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.

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    $\begingroup$ I don't think this is a place to ask for solution manuals, but you can ask for help with the problems. $\endgroup$
    – user10444
    Apr 11, 2014 at 21:47
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    $\begingroup$ You can try and look up a course that follows that book. They assign homework problems every week, and lot of the questions are similar to that given in the book. Lot of courses have also the solutions uploaded. For example- math.uiuc.edu/~ekerman/518-12.html. I haven't checked it properly though.. $\endgroup$ Apr 11, 2014 at 21:49
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    $\begingroup$ I just want to point out that the version of my book that you linked to is not "freely available." It's copyrighted material, as the copyright page clearly says, and I have not given anyone permission to post it online. It's particularly unfortunate that this version is still hanging around on the Internet, because it's a preliminary draft that's full of errors, and I would not recommend that anyone use it to try to learn differential geometry. $\endgroup$
    – Jack Lee
    Apr 12, 2014 at 4:18
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    $\begingroup$ @JackLee I am sorry to read this. I would not be committing a crime in public. The amount of the help I got from the first edition deserves its appreciation - I have bought the 2nd edition of your ebook now. $\endgroup$ Apr 12, 2014 at 11:25
  • $\begingroup$ @user10444 I included a reference request tag. I think that if the solutions are available then it is more efficient for the community if the asker tries to solve the problem with the solutions before asking someone else to reproduce them again. $\endgroup$ Apr 12, 2014 at 11:27

1 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!)

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    $\begingroup$ Hooray, Jack. I get the same pestering and I hope you stand firm. Sadly, we can't control the internet. $\endgroup$ Apr 22, 2014 at 23:56
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    $\begingroup$ This is one thing I love about the math.SE community: If you ask a question about some part of the book, you just might get a response from the author! :) $\endgroup$
    – apnorton
    Apr 23, 2014 at 0:19
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    $\begingroup$ I disagree with this sentiment entirely. Without an official solution, there's always reasonable doubt as to whether one has a correct solution or just thinks one does, especially while learning. Everyone makes errors. Even the most careful will end up reinforcing incorrect behaviors, and the reinforcement is less effective when there is doubt. Plus, not trusting students to use material effectively is incredibly condescending. I can (attempt to) optimize my own studying, and categorically assuming that access to solutions is a hindrance in all cases is presumptuous. $\endgroup$
    – user144527
    Jan 17, 2018 at 15:27
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    $\begingroup$ Furthermore, a student may have a solution, and it may be correct, but it may not be the best solution, and having access to another's solution can introduce a new technique or even a new way of thinking about the material. Without feedback, how is one supposed to learn best practices? How is one supposed to refine one's technique? Not everyone has professors to train them how to think like mathematicians, and even those who do don't have unrestricted access to their time. I agree, however, that theorems and examples are "problems with solutions," but that doesn't mean more wouldn't help. $\endgroup$
    – user144527
    Jan 17, 2018 at 15:49
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    $\begingroup$ @SeleneAuckland: Actually, I would say that it becomes even more true as the material becomes more advanced. If I'm seriously working through a book about an advanced topic that I don't yet understand, and I come across an exercise, I'll stop and try to do it. If I figure it out, I'll know that I've got it -- one of the things we learn as we get better at mathematics is how to know if we have a correct proof or not. If I don't figure it out, I'll go back and read the text more carefully, or check out other books, or ask my colleagues. "Answers" are not the point; understanding is. $\endgroup$
    – Jack Lee
    Mar 15, 2019 at 18:15

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