Assuming theorems/results in exams

[Ted123]

In general would you say it is OK to assume theorems/results etc. in exams without proof?

For example if I was asked to prove that the only central element of a lie algebra $\mathfrak{g}$ was the zero matrix and I had a theorem that said that the centre of $\mathfrak{g}$ is trivial if $\mathfrak{g}$ is simple, could I prove $\mathfrak{g}$ is simple and then just state that $\mathfrak{g}$ being simple $\Rightarrow$ centre of $\mathfrak{g}$ is 0 i.e. zero matrix is the only central element, or would I have to prove the theorem to get the credit?

 

[Hurkyl]

It really would depend. e.g. if you learned the theorem in class, it would almost certainly be okay, unless the problem explicitly stated otherwise.

If you got the theorem from a different source, though, it would depend on the intent of the exam question, and how different the problem's intent is from the actual work you would do to invoke the theorem, and even then it would depend to some extent on the professor's tastes.

And, of course, you have the option to do the problem both ways. In real life, of course, it is usually right to do that. Researching facts to apply to the problems you're trying to solve is an important mathematical skill!

 

[Ted123]

It really would depend. e.g. if you learned the theorem in class, it would almost certainly be okay, unless the problem explicitly stated otherwise.

If you got the theorem from a different source, though, it would depend on the intent of the exam question, and how different the problem's intent is from the actual work you would do to invoke the theorem, and even then it would depend to some extent on the professor's tastes.

And, of course, you have the option to do the problem both ways.


In real life, of course, it is usually right to do that. Researching facts to apply to the problems you're trying to solve is an important mathematical skill!

OK, thanks for that.

Thing is, I've come across a question with 2 parts. The first is to describe the derived lie algebra of so(3) explictly, the 3x3 antisymmetric matrices and the second part is to prove that the only central element of so(3) is the zero matrix and I could prove both parts using one theorem: by proving so(3) is simple implies the derived lie algebra of is just itself and also proves that the centre of so(3) is trivial!