Solving problems = 90% of what one needs to do to master a subject?

[KCL]

There are so many learning resources out there -- school lectures, online lectures, books, and lots more books... all kinds of books.

It's easy to get lost, however I think what I always knew is that doing problems is what really matters at the end - that's what solidifies what you know and shows you all the things you missed.

... is that true? I simply want to know what your opinion is, especially since a lot of people here made it all the way to earning a PhDs and doing research and whatnot.

 

[andytoh]

https://www.physicsforums.com/showthread.php?t=151986

 

[nightdove]

I think it is true in the case of doing well in exams. I don't know if it is the case in research.

I would say that for exams, the majority of the marks (some 50% ?) you get from practising past year papers well enough, and only 25% comes from the lecture notes and textbook examples. Of course, the remaining 20% derives from experience in similar subjects, and about 5% from diligently attending lectures (almost useless given the opportunity cost).

Yes, building a foundation is important and I would say the stuff you learned in trivial first year courses, if you studied them well, would really payoff once you find you need to revisit those skills in your second and third year. A little bit of rustiness in a particular technique in the earlier years of university can result in a B grade on later year courses, really. Your lecturer may suddenly decide to pose a problem which requires the use of some boring and mundane approximation like Taylor's technique.

Did anybody else find the same thing? That lectures are almost useless... And that doing well on an exam depends on finding examples / problems set at the right level of difficulty... Problems that are too easy waste your time without giving you a corresponding improvement in mathematical agility... At university I wasted far too much time on those... I used to blindly repeat problem sets from question 1 to question 10, even the most trivial ones, as I feared that I may have forgotten simple techniques.

Perhaps it was not so much understanding that gave me difficulty,but expressing that understanding in a way that would satisfy some of the more anal and pedantic lecturers who would find any excuse (untidy notation or a single arithmetic slip for example), to deduct large amounts of marks.

 

[J77]

You read books and learn things to pass exams.

Imagination's what you need to push forward in research

 

[leright]

I think it is true in the case of doing well in exams. I don't know if it is the case in research.

I would say that for exams, the majority of the marks (some 50% ?) you get from practising past year papers well enough, and only 25% comes from the lecture notes and textbook examples. Of course, the remaining 20% derives from experience in similar subjects, and about 5% from diligently attending lectures (almost useless given the opportunity cost).

Yes, building a foundation is important and I would say the stuff you learned in trivial first year courses, if you studied them well, would really payoff once you find you need to revisit those skills in your second and third year. A little bit of rustiness in a particular technique in the earlier years of university can result in a B grade on later year courses, really. Your lecturer may suddenly decide to pose a problem which requires the use of some boring and mundane approximation like Taylor's technique.

Did anybody else find the same thing? That lectures are almost useless... And that doing well on an exam depends on finding examples / problems set at the right level of difficulty... Problems that are too easy waste your time without giving you a corresponding improvement in mathematical agility... At university I wasted far too much time on those... I used to blindly repeat problem sets from question 1 to question 10, even the most trivial ones, as I feared that I may have forgotten simple techniques.

Perhaps it was not so much understanding that gave me difficulty,but expressing that understanding in a way that would satisfy some of the more anal and pedantic lecturers who would find any excuse (untidy notation or a single arithmetic slip for example), to deduct large amounts of marks.

I find attending lectures is very helpful. Also, it is very helpful to go over every chapter (reading assignments and assigned problems) with a fine too comb.

In the end though, I do these things to master the subject...not in order to get a good grade...I really do not care much about grades. I care a little bit because they are important to employers and grad schools, but it's not the most important thing to me.