This is a problem all through academia. I strongly suggest a hobby (like drawing a webcomic) if you find yourself in this situation.
In mathematics, the terms “necessary” and “sufficient” have technical meanings. These terms come about when looking at two statements P and Q. If we say that P is sufficient for Q, then that means if P is true, Q automatically has to be true (P implies Q). On the other hand, if P is only necessary for Q, having P be true doesn’t mean Q has to be true (but the other way works, so…
“When I was your age, I did all the problems before the test!”
“To get to the last equality, the steps should be obvious. If they aren’t, please close this book and find something easier to read.”
“I’m going to get started early and finish this way before the deadline!” (Ten minutes later.) “Well, maybe I’ll just take it easy. I mean, just look at how much time is left!”
Educators have unrealistic views about memorization. If you’re reading this as a student, think about any time a teacher spoke about their thoughts on memorization. Unless the point of the class was to memorize certain facts, I’m guessing the teacher did not love the idea of memorization. In fact, for those who teach subjects such as physics or mathematics, they might have gone on a rant about how memorization is a terrible thing to do…
Ah, do I just love the simple life of a theorist!
As you do more problems, you groan at an “easy” but tedious integration, but you love it when you can pull out a neat trick to simplify things.
The more advanced the problem, the more frustrating this becomes.
This sounds like an easy question, but I think I have a bit of a different perspective on it. In science and mathematics programs, it’s not too difficult to cheat. I’m not talking about cheating on tests or exams, but on assignments. That’s because most professors don’t write their own problems. Instead, they assign them from textbooks. The upside is obvious: they don’t have to spend time crafting new questions every semester. Unfortunately, the downside…