Asking questions about difficulty reading proofs.

Question

This is a question about advice specifically for reading proofs, not really about writing them. I have recently been reading Algebra by Hungerford (the standard graduate level 400 some page one) and a few times I have been finding myself getting stuck as long as hours trying to read one proof. Normally this happens towards the end of a section (some good examples: P. Hall theorem (II.7.14) and Krull-Schmidt Theorem (II.3.8) (somehow this has only happened in chapter 2 so far and I have read chapters 1,2,most of 10, part of 3, and half of 4 and other bits here and there; I am still stuck on II.3.8, but that is a matter for MSE itself). Whenever I am not stuck, it goes pretty fast (I have done a lot of algebra more advanced and tricky than most of this book), even a lot of the exercises so far just feel trivial.

I am asking if it is ok if simply post a proof in MSE itself (one that has not specifically been asked about in the same way before) and basically put circles around the inferences that I am stuck on and ask if someone can explain them to me? If I have spent an hour on a 2 page proof I hope it is not considered "lazy" but I just wanted to ask if there is maybe something else I should be doing (it doesn't happen extremely often to the extent of an hour or more, but either I am racing through the text no problem at all or I am just stuck in the mud completely, multiple times more so and more often than when I read the first $\frac{2}{3}$ of Altman Kleinman or any of Lang's Linear Algebra).

I think some of the theorems later in the section I might not ever use, but at the same time it really bothers me to just skip things due to not understanding them. If you're wondering, yes I try to spend a good amount of time writing out a 2-3 page proof of something that Hungerford just sort of states like it's obvious, but I don't always get it. Also I am a first year M.A. student, so this is to prepare for eventual research after qualifying exams (I am doing this alongside a first lower level M.A. course in algebra, and by the way I have more or less never gotten stuck reading the professor's notes, this problem is something unique to Hungerford).

Answer 1

No, simply posting a screenshot of something, circling bits, and saying "help" (to paraphrase your second paragraph) is not acceptable. It's pretty much the definition of a PSQ -- problem-statement question.

First off: by posting screenshots you're making the body of your post effectively unsearchable, which is detrimental to the site's goals, and you're preventing people using screen-readers or other aids for viewing the site from seeing your question. That's slightly discriminatory to them, and detrimental to you because you're lowering the pool of potential answerers. So please MathJax out the bits that are concerning to you.

Second: all the context that someone would need to help you is in this post, separate from where it would be needed! The reason we ask for context is so that you can provide information like "I've done a lot of algebra more advanced that this and can't understand why I'm stuck here". That tells answerers that there's a conceptual misunderstanding so just writing out a step-by-step proof is probably the wrong approach (bear in mind this won't stop this from happening, just increase your chances of getting the explanation you actually need).

Finally, the site aims to be a searchable repository of knowledge, so taking the time to phrase your questions the way other people might is worthwhile: other people with similar problems can then find your question easily and benefit from it.

There's a veiled concern in your post (I think; correct me if I'm wrong) that you're expected to write out a two-page proof up to the point where you're stuck. No, you're not, and people are unlikely to read it anyway. What you need to do is excerpt the part where you're getting stuck and provide enough information around it (definitions, assumptions, your reasoning at a high level). This is a useful skill, not just in mathematics but in all walks of life, and its worth getting the practice when you can.