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Applications of “finite mathematics” to physics

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1

$begingroup$

Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias.

When I think of applications of maths outside of itself, I have the impression that applications in physics are mostly related to "continuous/smooth mathematics" : representation theory of Lie groups, PDEs, functional analysis, different kinds of differential geometry (I don't know if they technically fit into that, but I include, say, symplectic geometry and riemannian geometry in that word), probability theory, and a bunch of other stuff, but all somehow related to $mathbb{R,C}$ and the differential or topological or measurable structure on these (or related structures);

while "discrete/finite mathematics" (here I'm almost sure I'm not using the right terminology - what I mean by that is stuff like finite group theory, representation theory of abstract groups, ring theory, linear algebra over finite fields, algebraic geometry, combinatorics, finite probabilities, number theory, graph theory and again a bunch of stuff that somehow fits the intuitive meaning one could put behind "finite" or "discrete" mathematics) seems to have applications mainly in computer science and related fields.

Now this view is probably very biased, and that's because I don't know that many applications of maths/much applied maths. The point of this question is to, if possible, get rid of some of that bias. Since asking "what are applications of mathematics ?" would be way too broad, I'll ask something more specific and more related to my personal interests.

What, if any, are some applications of "finite/discrete mathematics" to physics ? More specifically of "finite/discrete" algebra ?

(Note that here I use words "finite/discrete mathematics" in the sense that I tried to describe vaguely above, not in the common sense, if it is different)

discrete-mathematics soft-question physics applications

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asked Mar 4 at 16:51

MaxMax

15k11143

$endgroup$

This question has an open bounty worth +50
reputation from Max ending in 6 days.

This question has not received enough attention.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For general case_ en.wikipedia.org/wiki/Group_field_theory For a concrete case_ math.columbia.edu/~woit/QM/qmbook.pdf
  $endgroup$
  – Vinyl_cape_jawa
  Mar 4 at 16:57
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Vinyl_coat_jawa : both of these are very interesting, but they deal with Lie groups
  $endgroup$
  – Max
  Mar 4 at 17:06
  

  
  
  
  


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  $begingroup$
  Possibly an interesting read: arxiv.org/abs/1302.4378
  $endgroup$
  – Minus One-Twelfth
  15 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias.

When I think of applications of maths outside of itself, I have the impression that applications in physics are mostly related to "continuous/smooth mathematics" : representation theory of Lie groups, PDEs, functional analysis, different kinds of differential geometry (I don't know if they technically fit into that, but I include, say, symplectic geometry and riemannian geometry in that word), probability theory, and a bunch of other stuff, but all somehow related to $mathbb{R,C}$ and the differential or topological or measurable structure on these (or related structures);

while "discrete/finite mathematics" (here I'm almost sure I'm not using the right terminology - what I mean by that is stuff like finite group theory, representation theory of abstract groups, ring theory, linear algebra over finite fields, algebraic geometry, combinatorics, finite probabilities, number theory, graph theory and again a bunch of stuff that somehow fits the intuitive meaning one could put behind "finite" or "discrete" mathematics) seems to have applications mainly in computer science and related fields.

Now this view is probably very biased, and that's because I don't know that many applications of maths/much applied maths. The point of this question is to, if possible, get rid of some of that bias. Since asking "what are applications of mathematics ?" would be way too broad, I'll ask something more specific and more related to my personal interests.

What, if any, are some applications of "finite/discrete mathematics" to physics ? More specifically of "finite/discrete" algebra ?

(Note that here I use words "finite/discrete mathematics" in the sense that I tried to describe vaguely above, not in the common sense, if it is different)

discrete-mathematics soft-question physics applications

share|cite|improve this question

asked Mar 4 at 16:51

MaxMax

15k11143

$endgroup$

This question has an open bounty worth +50
reputation from Max ending in 6 days.

This question has not received enough attention.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For general case_ en.wikipedia.org/wiki/Group_field_theory For a concrete case_ math.columbia.edu/~woit/QM/qmbook.pdf
  $endgroup$
  – Vinyl_cape_jawa
  Mar 4 at 16:57
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Vinyl_coat_jawa : both of these are very interesting, but they deal with Lie groups
  $endgroup$
  – Max
  Mar 4 at 17:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Possibly an interesting read: arxiv.org/abs/1302.4378
  $endgroup$
  – Minus One-Twelfth
  15 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias.

When I think of applications of maths outside of itself, I have the impression that applications in physics are mostly related to "continuous/smooth mathematics" : representation theory of Lie groups, PDEs, functional analysis, different kinds of differential geometry (I don't know if they technically fit into that, but I include, say, symplectic geometry and riemannian geometry in that word), probability theory, and a bunch of other stuff, but all somehow related to $mathbb{R,C}$ and the differential or topological or measurable structure on these (or related structures);

while "discrete/finite mathematics" (here I'm almost sure I'm not using the right terminology - what I mean by that is stuff like finite group theory, representation theory of abstract groups, ring theory, linear algebra over finite fields, algebraic geometry, combinatorics, finite probabilities, number theory, graph theory and again a bunch of stuff that somehow fits the intuitive meaning one could put behind "finite" or "discrete" mathematics) seems to have applications mainly in computer science and related fields.

Now this view is probably very biased, and that's because I don't know that many applications of maths/much applied maths. The point of this question is to, if possible, get rid of some of that bias. Since asking "what are applications of mathematics ?" would be way too broad, I'll ask something more specific and more related to my personal interests.

What, if any, are some applications of "finite/discrete mathematics" to physics ? More specifically of "finite/discrete" algebra ?

(Note that here I use words "finite/discrete mathematics" in the sense that I tried to describe vaguely above, not in the common sense, if it is different)

discrete-mathematics soft-question physics applications

share|cite|improve this question

asked Mar 4 at 16:51

MaxMax

15k11143

$endgroup$

share|cite|improve this question

asked Mar 4 at 16:51

MaxMax

15k11143

share|cite|improve this question

asked Mar 4 at 16:51

MaxMax

15k11143

asked Mar 4 at 16:51

MaxMax

15k11143

asked Mar 4 at 16:51

MaxMax

15k11143