Finding the Creative Side of Math: Advice for Undergrads

[27Thousand]

I'm not sure if I'm the only undergrad who has ever felt this way but I hope this is the right forum to ask for advice in.

In math classes, generally we were given a bunch of very silly, trivial problems and made to solve the same exact thing fifty times (what's the root of (x^2)+3? Now what's the root of 3(x^2)+4? And on and on and on). Math is taught by 'memorize this stuff and stick it here and watch your signs'.

Historically, I've done well in these sorts of classes but sometimes I can't help but feel that there's a whole side of math that I'm missing. I know methodology and memorizing are important but it's taught to the exclusion of anything else. It's like being stuck in a gray room but there's a peephole in the wall that shows something more more exciting and creative than memorizing example problems. This simply can't be all there is to math. I talked to my adviser and his only advice was 'wait until you get to the proofs class, it gets a lot more 'fun' then'. The textbook isn't any help either, since it has the same tired problems and definitions.

My question, if I'm making any sense at all, is how can I get to this other side of math? I enjoy finding things out seeing patterns (that's why I'm majoring in physics) but I want to do the same in math. I know it's possible, but I just don't know how to get there. Any advice would be vastly appreciated and sorry for all the questions. Thank you.

I'm like you, I don't like rote memorization either. It's always more fulfilling to grasp the concept of how something really works. Just like you can use sticky tape to grab a piece of paper, you can grasp the concept by doing whatever you can to turn details into concepts, or the process of concept-ualizing.

I always try to do my best to visualize in my mind why/how the equations work, why something may specifically be in the denominator, etc, etc. Then I think about what I worked out to myself when doing the practice exercises, so the grasped concept is strengthened. Then relating to what you already know/outside knowledge helps.

Although this sounds elementary, some of the Complete Idiot's Guides and for Dummies have ways of visualizing.

 

[pbandjay]

I never force myself to "memorize" math. Rather, I strive for understanding of proofs of theorems and such...

I have a professor who once said: "People assume: I am a mathematician, therefore I solve numerical problems... This is equivalent to: I am a novelist, therefore I write words."

 

[lurflurf]

^Well good on you. So do you just remember all the theorems, proofs, and definitions or do you just not worry about the ones you forget. I know if I did not "memorize" I would not remember trigonometric identities, integrals, all those variations on compact, which types of rings are named after which people, 7 times seventeen, or many other things.

 

[DukeofDuke]

^Well good on you. So do you just remember all the theorems, proofs, and definitions or do you just not worry about the ones you forget. I know if I did not "memorize" I would not remember trigonometric identities, integrals, all those variations on compact, which types of rings are named after which people, 7 times seventeen, or many other things.

Well, mainly for the little theorems they are pretty obviously true, its just a matter of remembering whether or not its true by theorem and whether or not you can say it. For the bigger ones, there's a difference between straight memorizing, or understanding and then remembering. I try to do the latter, where you create the concept in your mind and develop the theorem out of that, rather than just trying to remember the words. But yeah, some things are unavoidable, you have to straight up memorize names. But things like integrals are so second nature now its not really memorizing. And I only remember two trig identities, takes me all of 12 seconds to derive all the others.