PhysicsPdx wrote:It would be a miserable experience to wade through all of the underlying mathematics if all you want to do is apply it vs. really understanding the underpinnings. It comes down to your motivations.

I do not really like working with stuff if I do not have a good grasp of the foundations. When it comes to 'proof based, abstract math brain,' I really enjoyed the challenge posed by Real Analysis.

Summing it up, I do want to learn its application to HEP, but, at the same time I want to have a good grasp of its foundations as well.

Thanks, PhysicsPdx for helpful comments ( I have no exposure at all to Lie algebra and did not know that group, ring / fields form the foundation for Lie algebra). Hopefully, that'll change by the end of the semester