- #1

Ulagatin

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Perhaps this should go in the career guidance section, but I had a question directly related to differential geometry. I'm in Year 10 in Australia, and I'm very, very passionate about theoretical physics (perhaps mathematical physics too). String theory interests me, and I'm aware of such things as Calabi-Yau manifolds, but I wanted to ask about the subject of differential geometry itself.

What is the subject like? How enjoyable is it and how does it compare to all other areas of mathematics that people have studied (whether it be pure or applied)? It looks interesting from what I've seen, but I have only heard about it from a physics point of view.

Just to give everyone a background, I do a top-course year 10 mathematics course, which I am doing very well in, and I also do Mathematics Methods 4B (this is a 100-hour, pure maths course one step down from pre-tertiary level pure mathematics), however I didn't do so well with cubics (made up lost ground with exponential functions and logs though, no test on those yet, however...).

Also for note, my least favourite aspect of mathematics is statistics, and my absolute favourite would have to be geometry (I've done quite well here too, with marks like B+'s etc).

So, what is diff. geometry like as a subject (perhaps, even if I don't understand it, an example problem might be useful just to showcase it)?

I am guessing the required subjects to study diff. geometry would be topics like multivariable calculus, partial diff. equations (?) and some abstract and linear algebra?

Is the path leading to diff. geometry more fun that diff. geometry itself? And how fun is it as a subject? I'm really deeply curious about many physics concepts relating to the universe (like particle physics, string theory and the like), and so, is this the mathematics underlying many of these models (if it's just string theory, that is fine too)?

What about algebraic geometry? How does this compare? Is this fun, or perhaps more fun that diff. geometry?

I know one of the above is more useful for relativity and one for string theory, but I can never really remember which...!

Cheers

-Davin