How to study maths quickly and efficiently?

  • #26
239
5
I show as proof math average right now is about a B+ and that is only because I had to take Calc II over the summer, it was crammed into five weeks.
Proof that your method does not work as well as you think it does?
 
  • #27
ZombieFeynman
Gold Member
327
12
Why yes, I have taken a math class, I don't know what sort of connotations you're associating with the term actual math class but whatever.

And yes I find myself rather capable of telling others how to study math, weather my advice is good or not is a point for a subjectivist but I really feel that my ability to do so has been rather obvious.

Maybe you could look into some actual sociological classes, because the generation gap is very clear. My generation simply needs to read less in order to get information effectively, we simply don't need to sit down like military children and drill readings into our head. Rather, a lot of us are like me and let technology supplement many of the things we don't like to do.

Just to drive home your appall-o-meter, I can also tell you there is a direct correlation between the textbooks I can buy on ebook and my respective classes grade point average because I simply don't read textbooks anymore, I have my computer read them to me. So, yeah, I hardly look at my math textbook other than problem sets and solutions, not a big deal, the old methods of learning are starting to die anyway, I don't feel like picking them up as they go out the door.
Speak for yourself. I am only perhaps 5 years older than you and therefore in your generation. If you are a shining example of our generations learning in action, we may be doomed after all.
 
  • #28
member 392791
To be fair, sometimes math books are far too tersely written (whether unintentional or intentional is unknown to me) and yes, reading proofs of theorems is more or less a waste of time for me, because I simply can't understand what the proof is trying to say.

To give an example, I can't prove that a subspace of a vector space is closed under addition and closed under scalar multiplication. I have given up on the prospect of trying to understand it, so I just accept it as truth and use it so solve the questions asking whether something is a subspace or not. I am doing engineering though, so perhaps this is more acceptable to me? I'm not too interested in math theories anymore, I simply don't follow the logic well enough (this is bad on my part, not their fault I can't follow them).
 
  • #29
64
0
To be fair, sometimes math books are far too tersely written (whether unintentional or intentional is unknown to me) and yes, reading proofs of theorems is more or less a waste of time for me, because I simply can't understand what the proof is trying to say.

To give an example, I can't prove that a subspace of a vector space is closed under addition and closed under scalar multiplication. I have given up on the prospect of trying to understand it, so I just accept it as truth and use it so solve the questions asking whether something is a subspace or not. I am doing engineering though, so perhaps this is more acceptable to me? I'm not too interested in math theories anymore, I simply don't follow the logic well enough (this is bad on my part, not their fault I can't follow them).
Less people are interested in math for this reason, while the PF mentor up there jumps up and down if your don't use the Atypical methods which have failed students for generations. I hated math until I discovered youtube, yes, I discovered it, my family and I lived in an area with terrible internet service for a while, once I moved to a place would good internet service I love math.

And to the other guy, your not in my generation you didn't grow up with KhanAcademy and other methods of the like in your back pocket.
 
  • #30
64
0
i love it. mr drew you have just described the absolute most clueless losers way to attack a math course, always with disastrous results, unless the course is a joke.

pardon me but to us this is funny, if it weren't sadly the same way so many of our hapless students proceed.
There is no reason to go over proofs you already know, and you find your gaps more effectively by trying a math problem. Ever read a math text, tried the example problem, then realized you still don't have a clue of what your doing. Everyone knows you've done it, we've all done it, in this case you may hove just wasted a half an hour or maybe even an hour learning nothing. I understand math often works this way I find my method more effective, problems first, it finds your gaps in knowledge, then you fill them in.
 
  • #31
WannabeNewton
Science Advisor
5,800
532
And to the other guy, your not in my generation you didn't grow up with KhanAcademy and other methods of the like in your back pocket.
LOL Khan Academy...yeah good luck using Khan Academy when you start taking actual math classes.
 
  • #32
22,089
3,286
Less people are interested in math for this reason, while the PF mentor up there jumps up and down if your don't use the Atypical methods which have failed students for generations. I hated math until I discovered youtube, yes, I discovered it, my family and I lived in an area with terrible internet service for a while, once I moved to a place would good internet service I love math.

And to the other guy, your not in my generation you didn't grow up with KhanAcademy and other methods of the like in your back pocket.
There is no reason to go over proofs you already know, and you find your gaps more effectively by trying a math problem. Ever read a math text, tried the example problem, then realized you still don't have a clue of what your doing. Everyone knows you've done it, we've all done it, in this case you may hove just wasted a half an hour or maybe even an hour learning nothing. I understand math often works this way I find my method more effective, problems first, it finds your gaps in knowledge, then you fill them in.
I know you talk about being a new generation and things like that (even though I'm just a few years older than you), but trust me: your approach is not the right one. There are many people on this forum who struggled through physics and math and who have much experience in the field. Why do you refuse to listen to them?

How well do you really know your mathematics? I'm sure you can solve the exercises in Stewart and ace your exams, but that doesn't say much. If you just memorize derivative and integral rules without knowing where they come from, then I'm afraid you are not much more than a parrot who just shouts whatever he was taught.

To be fair, there is something interesting in an "exercises first" approach. The idea is to first give a few exercises which are easy to understand but difficult to solve. After an attempt of solving it, you read the chapter and learn how the material in the chapter helps you with the practical problems. If you have a good professor/tutor, then I think this approach can yield very good results. However, it is absolutely not the idea to skip the proofs.
 
  • #33
22,089
3,286
And to the other guy, your not in my generation you didn't grow up with KhanAcademy and other methods of the like in your back pocket.
Please, please do not only rely on khan academy or internet videos. These give you a false feeling of knowing the material.
One of the troubles with khan academy is that it is easy. Too easy. Once you get to more difficult courses such as QM or GR or real analysis or else, then there are no more easy videos available. You will have to start reading the textbook to understand the material. If you only watched khan academy videos, then you are not prepared for this step. The idea of textbooks is to slowly increase the difficulty and to get you used to abstract arguments. So when you start real analysis, you will find the step less steep (even though it is still quite difficult).

Khan academy is an excellent secondary resource. It should never replace a textbook. If you do allow it to replace your textbook, then you will feel the consequences later. And I also doubt that you will be able to solve more complex problems in physics and mathematics.
 
  • #34
834
1
And I also doubt that you will be able to solve more complex problems in physics and mathematics.
Especially when just about every exercise asks you to prove a theorem or derive a relation not mentioned in the main text.
 
  • #35
64
0
I know you talk about being a new generation and things like that (even though I'm just a few years older than you), but trust me: your approach is not the right one. There are many people on this forum who struggled through physics and math and who have much experience in the field. Why do you refuse to listen to them?

How well do you really know your mathematics? I'm sure you can solve the exercises in Stewart and ace your exams, but that doesn't say much. If you just memorize derivative and integral rules without knowing where they come from, then I'm afraid you are not much more than a parrot who just shouts whatever he was taught.

To be fair, there is something interesting in an "exercises first" approach. The idea is to first give a few exercises which are easy to understand but difficult to solve. After an attempt of solving it, you read the chapter and learn how the material in the chapter helps you with the practical problems. If you have a good professor/tutor, then I think this approach can yield very good results. However, it is absolutely not the idea to skip the proofs.
Which proofs are you referring to? The proof for the derivative with Reman-sums (or however you spell it)? I haven't run into many proofs that couldn't be explained in a ten minute video with the exception of Eulers formula/identity, and I agree they help a heck of a lot intuitionally.

Linear algebra proofs are the only things I've skipped because I am in Diff. Eq. and am supposed to have already taken Linear A, there just to complex to try. Anyway still if you guys really think these proofs are so important in the upper math courses which don't have video proofs, I would really appreciate it if you made the videos yourselves, there is a whole generation coming who have never learned a single math concept from a textbook. Screen cast are extremely easy to make especially with a PC, look it up. All you need is a basic editing software and a drawing program called smooth draw its free. Bring out your inner philanthropist, and put these up for the world to see, you know the methods which you learned these things sucked so make it easy for the next generation.

And to the other guy Khan is just the poster child and innovator, there are many who have theorem proofs in much higher level math and physics ranging from string to measure theory. Really, I think you guys are pretty ignorant of this stuff. this is why I made the https://www.physicsforums.com/showthread.php?t=644282 post.

P.S. to make the video you also need a drawing tool, but you can get one used for cheap.
 
  • #36
64
0
Especially when just about every exercise asks you to prove a theorem or derive a relation not mentioned in the main text.
We already do this all the time in Modern Physics, no significant surprises yet. I really think you guys are on the wrong side of the coin, screencast learning is going to replace the textbook, nobody wants to read about the stuff when they can watch a video explaining it. Yes, its A Lot easier then from the book I know that, but you guys are pretty much telling me to make it hard on myself when it doesn't have to be, for mathematicians/physicist you really have a bad eye for seeing progress when it happens. Like seriously when I discovered youtube my mind was blown wide open, really.
 
  • #37
225
8
As a high school student, I am surrounded by technology. My school has actually, just this year, given our freshman and sophomore students iPads to help their learning. Disregard the fact that I have only seen one person actually using it for something other than games, then this could maybe be beneficial. One of my friends in my AP Physics class actually bought a $40 subscription to a website that has solutions to every problem in our physics book. They are, obviously, helpful if you ever get stuck and need something for reference if you can't figure out your own mistakes. I, myself, own a Kindle Fire (thank you, rich grandparents) that I use to read and do pretty much everything else that it was designed for.

Now, despite all of this, I still take heavy notes in my physics textbook. I actually entirely neglect my school-supplied math textbook, but that's because it's Stewart's pre-calc, so I don't think it would be beneficial if were I to do so anyway. I do, however, read, note, and think about a Calculus textbook that I'm going through, that actually contains legitimite proofs and theorems.

Now, with google, and youtube (which you oddly think of as a useful place), people don't feel the need to actually learn anything, because it's all just a quick search away. Why actually take the time to understand a proof, when you can just watch someone else show how well they understand it themselves?

Technology is meant to supplement our learning, and to be used, ocassionally, as a medium for accessing help (ie. a forum like this one). You are entirely stupid if you think that the future of education is going to be replaced with online videos.

Understanding a video of someone explaining something does NOT mean that you yourself understand it.

I won't try to get you to change the way you approach mathematics, because it appears that you are going to be too stubborn to change your view, after having some of the most brilliant people on this forum try to help you, obviously with no avail. What I will ask of you, however, is for you to not act like you know how to study math, and therefore act as if you have the authority to tell others how they should study math.
 
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  • #38
Evo
Mentor
23,153
2,773
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