- #1

battousai

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Outside of pure mathematics, where is group theory used?

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- Thread starter battousai
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In summary, group theory is used extensively in Mathematical Physics, cryptography, musicology, and in symmetric artistic design elements.

- #1

battousai

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Outside of pure mathematics, where is group theory used?

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- #2

HallsofIvy

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Also group theory can be used to determine which polynomial equations can be solved in terms of radicals. (That was, in fact, the main reason for the development of group theory.) That is still mathematics but not what I would consider "pure" mathematics.

- #3

Karlx

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Group theory is extensively applied in Theoretical Physics:

General and Spacial Relativity

Elementary Particles

Quantum Physics

- #4

SteveL27

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http://www.google.com/search?sourceid=chrome&ie=UTF-8&q=rubik's+cube+group+theory

- #5

Deveno

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group theory is an important part of cryptography (the study of codes), and plays a prominent role in understanding such techniques as RSA encryption.

cyclic groups play a role in musicology, and form a mathematical basis for the 12-tone system.

group theory is important in algebraic topology, which finds application, among other things, in design of computer networks and communication systems.

finally, there is group theory in symmetric artistic design elements (the so-called "frieze groups" and "ornament groups") used in textiles, printing, wall-papers, tiling (especially in arabic mosques), and such common-place items as kaleidoscopes (reflections form a group).

in short, groups are everywhere! if you've ever "counted by 2's or 3's" you were using intuitively a natural group property of the integers. the shuffling of a deck of cards, rotating a sphere in space, even our way of using a circle to measure time, these are all groups at work in our everyday lives.

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battousai

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- #7

mathwonk

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group theory is the mathematics of symmetry, so just think about the places where symmetry occurs.

Group theory is a mathematical concept that studies symmetry and patterns within groups of objects. Its applications are diverse and can be found in fields such as physics, chemistry, cryptography, and computer science.

Group theory is used extensively in physics to understand the fundamental laws of nature. It helps in describing the symmetries of physical systems, such as the symmetries of molecules, crystals, and subatomic particles. It also plays a crucial role in the development of quantum mechanics and the study of symmetries in the universe.

In chemistry, group theory is used to understand the structure and properties of molecules and crystals. It helps in predicting the possible shapes and arrangements of atoms in a molecule based on its symmetries. This knowledge is crucial in understanding chemical reactions and designing new molecules with specific properties.

Group theory is used in cryptography to develop secure methods for communication. It helps in creating complex encryption algorithms and analyzing their strength against attacks. Group theory is also used in the design of secure digital signatures and authentication protocols.

In computer science, group theory is used in various applications such as coding theory, network security, and computer graphics. It also plays a significant role in data compression techniques and error-correcting codes. Additionally, group theory is used in the development of efficient algorithms for data processing and analysis.

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