Difficulty of undergraduate homework problems

[spaghetti3451]

I am an advanced undergraduate student, and I still remember the days when I could open my mathematics textbooks, read through a few sample problems, and then blaze my way through the exercises with little or no help.

Come university, and my freshman year, and things changed dramatically. I could still more or less blaze through the Resnick and Halliday exercises, but I was beginning to see that textbooks such as Griffiths, Purcell, Marion and Thornton (I mean, sophomore and beyond) contain exercises I could never solve on my own. In the majority of the cases, I've had to rely on solution manuals to work my way through the problems. It's not like I don't understand the solutions - once I understand the solutions, I can again blaze my way through similar calculations, but for some reason, every problem is different and poses new challenges.

I have been wondering if I have reached the pinnacle of my academic ability. Are there really students who could simply take a look at those problems and figure out the answers instantly?

 

[jedishrfu]

No youve seen the reality of college. For some students, the first year is a refresher course to get you prepared for what's to come.

For me one year of college was equivalent to three years of high school. My junior year was when I hit the brick wall of really difficult topics that i had to really focus on.

 

[spaghetti3451]

It's nice to hear that I'm not alone!

Thus far, all the top-notch undergraduate students I've encountered get stuck in the exercises, but what separates them from the rest is that they've actually been able to work their way through textbooks so that they've struggled with these exercises, unlike the majority of the students who don't solve all the exercises in the textbook. Therefore, when these top-notch students encounter similar exercises in future courses, they can actually blaze through the calculations, seemingly giving the impression that they've produced the solutions out of nowhere. That's why I think it's so very important to read through textbooks and solve all the exercises because the techniques you learn becomes indispensable in future courses.

I think that's what separates the top-notch students from the rest - Hard work and perseverence!