math (higher)...what is it good for? Absolutely nothing...huh! Say it again. Math!

[KrazyHorse]

like my analysis 2 course...

[TCO]

Originally posted by KrazyHorse
In physics, we use

Differential geometry
Topology
Group/algebra theory
Complex analysis

on a regular basis

what are they and what are they good for. Like calculus is good for finding min and max and it is just slope of curves and areas under.

[KrazyHorse]

differential geometry is used extensively in GR (diff geo on curved 4-space)

it can also be used to give geometric interpretations of field theories (wrt lagrangian densities etc)

topology is used in condensed matter to describe defects in ordered systems (superfluids, liquid crystals, etc)

group theory is used by mat sci people to describe crystallographic modes of excitation. Continuous groups/lie algebras are used to describe the gauge symmetries of particle physics theories

complex analysis is used all over the place in QFT to do sums and integrals which would be difficult or impossible otherwise

[KrazyHorse]

other than complex analysis, analysis is fairly useless in physics. people just assume that you're allowed to manipulate things in the intuitive way (doing many things that would make mathematicians tear their hair out)

[TCO]

Originally posted by KrazyHorse
differential geometry is used extensively in GR (diff geo on curved 4-space)

it can also be used to give geometric interpretations of field theories (wrt lagrangian densities etc)

topology is used in condensed matter to describe defects in ordered systems (superfluids, liquid crystals, etc)

group theory is used by mat sci people to describe crystallographic modes of excitation. Continuous groups/lie algebras are used to describe the gauge symmetries of particle physics theories

complex analysis is used all over the place in QFT to do sums and integrals which would be difficult or impossible otherwise

GR doesn't do much for me. The CM/Mat sci stuff sounds ok. Group theory and crystallography are very basic and central to many useful things. How about that topology crap. is it too?

[KrazyHorse]

sort of, yeah

[TCO]

what about tensors. What's their place in the zoo?

[KrazyHorse]

uh....everywhere

now used to describe everything. including classical EM...

[Drake Tungsten]

Edwin Starr

[civman2000]

Math is the purpose of life. Math is what makes us happy.

Only silly people who don't understand the wonderfulness of math care about whether it's "useful".

[TCO]

I'm used to them with things like mechanical properties and some electrical properties (NLO) stuff like that. But where do you learn them? Like where in the curriculum? Whole course? Or special topic in engineering math?

[TCO]

Originally posted by civman2000
Math is the purpose of life. Math is what makes us happy.

Only silly people who don't understand the wonderfulness of math care about whether it's "useful".

humor me.

[KrazyHorse]

you learn them because they're used everywhere. nobody actually taught me tensor analysis. that's something I get really annoyed about.

I picked them up through a combination of differential geometry, general relativity and graduate EM

[TCO]

yeah. I think it is a common gap. Is it a big enough subject to justify a course? Is it equivalent of matrices? differential calculus?

[TCO]

What was wrong with the Brittney Spears topic? Sure it was OT, but this is OT. And people were discussing the content. I think you're getting too quick to shut me down...