I am not a big fan of preparing homework solutions. I have written a "problem book" --- the world-famous Cauchy-Schwarz Master Class, and from that experience I know that writing the solution to a problem is no easier than writing any other part of a book. In some ways, writing a good solution may even be harder than writing the linear text, just as poetry is typically harder to write than prose.
So, writing good solutions is hard, but that is not the only reason not to give out solutions. Other reasons are perhaps more important:
In general I am happy to comment on a HW question via e-mail (if there is not a deluge!), but there are two versions of requests were I can't be of much help.
In office hours I can sometimes get talked into a "find the mistake" exercise, but you'll usually see me growl and grimace. I do know that sometimes a person can get "hooked" and really wants to know if a certain idea can work. On the other hand, it is really best not to get "hooked." If an idea gets too confusing or too messy, be lazy --- look for an easier argument. That's what the "Pro's" do.
In my experience, if you think your solution may be wrong, it is probably even worse than you think. It is good to have doubts about solutions. By resolving those doubts for yourself, you greatly deepen your understanding. This is the much of mathematical discovery proceeds.
Also, if you are tempted to cite some theorem that we have not developed in class, then even if you happen to be "right" you haven't really landed on the place you really should want to land. What we do here is pretty pretty basic --- but the goal is mastery of the basic material we do cover.
Examples of comments that I love? "On Problem 15, don't we have to assume that X has a finite variance?" Quite often, you are right and I left out a hypothesis. Other times, I can explain, "No, the charm of this problem is that we can overcome the objection that there is no finite variance."
It is also fine to say, "I have worked on this for two hours, are you sure it is right? Can you give me a hint?" if this appeal does not come too often, I am usually happy to oblige.
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