Asking a question that might be too broad

Question

Being over half a year in this advanced maths course, time has come for the finals. As I was browsing through some of the tests from previous years, I' ve encountered several difficult questions. After not being able to succesfully gain a deeper understanding on them, I argued that posting them here might be helpful, however, the questions were mostly in several parts from a to e, and such a question on math.se is simply too long. Should I make smaller subdivisions and ask several questions or is it acceptable to put it in one big paragraph. Note that the questions, are of the homework type, but aren't trivial or can be simply googled. I wouldn't ask for solutions. I seek only to understand the problem.

Answer 1

In my opinion, it is difficult to give any general rule for this. (If you have scanned picture, link to a pdf or if you are willing to retype one typical example of such assignment, maybe some users can give you advice tailored to your specific situation. But I'd like to post an answer which addresses this issue in general.)

I think the answer strongly depends on the nature of the question and, perhaps more importantly, on the fact to which extent the subquestions are related to each other. As you said in your post, length of the question might be a factor, too.

Imagine the following question:

Decide which of the following facts is true:
(a) Every subspace of a vector space contains $\vec 0$.
(b) Union of two linear subspaces is again a subspace.
(c) If the vectors $\vec\alpha_1,\dots,\alpha_n$ belong to finite-dimensional space $V$ and $n\le \dim(V)$ then they are linearly independent.
...

It is clear, that these question were given to test how the students are familiar with some area, but the subquestions are not very closely related to each other. In this case, they should be definitely not posted as a single question.

But we might have a different type of question:

For any matrix $A$ we denote by $V_A$ the row subspace, i.e., the subspace generated by rows of the matrix $A$. By $\operatorname{rank}(A)$ we denote the rank of the matrix $A$ which is defined as $\operatorname{rank}(A)=\dim(V_A)$.
(a) Prove that for any two matrices $A\in M_{n \times k}$ and $B\in M_{k\times m}$ the rows of the matrix $AB$ are linear combinations of rows of the matrix $B$.
(b) Show that $V_{AB}\subseteq V_B$.
(c) Using the above show that $\operatorname{rank}(AB)\le \operatorname{rank}(B)$.
(d) Can you also show that $\operatorname{rank}(AB)\le \operatorname{rank}(A)$?

In this case the question in the test is clearly formulated in the way that you are expected to use the preceding parts. In my opinion in such cases it would be reasonable to include the whole question.

Even in the cases if you don't ask for solutions of all parts, it is good to include the whole question.

For example, if you want to ask only about (c) and (d), it is good to see also (a) and (b), so that we know what solution your instructor is expecting. (This will not prevent people from posting alternative solutions.) However, it is advisable that it is clearly stated that you are asking only about one part of the exercise.

Or your question might be: "I have managed to prove (c) in a completely different way, the assignment asks me to prove it using (b). How can this be done?" In such case it is very natural that all preceding parts should be included.

One last comment to this second example: Typically the definitions would not be included in the test question. (As the students doing the exam are supposed to know them.) But when posting here, you should also include the definitions, at least in the cases where you suspect that they might be not standard on well-known.

Answer 2

I suggest you ask in the smallest possible scope and link your questions if someone is interested in follow-ups. This way any member can decide exactly wich part from a to e he wants to answer without making it a "partial" answer.
As for the tone, unless you include some of your own thoughts / progress on the problem, the community tends to quickly close homework-type questions, but that doesn't stop you from asking them. You should definitely watch the actual community feedback on the questions and react accordingly. Given that you put time and effort into even asking if such questions are allowed, I trust that you can formulate your questions in a way that will generate a positive response from the community, so just go ahead, maybe linking to this meta question for some context (why you are asking those questions).

Answer 3

I'd avoid posting all of an a through e question. It's definitely not a good idea to post such a question as a single question, since that would be requiring a lot of effort from answerers and would likely diminish the quality of answer your receive. However, I would also advise against posting the question separately, since this site is best at providing help with more abstract ideas rather than specific answers.

The best way to proceed would be to try and figure out what's making these problems difficult for you and what you need to overcome that. Perhaps its the case that if your knew the answer to part a, you could proceed to the rest - in which case, post a good question addressing your difficulty on that part. Or, perhaps it's a more general issue of not understanding what techniques might apply to all of the problems - in which case, you should ask about that, and perhaps choose some particular instance of a problem. Whatever it is, you ought to do something to guide answerers to where they can help you grasp a concept rather than just provide an answer.

As long as each question is good, feel free to ask as many as you need. It's perfectly acceptable to ask follow-up questions (as new questions, not as comments) if you find that you have new difficulties after overcoming the old ones - and, as @AlexR suggests, linking such questions together is wise in such a case.