Can using mathematical concepts in problems help with memorization?

[GregA]

I'm having difficulty at the moment working through pure maths with the limitation that regardless of the time I spend on a subject..no matter how straight-forwards things seem...2 weeks or so afterwards I can only vaguely remember the concepts, such that when I'm reading another proof that uses something proven or stated elsewhere I have to re-read what I have read from a different chapter and find myself surprised at what I have forgotton
Thing that really worries me is that I'm having to flog myself much harder now because in the last 3 months I have diverted most of the time I would have spent with pure maths playing a stupid game and concentrated only on mechanics (partly because I can visualise concepts in this subject easier, I also find it fascinating...and got annoyed with advancing at a snails pace in maths)...but worse still, even in the lower end of the grand scheme of things I am absolubtely nowhere! and at the rate I'm going might be stuck in nowhere.

I've recently stopped playing this game and bought a book on mathematical reasoning and number theory to try and alleviate this problem and help me to write and understand proofs better...but I'm way behind where I wanted to be and will reach a point soon that I shall need to keep traversing between books to follow the material, and thus slow me down even further.

Has anyone else had this sort of problem and found ways to overcome it or is it unforunate that being able to consign many things to memory is necessary and some of us (like me) just don't have this facility?

 

[Pseudo Statistic]

I'm having a similar problem right now. In my physics class we did stuff like thermodynamics, sound, and light and stuff; even though I understood the stuff when we did it (and probably still do), I can't quite remember a couple of things... especially when it comes to thermodynamics and naming processes and such. (I still don't remember what an adiabatic process is. :\ Not sure if that's Q = 0 or W = 0)

I'm guessing at one point in everyone's academic "life" a person encounters a problem like this...

 

[matt grime]

You'll find it easier to memorize things with practice since you'll quickly learn that memorizing details is not necessary, and all you need to do is recall some vague outline of the proof and the rest drops into place.

 

[0rthodontist]

My professor for theory of computation has a saying:
"Never memorize a theorem, never forget a proof"

 

[GregA]

Cheers for the replies folks but I just found out today that things are going to get a hell of a lot worse on the learning side of things!...got 5 months to work every hour I can so that I can accumulate a years tuition fees upfront (not including my other expenses such as rent, food etc...) because I'm going to get absolubtely no support whatsoever in my first year at Uni...just found this out this morning

 

[AKG]

A good way to get used to definitions, concepts, theorems, etc. is to apply them in very simple, basic exercises. This won't challenge you, it will just allow you to get your hands on these concepts, and actually get a feel for them. For example, if you had just learned what a group is, find some very basic problems that ask whether set X with operation # a group, or something like that.

 

[kdinser]

WoW player? Just curious

edit: should have added something to the thread.

Today I had a diff EQ/lin algebra test. As I was going over things one last time, I noticed that I couldn't recall anything that I had gone over less then 10 mins beforehand and I started to panic. Before I knew it, I was out of time had to run to class, got there just as the test was being handed out. I again started to panic, Ack, only 5 questions, Ack, 1 of them I'm sure I can't answer, ACK!, I don't remember how to do this one... and so on. Before I had even written my name on the paper, I had already convinced myself that I could only hope to get 40% on this test. Then I started to relax, I found a problem that I was very confident in, just show that vectors were linearly dependant and that those 2 vectors could linearly combine to form a 3rd specified vector. Despite that fact that I couldn't remember anything from the book or the lecture, I just stuck them into a matrix, then I remembered that if the determinate=0 they were linearly dependant, then I remembered how to find the coefficients and then... The rest of the test went the same way, even though I couldn't have possibly given a verbal description of how to find the formula(or even remember the basic formula) of an undampend free oscillating system 2 minuets before I walked into class, I managed to provide a correct(I'm pretty sure) formula describing such motion on the test. All in all, I would be surprised if I didn't get around 85% on this test despite only being able to fill in some basic formulas on 1 problem.

I assume your taking higher maths then me, but I don't think it matters. From what I've seen, almost everyone who actually works hard learning a subject learns and remembers a LOT more then they actually realize. Sometimes it just takes a right clue to bring it out.

 

[cscott]

WoW player? Just curious

That was my first thought.

 

[GregA]

Thanks for the replies, Your suggestion AKG is sort of what I'm currently trying at the moment...writing out theorems, statements and proofs in my own terms (though not devising them yet...barring simple exercises) so that hopefully I can remember them, shall have to see how things go...For what it's worth, what I'm studying right now is way below what you're doing Kdinser

Oh and that game?...not WoW (from what I've heard about that game if I was to get my grubby mitts on it then my academic life would be completely dead...well for a couple of years at least) ...tis by the same company though...Diablo 2 (yah its old...but they brought out a new patch...and I found out!)

 

[AKG]

Don't just write them out, use them! Often when kids are learning words, they don't just read the definiton and write it out and stare at it, they use it in a sentence. Most words you know you can probably use in a sentence with perfect facility, but if you were asked to write out a definition, it would take some time and thought. As soon as I say the word "respect", you know what I mean and if asked to use it in a sentence, you'd be able to do it right away. If you're asked to define it, you'd at least have to think about it. So get familiar with mathematical concepts and facts by using them. The analogue to using them in sentences is using them in basic problems.