Any Math wizards here?

Long story short, I decided to go to get more education (grad school) as a physicist. However, my focus is quantum gravity (always fun stuff when the adjective quantum is being used ;)) and I need to learn qualitative mathematics.

So my problem is I need to learn qualitative math but I don't have a clue where to begin! I have been told "Topos theory" and "Category theory" are a "good start", but frankly I would like to verify this with a math wizard...someone with experience or knowledge of these things.

Any help would be greatly appreciated!

Goto a local university, ask the professor of quantum mechanics.

Hi

Good knowledge of differential geometry[1], differential topology[1] and
functional analysis[2] is mandatory if you want to understand anything
involving the word quantum :)

These mathematical fundamentals will allow you to understand quantum
states and quantum operators - whether they are well-defined, not well-defined - and which are hoped to be well-defined ...

These fundamentals will also allow you to understand curvatures of spaces,
which are extremely important for general relativity (e.g. Ricci tensors).

They will also help you to understand statistical mechanics - a topic
extremely important to understand mechanism in the evolution of the
universe (expansion, cooling down, phase transitions, ...).

Good luck!
Cheers.

[1] http://en.wikipedia.org/wiki/Differe...y_and_topology
[2] http://en.wikipedia.org/wiki/Functional_analysis

Hey will u first explain me this "quantum". Wats this all about? I got my first college course on the topic earlier this year, but frankly speaking I got none of it into my head. So plzzz tell me wat fascinates u,Arkimedes? btw gud name! lol

Well, first of all, I'm sorry I haven't replied since I started this thread. I am at school, and I've been swamped with work.

Thanks sec_ware, but I am interested in foundational problems of quantum mechanics (basically answering the question "Why is quantum mechanics so ****ed up?"). I've been reading Relational quantum mechanics by Carlo Rovelli, Geometry of Quantum Mechanics by J.M. Isidro, and a few other papers directed towards answering this question.

I've been consulting the local quantum gravity guru on his opinion, and I think I've been pointed to an interesting direction. Take topos (categorical logic a sort of insanely obscure modal logic) and apply it to relational quantum mechanics.