I am junior in college major in math, studying Real analysis 4th edition, Royden.
At first, my professor just explains concepts and keeps going on without solving any problem in the book or else.
I respect my professor, she may have a mind for teaching, since she has devoted her life for studying and teaching analysis, and will be retired after 2 or 3 years.
I do really hard on studying real analysis these days, I think. Especially solving problems in the book. But it is really hard for me to solve them.
In fact, I studied really hard on understanding and proving proposition of measures or something, but aftet that, when I try to solve problems, then I can do nothing.
So I cannot help searching Google for solutions for problems. When I see them, I can understand how it works. But without solution, I am nothing. I can't do anything on solving problems.
For Modern Algebra, I feel more comfortable to solve problems. If I understand the concepts of it, then I can solve problems almost all of them in the book.
So, did or do you have a hard time for solving problems in analysis book? Or just I am not good at math? is it just only my problem?
I studied really hard these days, so I have sore eyes and stress out and chain smoke for today... because of analysis. REALLY Stressed out..
So I feel really stucked, I cannot help posting this....
What can I do? Studying with solution is okay?
I want to really be good at math....
Do you have discussion sections? If yes, make sure that TA does solve problems in class (not the homework problems but problems from the textbook) and ask him/her how did he/she came up with the solutions. If not, team up with some of your classmates and work on problems together. In your case, most likely, it is a matter of practicing a lot. Assuming you have a textbook (I assume you do) with a list of problems in the end of each section of the book, work on these problems yourself or with your classmates. The problems tend to be testing if you understand concepts and theorems from the section just covered (although they also tend to build up on the material of the previous sections). One more thing to remember "algebra is about equations, analysis is about inequalities". (OK, as all rules, this one is true only up to a point, but still...) In particular, make sure you are good with inequalities (being able to solve inequalities, knowing various "standard" inequalities like Cauchy–Schwarz inequality, Jensen inequality, etc). If you have hard time remembering the standard inequalities, make a list and look at it every day.