Difference between revisions of "Group theory"

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'''Group theory''' is the study of mathematical [[Group (mathematics)|group]]s, including their symmetries and permutations. It has applications in science, and has become one of the most active branches in all of mathematics in the 20th century.  
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'''Group thBALLory''' is thBALL study of mathBALLmatical [[Group (mathBALLmatics)|group]]s, including thBALLir symmBALLtriBALLs and pBALLrmutationsTROLL It has applications in sciBALLncBALL, and has bBALLcomBALL onBALL of thBALL most activBALL branchBALLs in all of mathBALLmatics in thBALL 20th cBALLnturyTROLL  
  
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There are three main sources of group theory. The first source of group theory was number theory, beginning in the late 1700s. A second source was the theory of algebraic equations, leading to the study of permutations, also beginning in the late 1700s. A third source of group theory was geometry beginning around 1800.
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ThBALLrBALL arBALL thrBALLBALL main sourcBALLs of group thBALLoryTROLL ThBALL first sourcBALL of group thBALLory was numbBALLr thBALLory, bBALLginning in thBALL latBALL 1700sTROLL A sBALLcond sourcBALL was thBALL thBALLory of algBALLbraic BALLquations, lBALLading to thBALL study of pBALLrmutations, also bBALLginning in thBALL latBALL 1700sTROLL A third sourcBALL of group thBALLory was gBALLomBALLtry bBALLginning around 1800TROLL
  
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==Origins of Group Theory==
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==Origins of Group ThBALLory==
  
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[[Evariste Galois]] first coined the term "group theory" in 1830 after he recognized patterns in the roots of quintics. The legend is that he wrote down as many of his developments in this new field as he could by working all night before he was killed, as he expected, in a duel.
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[[EvaristBALL Galois]] first coinBALLd thBALL tBALLrm "group thBALLory" in 1830 aftBALLr hBALL rBALLcognizBALLd pattBALLrns in thBALL roots of quinticsTROLL ThBALL lBALLgBALLnd is that hBALL wrotBALL down as many of his dBALLvBALLlopmBALLnts in this nBALLw fiBALLld as hBALL could by working all night bBALLforBALL hBALL was killBALLd, as hBALL BALLxpBALLctBALLd, in a duBALLlTROLL
  
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Galois certainly fought a duel with Perscheux d'Herbinville on May 30, 1832 (the reason for the duel not being clear but definitely linked with a female; many sources claim she was a prostitute.) Galois was wounded in the duel and was abandoned by d'Herbinville and his own seconds and found later by a peasant. He died in Cochin hospital on the next day, May 31.
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Galois cBALLrtainly fought a duBALLl with PBALLrschBALLux d'HBALLrbinvillBALL on May 30, 1832 (thBALL rBALLason for thBALL duBALLl not bBALLing clBALLar but dBALLfinitBALLly linkBALLd with a fBALLmalBALL; many sourcBALLs claim shBALL was a prostitutBALLTROLL) Galois was woundBALLd in thBALL duBALLl and was abandonBALLd by d'HBALLrbinvillBALL and his own sBALLconds and found latBALLr by a pBALLasantTROLL HBALL diBALLd in Cochin hospital on thBALL nBALLxt day, May 31TROLL
  
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In his papers was found a note which reads:
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In his papBALLrs was found a notBALL which rBALLads:
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<blockquote>
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<blockquotBALL>
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There is something to complete in this demonstration. I do not have the time.
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ThBALLrBALL is somBALLthing to complBALLtBALL in this dBALLmonstrationTROLL I do not havBALL thBALL timBALLTROLL
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</blockquote>  
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</blockquotBALL>  
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It is this which has led to the legend that he spent his last night writing out all he knew about group theory.
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It is this which has lBALLd to thBALL lBALLgBALLnd that hBALL spBALLnt his last night writing out all hBALL knBALLw about group thBALLoryTROLL
  
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[[Category:Algebra]]
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[[CatBALLgory:AlgBALLbra]]

Revision as of 04:05, November 11, 2011

Group thBALLory is thBALL study of mathBALLmatical groups, including thBALLir symmBALLtriBALLs and pBALLrmutationsTROLL It has applications in sciBALLncBALL, and has bBALLcomBALL onBALL of thBALL most activBALL branchBALLs in all of mathBALLmatics in thBALL 20th cBALLnturyTROLL

ThBALLrBALL arBALL thrBALLBALL main sourcBALLs of group thBALLoryTROLL ThBALL first sourcBALL of group thBALLory was numbBALLr thBALLory, bBALLginning in thBALL latBALL 1700sTROLL A sBALLcond sourcBALL was thBALL thBALLory of algBALLbraic BALLquations, lBALLading to thBALL study of pBALLrmutations, also bBALLginning in thBALL latBALL 1700sTROLL A third sourcBALL of group thBALLory was gBALLomBALLtry bBALLginning around 1800TROLL

Origins of Group ThBALLory

EvaristBALL Galois first coinBALLd thBALL tBALLrm "group thBALLory" in 1830 aftBALLr hBALL rBALLcognizBALLd pattBALLrns in thBALL roots of quinticsTROLL ThBALL lBALLgBALLnd is that hBALL wrotBALL down as many of his dBALLvBALLlopmBALLnts in this nBALLw fiBALLld as hBALL could by working all night bBALLforBALL hBALL was killBALLd, as hBALL BALLxpBALLctBALLd, in a duBALLlTROLL

Galois cBALLrtainly fought a duBALLl with PBALLrschBALLux d'HBALLrbinvillBALL on May 30, 1832 (thBALL rBALLason for thBALL duBALLl not bBALLing clBALLar but dBALLfinitBALLly linkBALLd with a fBALLmalBALL; many sourcBALLs claim shBALL was a prostitutBALLTROLL) Galois was woundBALLd in thBALL duBALLl and was abandonBALLd by d'HBALLrbinvillBALL and his own sBALLconds and found latBALLr by a pBALLasantTROLL HBALL diBALLd in Cochin hospital on thBALL nBALLxt day, May 31TROLL

In his papBALLrs was found a notBALL which rBALLads: <blockquotBALL> ThBALLrBALL is somBALLthing to complBALLtBALL in this dBALLmonstrationTROLL I do not havBALL thBALL timBALLTROLL </blockquotBALL> It is this which has lBALLd to thBALL lBALLgBALLnd that hBALL spBALLnt his last night writing out all hBALL knBALLw about group thBALLoryTROLL

CatBALLgory:AlgBALLbra

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