# real life applications of group theory

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hey frnds...plzz help me in finding applications of group theory used in real life.....plzz help me....

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In mathematics applications of group theory are endless.

In physics the relation of groups with symmetries means that group theory plays a huge role in the formulation of physics. Fundamental in modern physics is the representation theory of Lie groups. Lie groups like the Poincare group, SU(n), O(n) etc all play fundamental roles in physics.

In chemistry group theory is used to describe symmetries of crystal and molecular structures. This is then important in understanding the physical and spectroscopic properties of materials, for example. Probably, group theory is the most powerful branch of mathematics when it comes to quantum chemistry, spectroscopy and condensed matter physics.

Edited by ajb

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thank u so much yr..

bt i want sumthing like where group theory is used in daily life...in our daily routine...

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Integers with the standard addition form an abelian group.

Real numbers form an abelian group under addition and non-zero real numbers form an abelian group under standard multiplication. (We have a commutative ring, in fact we have a field.)

These are the only thing that springs to mind in "everyday life". For example, the fact that the real numbers form an abelian group under addition is used when working out change when you buy something. That said, it maybe a bit of an overkill.

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Group actions can be performed on decks or hands of cards - so that could be considered an application of group theory, even though you wouldn't really think of it like that.

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I know of an application of group theory to music theory.

The chromatic scale of Western music consists of 12 notes: C, C#, D, D#, E, F, F#, G. G#. A, A#, B. An interval is the distance from one note to the another – e.g. C–C# is an interval of a semitone, C–D is a whole-tone interval, C–D# is an interval of a minor third, etc. Note that the starting note can be any note, so F–F# is also a semitone interval. The unison interval is the interval from one to itself (e.g. C–C). All intervals that are whole octaves can be identified with the unison interval.

Intervals can be “added”, the result being the number of semitones (modulo 12) from the first note the last (e.g. the sum of C–D and C–F (which is the same as D–G) is the interval C–G). It follows that the set of all intervals under this addition operation forms a group, the cyclic group of order 12. The identity element is the unision interval, and the group is generated by four intervals: semitone ( C–C# ), perfect fourth ( C–F ), perfect fifth ( C–G ), and major seventh ( C–B ).

This cyclic group of order 12 is the basis on the theory of the circle of fifths. It also explains why there are only two whole-tone scales – namely, because the subgroup generated by the whole-tone interval (C–D) is a subgroup of order 6 and so has index 2.

Edited by shyvera

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you can consider Election Methods applied on a Group that gives back an Integer Set which outputs an Elected member,

the Integer Set S = { S1, S2, S3, .., Sn } where Si = [1,n] represent election choices for n members of a Group ...

and then a Frequency Test can be one way for Election, where Elected Member has Max Frequency in S,

given example: group of 10 members made an election, S = { 3, 10, 6, 2, 2, 3, 7, 3, 1, 5 }, Elected = 3

Election is one important example in daily-life from Mathematics of Statistics ...

Edited by khaled

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Not quite sure it's real life...

http://www.geometer.org/rubik/group.pdf

But it's certainly real...

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In chemistry group theory is used to describe symmetries of crystal and molecular structures. This is then important in understanding the physical and spectroscopic properties of materials, for example. Probably, group theory is the most powerful branch of mathematics when it comes to quantum chemistry, spectroscopy and condensed matter physics.

Very true. I use the symmetry operations on a daily basis in analyzing UV spectroscopy [looking for specific electronic transitions]. The concepts were difficult to get a handle on at first, but well worth it. Maybe one day DFT will advance to the level to were I don't have to consciously remember symmetry operations and point groups. That would be nice.

I hope computer scientists don't engineer me out of a job though!

EDIT:double post deleted

Edited by mississippichem

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Very true. I use the symmetry operations on a daily basis in analyzing UV spectroscopy [looking for specific electronic transitions]. The concepts were difficult to get a handle on at first, but well worth it. Maybe one day DFT will advance to the level to were I don't have to consciously remember symmetry operations and point groups. That would be nice.

I hope computer scientists don't engineer me out of a job though!

EDIT:double post deleted

It's funny, because I avoid symmetry operations on a daily basis.

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hey frnds...plzz help me in finding applications of group theory used in real life.....plzz help me....

All the above are true. But for an everyday mundane application, balancing your ckeckbook uses only the abelian group operations of the integers.

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plzzz help me in finding application of group theory in the field of computer science

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Just a quick thought about the importance of group theory in spectroscopy.

The

groups concerned are the symmetries of the molecules and they "predict" the transitions between energy states that are permitted.

According to the maths, hydrated copper sulphate isn't blue; Cobalt chloride is white and certainly doesn't change colour from blue to pink in response to humidity changes; and rubies are colourless.

It's fair to say there's more to it than group theory.

Edited by John Cuthber

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Just a quick thought about the importance of group theory in spectroscopy.

The

groups concerned are the symmetries of the molecules and they "predict" the transitions between energy states that are permitted.

According to the maths, hydrated copper sulphate isn't blue; Cobalt chloride is white and certainly doesn't change colour from blue to pink in response to humidity changes; and rubies are colourless.

It's fair to say there's more to it than group theory.

Definitely. Another good example are permanganates, which are purple due to a ligand to metal charge transfer band (or maybe metal to ligand...), a phenomenon not understandable by group theory operations.

The group theory is invaluable to those chemists interested in excited states and how they arise in electrochemistry.

Edited by mississippichem