| HN Mirror

Being unable to solve some tough problems is entirely normal - there is only a handful of people gifted enough to go though a mathematics curriculum, getting 100% on all their assignments, working in isolation. I certainly didn't! Having been a TA in upper-level math courses, many/most of the students averaged 80% on homeworks which were certainly NOT made up of entirely tough problems - and they probably worked together quite a bit, and had teachers to ask for help if they want. So don't get frustrated if you get stuck regularly, just move on, then come back later in a couple of weeks when you're reviewing and try again. If you're still stuck, go to an online forum to ask for a hint, or you don't have to feel guilty about skipping some of the hardest problems entirely.

Two book suggestions:

Strichartz - The way of analysis. MUCH more user friendly than the standard analysis texts. The book is filled with long paragraphs if english sentences explaining what your are doing, and why you are doing it (if you can imagine a mathematics book committing that sin!).

Pressley - Elementary Differential Geometry. The appeal of this book is that it teaches only the more concrete classical formulation of the theory, so you don't have to confront tensors and n-dimensional abstractions at first, and also that it provides outlined solutions to every problem in the text!