I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've gotten decent grades in all of them. I studied Probability and Statistics on my own with videos and textbooks. I'm taking Abstract Algebra and Intro to Algebraic Topology this year (third year) and I was wondering what the best method to studying these courses and Mathematics in general is.
I attend all the lectures and watch additional lectures from a different university (I usually pick one lecture series with the best quality) from beginning to end for review and different insights. I read my textbooks but do not do much problems in it. I usually just try to spend all the time solving p-sets. Is this a good way to study Mathematics? Should I do more problems from the textbook? I usually do only p-sets but I think it might be better to spend some time doing applications from textbooks as well. I also do not bother with proving theorems myself. I look at the proofs in the textbook, read the annotations, and if I think I understand it, then I don't bother doing it myself :( Are doing these theorems independently important in learning Mathematics? Also, are combinations of lectures, video lectures, textbooks, textbook problems, and p-sets enough to succeed throughout undergraduate courses and graduate courses? I really hope I get into a graduate school for studying Mathematics! Hopefully, I can get some feedback on the way I'm studying Mathematics. Constructive critism/suggestions are very welcome.
P.S. It would be helpful if you guys can provide me with good online lectures for courses that I would have to take later (more advanced courses; preferably from YouTube!) and it would also be helpful if you could provide excellent textbooks for these courses!
P.S.2. It would also be helpful if you guys could tell me if studying with 1 textbook is optimal, or studying with 2 or more would be better. Personally, I think that 2 would be best for reviewing and getting different approaches but it might take some time :( I want to know your thoughts on it!
P.S.3. The reason I tagged this into self-learning is that I want to apply this method of learning to courses that I wouldn't take in the University itself but for interest and knowledge only. I am aware that I cannot take all the math courses at the University but I don't wanna miss out on many things so I'm trying to teach myself a few courses that I wouldn't be able to take and be more relaxed when learning (for fun!)