain material that was never covered in class. Always try to get your hands on exams from previous years for your courses and compare them with what is covered in class.

    My analytical mechanics classes were 90% theory, most of which you could toss right out the window when faced with 2 final exam problems that are worth 80% of the grade.

    I don't see the problem with going straight to the TA/prof as soon as you get stuck unless its a problem with preliminaries. If not, then make good use of you're time and don't dwindle too much on a problem if you see you're not getting anywhere without a hint.
  8. Jun 22, 2011 #7
    Wow, that must have been a really horrible semester. Did the professor not offer any office hours, as well? This is what really worries me. I haven't academically transitioned to the university life, and I get stuck with professors like that. Aside from the textbook, what other resources did you use that were at your disposal to do well?

    That is good to hear, but I will definitely start taking the initiative of looking through the textbook to answer my question and go to the professor as a last resort. Based on your personal experience, aside from that first math professor, would you say most math professors are competent teachers and teach concepts to an extent that most students in the class understand?


    Lol, my class had its knuckleheads and even then we wouldn't get questions like that. What are they doing in a calculus class if they don't even have a strong foundation in algebra, to begin with? What was the class average for that class, if you don't mind me asking?

    I kind of see it as too big of a challenge, though. Not only will I have to adjust to university academically, but I also have to adjust to all the proofs in the course. Don't get me wrong, I love to challenge myself and that is what university is all about, but I also don't want to spend 5 hours/day on 11 questions while still having homework from my 4 other classes. Unfortunately, the school I'm going to attend does not allow you to take analysis after taking the regular calculus, so I wouldn't be able to take real analysis even if I feel I am ready for proof-y mathematics (say in my second year, for example). That is why I'm having trouble deciding.
  9. Jun 22, 2011 #8


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    You'd be surprised how many students I've tutored in Calculus and higher level classes and don't know the quadratic formula.
  10. Jun 22, 2011 #9
    How would you suggest I start? Should I start memorizing the theorems and how they are derived, and then continuously prove them until they become natural to me?

    Again, how? It's kind of difficult to learn an entire new way of thinking and problem-solving. Should I memorize them?

    I plan to take linear algebra, already. Also, the school I am planning to attend apparently does have prerequisites for discrete mathematics, so I can't take it.
  11. Jun 22, 2011 #10
    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.


    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.

    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.
  12. Jun 22, 2011 #11
    I've heard this as well reading other forums. Most successful students apparently spend 20% of their time on the class material and the other 80% working through past exams. But, do students really learn like that by being tested on material that isn't even covered instead of being tested on knowledge they are suppose to know i.e: was covered in class?

    I see.
  13. Jun 22, 2011 #12
    How did they make it past calculus and to higher level math classes without knowing the quadratic formula? :confused:

    Wow, all this time I was under the assumption that I'd be well behind my future genius classmates by not knowing how to do proofs.
  14. Jun 22, 2011 #13
    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.

    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.

    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.

    Do not worry if you are unable to prove much at first, it was the same with me. :) You'll get better with practice.
  15. Jun 22, 2011 #14
    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.
  16. Jun 22, 2011 #15
    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!
  17. Jun 22, 2011 #16


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    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!
  18. Jun 23, 2011 #17
    Why self-learn proofs if you don't need to?

    What program are you planning on taking? If it's Pure and Applied Math or some Mathematics program by all means learn proofs.

    I am doing Mechanical Engineering and I have never had to prove a thing--many here will say "but you MUST know proofs"; I disagree and feel it depends on your major.

    As an engineer if I'm trying to work out a calculation for the flow of water through a pipe the proof for the Fundamental Theorem of Calculus will not help (nor will any other proof I have come across in my time).

    I always went through the proofs and followed along but from personal experience, at least, I always found doing harder examples and then having a step-by-step version always helped more than a proof.

    I've always been at the top of my math classes too.

    Bottom line: your program will dictate whether you need to know proofs or not (in all honesty, many proofs were just confusing and hindered my ability to understand the concept but then again I am not/nor have I ever wanted to be a math major).

    If you do want to learn proofs try:

    How to Prove it: A Structured Approach by Daniel J. Velleman
  19. Jun 23, 2011 #18
    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.

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

    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.
  20. Jun 23, 2011 #19
    Of course, but the thing is, all my first year math courses will be proof-based.

    I see.

    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.

    I sure hope so. Thanks.
  21. Jun 23, 2011 #20
    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.

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

    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.
  22. Jun 23, 2011 #21
    Since you want to be a math major I take back everything I said.
  23. Jun 23, 2011 #22
    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?
  24. Jun 23, 2011 #23
    This is very helpful advice and answers many of my questions. Thank you, Sankaku.

    Thank you, bcrowell.
  25. Jun 23, 2011 #24
    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.
    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.
  26. Jun 24, 2011 #25
    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.
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