
#1
Jun2211, 01:24 PM

P: 286

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 selflearn the deltaepsilon 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
Jun2211, 01:35 PM

P: 380

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.
Selflearning 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. 



#3
Jun2211, 03:33 PM

P: 286





#4
Jun2211, 03:44 PM

P: 380

In university/college, are you expected to selflearn?Rereading your notes and working through a proof/example sidebyside with your notes can really help to clarify things when you're confused. You'll see some really idiotic people in your classes. You'll feel like a genius after some of the questions you'll hear. 



#5
Jun2211, 04:09 PM

Mentor
P: 16,690

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. 



#6
Jun2211, 05:22 PM

P: 849

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. 



#7
Jun2211, 06:51 PM

P: 286





#8
Jun2211, 06:55 PM

HW Helper
P: 805





#9
Jun2211, 06:59 PM

P: 286





#10
Jun2211, 07:03 PM

P: 380





#11
Jun2211, 07:05 PM

P: 286





#12
Jun2211, 07:08 PM

P: 286

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. 



#13
Jun2211, 07:31 PM

P: 9

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 proofbased 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. 



#14
Jun2211, 07:45 PM

P: 1,089

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



#15
Jun2211, 11:14 PM

P: 714

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! 



#16
Jun2211, 11:19 PM

Emeritus
Sci Advisor
PF Gold
P: 5,500

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!




#17
Jun2311, 04:14 PM

P: 119

Why selflearn 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 thingmany 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 stepbystep 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 



#18
Jun2311, 05:06 PM

P: 286

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 "plugnchug" that I'm used to. With the doublemajor, I wouldn't be allowed to take a proofy class until my third year because the first and second year classes proofy 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. 


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