I think this soft question may be marked "opinion-based" or "off-topic", but I really do not know where else to get help. So please read my question before it's closed, I am really desperately in need of help... Thanks in advance for all people paying attention to this question!
I am a high school student who has participated in mathematical olympiads, where there are tons of tough combinatorics problems. I already know the basic counting techniques (binomial coefficients, inclusion-exclusion principle, etc.), some notions and theorems in graph theory (trees, Ramsey numbers, etc.), yet I do not know much beyond the definitions. Accordingly, I plan to (self-)studying this subject systematically. (I actually study for fun, not for better performance in olympiads.)
A few days ago I stumbled upon the book A Course in Combinatorics and started working through this book with dilligence. It was not long before I found the problems way too hard. I am just halfway in chapter 2, and there are three problems (out of a dozen or so) that I cannot solve even after I read the hints and literally thinking for hours. I am unsure about whether I should pursue reading this book but a more important question arises:
Why do I find the problems too hard? Is it that I lack the so-called "mathematical maturity" required for an undergraduate text like that, or that I am not gifted enough, or something else?
I am not sure whether I do have the slightest degree of mathematical maturity, but I have been reading mathematics texts for at least half a year. I have worked through the first seven chapters of baby Rudin (and solved all the exercises, which would look "easy" to me compared to the problems in that combinatorics book), and I am learning linear algebra from Hoffman & Kunze and abstract algebra from Herstein, and having fun reading the three volumes Analysis from Amann & Escher. Then there are other books like Folland's Real Analysis or Artin's Algebra, which I have read only several chapters. Of all the books in mathematics I have read about, the problems of this book are the hardest. However, no one has ever mentioned that the book has tough problems. (Maybe it is just me?)
By the way, I posted a problem that I literally thought for an entire afternoon here.
All in all, my question boils down to these:
- Is it normal to find it hard to solve the problems in that book?
- Can you possibly tell me why I am finding it hard? I will surely provide more details if necessary. (This question seems impossible to answer, so feel free to ignore it.)
- What should I do if I still want to study combinatorics? For example, what books are recommended for my situation? And, more importantly, how can I improve my skills in solving combinatorics problems?
Please tell me what else I should add to get better answers. Again, thank you for reading this!