Question

[University] I feel like asking questions here on Reddit or StackExchange how to solve some problems and exercises, which I wasn't able to do on my own, has really hindered me from becoming better in Math

Answer 1

>I keep asking the people in that forum to explain me more details about their answer so I can 100% understand it.

To be able to get something useful out of an exercise or a solution to an exercise, if it's one you can do it needs to stretch you at least a little bit, and if it's one you can't do, it needs to be just beyond what you are capable of. If the solution to an exercise contains ten ideas that you wouldn't have had on your own, then it is probably too hard. The answer, ideally, is to study math closer to your own level and improve your understanding and ability gradually. Stack Exchange and Learnmath are full of people asking questions that are too hard for them because it is what is being asked of them in school or university, but they haven't kept up in terms of their ability to do math at the levels they've moved through.

Answer 2

Getting the answer is much less important than working on the problem.

There’s a reason most upper level math books don’t provide answer keys for the odd problems in the back of the book- like how calculus books do.

The learning is in the attempt, actually getting the solution is not the priority.

It’s great that you are spending 3-4 hours on a problem, trying different approaches!!! That’s a taste ( a very small one, but we must start somewhere) of what mathematics research is like.

If you really get stuck, it’s far better to ask for advice on how to solve the problem, instead of the answer. Ask if you are along the right path, or for advice on where to start the next step.

Both, going online or asking your professor for help are great ways of approaching a problem you are stuck on. But, don’t ask for the answer. - ask for what you are doing wrong or where you might start.

Also, it’s important to “play” with solutions. I think Terry Tao says it best:

“ When you learn mathematics, whether in books or in lectures, you generally only see the end product – very polished, clever and elegant presentations of a mathematical topic.

However, the process of discovering new mathematics is much messier, full of the pursuit of directions which were naïve, fruitless or uninteresting.

While it is tempting to just ignore all these “failed” lines of inquiry, actually they turn out to be essential to one’s deeper understanding of a topic, and (via the process of elimination) finally zeroing in on the correct way to proceed.

So one should be unafraid to ask “stupid” questions, challenging conventional wisdom on a subject; the answers to these questions will occasionally lead to a surprising conclusion, but more often will simply tell you why the conventional wisdom is there in the first place, which is well worth knowing.

For instance, given a standard lemma in a subject, you can ask what happens if you delete a hypothesis, or attempt to strengthen the conclusion; if a simple result is usually proven by method X, you can ask whether it can be proven by method Y instead; the new proof may be less elegant than the original, or may not work at all, but in either case it tends to illuminate the relative power of methods X and Y, which can be useful when the time comes to prove less standard lemmas.”

Answer 3

Unless you are in at least upper-level undergrad math, routinely spending 3-4 hours on a problem means you lack adequate preparation or background.  Math classes below that point don't routinely assign such work.  It's pretty unlikely that you will just stumble on a solution only after hours.

Answer 4

If you can rewrite their answer without looking at it while understanding each step of the proof and why each part is necessary you’re learning. You’re not supposed to be able to answer every question you come across. With each question you do you discover new tools and with time you’ll instinctively know which tools need to be used where. I kinda view it as an art, you eventually learn a proper way to think about things and this will be determined by the tools you acquire and where you see them used in the exercises you do

Answer 5

It sounds like what you really need is good hints, not answers. Unfortunately, it is perhaps more time consuming to create a hint that will be just right for your ability than to simply tell you the solution. So it's possible there are not very many people willing to take that time.

Answer 6

I think after you "understood" a Solution, you should always solve the problem again, from scratch and without any notes.

If you really understood the problem you will be able to explain the reasoning of every step in the solution to yourself.

For me i often got stuck again and found that i was still missing some steps of the solution even after i thought i already understand it, because i looked at the solution.

But following the solution and being able to replicate it are two different things.

Answer 7

> I try to solve that given problem for 3 or 4 hours. That's more or less how long I spend sitting in front of my desk, trying to wrap my head around that problem

Honestly, at the university level, giving up after 4 hours is doing yourself a disservice.

Let the problem simmer a little. Get back to it next day, and the next day after that. Then give it a pause, then get back to it. And only then, after you spent several days, each day several hours, and you're still stuck, ask the internet for help.

With this approach, you'll see how many problems can you actually solve on your own if only you give yourself a chance.