I'm not asking about Linear Algebra that's doubtless vital to Finance. I deliberately haven't stipulated the kind of Quant job, as I'm asking in general. This post lists examples of Abstract Algebra. But ought you learn it on your own? Or ought you study them in university? I see mixed messages. bigbadwolf counsels
Abstract algebra and complex analysis are probably redundant but still useful for developing that elusive "mathematical maturity." The problem with the applied courses is that though they may be more "relevant," you're always at risk of having no real theoretical understanding and merely having mastered a cookbook of techniques with no conceptual focus. So ideally you want your numerical analysis and applied linear algebra to have a theoretical backbone, something that gives intellectual coherence to the subject matter.
Completely agree with bbw. Learn something that will force you to think in a different way about maths. Abstract algebra and analysis will do that. Complex analysis did that for me, too, so I'd recommend that too. If you want to be a quant you can certainly do too much pure maths, though. Once you've learnt how to think like a pure mathematician there is little utility in taking lots of pure maths options. Advanced courses in pure maths tend to be rote learning and regurgitation of proofs rather than concepts, so avoid that.
Yet bigbadwolf discourages it:
Abstract algebra is also great fun. But also, alas, of little or no applicability to finance.
Abstract algebra and complex analysis are probably redundant but still useful for developing that elusive "mathematical maturity."