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**Ultima Black Gate****Member**- Registered: 2006-09-18
- Posts: 14

Maybe this post is a bit vague, but i want to know as much as I can about general real world use for advanced math subjects like abstract algebra, category theory, number theory, optimization, topology, funcional analysis, game theory any math-subject you may want to post.

Regarding purely theorical (no real world use) math... does such a thing exist?

im a newbie with advanced math, but im getting more and more interested.

Any replies will be appreciated.

*Post moved to Euler Avenue - Ricky*

*Last edited by Ultima Black Gate (2006-09-28 12:51:24)*

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Number theory has strong roots with cryptography as well as many other uses for integer computation. Computer scientists take advantages of shortcuts provided by number theory when having to preform calculations. I can't think of any off hand which are simple enough to explain.

Abstract algebra can be applied to advanced physics such as general relativity and the standard particles of physics. It also has a great deal of uses in string theory, although we are still waiting to hear whether string theory is a good model of our universe.

Functional analysis I believe is used in the encoding of sound waves for computers, although I am unsure of this.

Game theory of course has just about everything to do with computer science and AI.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**polylog****Member**- Registered: 2006-09-28
- Posts: 162

Number theory in cryptography is a great example. The security of online banking for example would not be possible without the RSA encryption algorithm which is based on number theory!

Image processing in software like Photoshop, for example compression and various image effects, require advanced topics like Fourier analysis and Wavelet analysis (a very complicated topic).

For example the new JPEG 2000 format for internet images is based on Wavelets. Here is some info:

http://en.wikipedia.org/wiki/Wavelet

http://en.wikipedia.org/wiki/JPEG_2000

Fractals are another advanced math topic with lots of applications. Here is a nice list of these:

http://library.thinkquest.org/26242/full/ap/ap.html

And of course a great deal of advanced mathematics is used in engineering, for example Partial Differential Equations, Tensor Calculus (e.g. in fluid dynamics), and some Complex Analysis (in circuit analysis).

As for purely theoretical math.. well I have so far never seen any applications of Group Theory for example. But it probably does...

I was going to add Knot Theory, but it seems even that has applications! (see http://en.wikipedia.org/wiki/Knot_theory)

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I was going to add Knot Theory, but it seems even that has applications! (see http://en.wikipedia.org/wiki/Knot_theory)

Does knot!

But as for Group theory, I believe it has applications in General Relativity, although that is just by reading it somewhere. And being very technical, group theory is involved in Galois theory which is extremely important when talking about the roots of polynomials of degree 5 or greater. But again, that would probably go under Galois theory rather than Group theory. Kind of hard to draw the line though.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Different areas of math simply put names to thought processes.

Now we can talk about things and communicate.

All studies of math or non-math subjects will help you in everyday life because we can draw from previous experiences we've had and jump to new conclusions or see similarities.

Hence, there is no waste of time.

**igloo** **myrtilles** **fourmis**

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**polylog****Member**- Registered: 2006-09-28
- Posts: 162

Ricky wrote:

I was going to add Knot Theory, but it seems even that has applications! (see http://en.wikipedia.org/wiki/Knot_theory)

Does knot!

hah.

Ricky wrote:

But as for Group theory, I believe it has applications in General Relativity, although that is just by reading it somewhere. And being very technical, group theory is involved in Galois theory which is extremely important when talking about the roots of polynomials of degree 5 or greater. But again, that would probably go under Galois theory rather than Group theory. Kind of hard to draw the line though.

Thanks, I'll need to read up on those topics!

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**All_Is_Number****Member**- Registered: 2006-07-10
- Posts: 258

Ricky wrote:

Game theory of course has just about everything to do with computer science and AI.

And Economics, though many economists would (or do) deny the fact.

*You can shear a sheep many times but skin him only once.*

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

Why? Involving imperfect competition, Game theory perhaps is the only way out.

**X'(y-Xβ)=0**

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