Lee, Introduction to Smooth Manifolds Solutions

Question

Does anybody know where I could find the solutions to the exercises from the book Lee, Introduction to Smooth Manifolds?

I searched on the Internet and found only selected solutions but not all of them and not from the author.

Answer 1

Here's what I wrote in the preface to the second edition of Introduction to Smooth Manifolds:

I have deliberately not provided written solutions to any of the problems, either in the back of the book or on the Internet. In my experience, if written solutions to problems are available, even the most conscientious students find it very hard to resist the temptation to look at the solutions as soon as they get stuck. But it is exactly at that stage of being stuck that students learn most effectively, by struggling to get unstuck and eventually finding a path through the thicket. Reading someone else’s solution too early can give one a comforting, but ultimately misleading, sense of understanding. If you really feel you have run out of ideas, talk with an instructor, a fellow student, or one of the online mathematical discussion communities such as math.stackexchange.com. Even if someone else gives you a suggestion that turns out to be the key to getting unstuck, you will still learn much more from absorbing the suggestion and working out the details on your own than you would from reading someone else’s polished proof.

So if you have questions about specific problems, by all means ask them here. But posting a complete list of solutions will not be doing anyone a favor. Many instructors assign those problems as homework, and if complete solution sets become readily available, it makes the problems (and therefore the book) far less useful.

It's interesting to note that when I've written chapters with everything proved and few or no problems at the end, readers invariably ask me to provide some problems for them to work on. If you want problems with solutions already written down, they're already there -- the theorems and examples in the book! Just look at the statement of a theorem or the claims made in an example, close the book and try to prove the theorem on your own, and then go back and compare your work to the proof in the book. (And if you find a better proof that the one I wrote, please let me know about it!)