Studying mathematics efficiently

Solution 1:

I don't think anyone is qualified to give you advice, including myself, since everyone will have their own method that works best for them. I'm a grad student in pure maths.

To me it sounds as if you are picking the wrong books. You need to think about two things:

1. Is the book you picked at the right level for you? By this I mean for example, do you know enough basic calculus to be doing analysis? If you do, how much analysis do you know and how much would be required to read the book you picked? Should you be revising more elementary topics before moving on to abstract algebra and analysis? Who cares about what Joe Bloggs read at high school, this is about you and not about what other people did or did not.

2. Does the book match your taste? This might be a bit subtler to figure out and fix, if not. There is an infinitude of books about analysis and similarly about algebra. I have not learned analysis from a book and the algebra I know I learned from Gallian's Contemporary Abstract Algebra which I have read more or less cover to cover. I suggest that you get yourself the most "famous" introductory books about the topic from the library, test each by reading a chapter and then decide which to use. The things I like best about Gallian is that it's well-written, easy to read, comes with lots of exercises and on top of that solutions for the odd numbered ones.

Hope this helps.

Solution 2:

I have quite a few years experience in what you talking about. In my opinion (and my profs too) if you want study mathematics only way is to exercise.

Find some book (I like something similar to Shaum's series) with examples and solutions and do them every day a few.

I don't think there really is another way to study mathematics.