Talk:Group theory/Brainstorming: Difference between revisions

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imported>Jared Grubb
(create the table)
 
imported>Jared Grubb
(some content)
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{|
{|
|-
|-
! colspan=3 | Topics to discuss on [[Group theory]]
! colspan=2 | Topics to discuss on [[Group theory]]
|-
|-
| ''Beginning topics''
| ''Basic topics (assume no prior knowledge)''<br>
| ''Intermediate topics''
(These should be written simply, undergrad/lay audience)
| ''Advanced topics (important, but not for the layman)''
(These can assume more rigorous background)
|-
| valign=top width="50%" | <!-- BEGINNING GROUP THEORY -->
* Definition
** Normal
** Abelian
** Cyclic
** Solvable
* Examples
** Z, R
** Dihedral groups
** General linear groups
* Applications
** Quintic polynomial
** Music theory
** Quantum physics
 
| valign=top width="50%" | <!-- ADVANCED GROUP THEORY -->
* Generalizations (monoids, etc)
* Definitions
** Free groups
** Lie groups
* Examples
** ??
* Presentation
* Operations on groups
** Homo/Isomorphisms
** Automorphisms
*** Aut() group
*** Inner automorphisms
** Group actions
 
|-
! colspan=2 | Topics to disucss on [[Group (mathematics)]]
|-
| ''Basic topics''
| ''Advanced topics''
| ''Advanced topics''
|-
|-
| <!-- BEGINNING GROUP THEORY -->
| <!-- BEGINNING GROUP -->




| <!-- INTERMEDIATE GROUP THEORY -->


| <!-- ADVANCED GROUP -->


| <!-- ADVANCED GROUP THEORY -->




|-
|-
! colspan=3 | Topics to disucss on [[Group (mathematics)]]
! colspan=2 | Topics to discuss elsewhere
|-
|-
| ''Beginning topics''
| ''Basic topics''
| ''Intermediate topics''
| ''Advanced topics''
| ''Advanced topics''
|-
|-
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| <!-- INTERMEDIATE GROUP -->
 
| <!-- ADVANCED GROUP -->




| <!-- ADVANCED GROUP -->


|}
|}

Revision as of 09:54, 4 May 2007

Topics to discuss on Group theory
Basic topics (assume no prior knowledge)

(These should be written simply, undergrad/lay audience)

Advanced topics (important, but not for the layman)

(These can assume more rigorous background)

  • Definition
    • Normal
    • Abelian
    • Cyclic
    • Solvable
  • Examples
    • Z, R
    • Dihedral groups
    • General linear groups
  • Applications
    • Quintic polynomial
    • Music theory
    • Quantum physics
  • Generalizations (monoids, etc)
  • Definitions
    • Free groups
    • Lie groups
  • Examples
    • ??
  • Presentation
  • Operations on groups
    • Homo/Isomorphisms
    • Automorphisms
      • Aut() group
      • Inner automorphisms
    • Group actions
Topics to disucss on Group (mathematics)
Basic topics Advanced topics



Topics to discuss elsewhere
Basic topics Advanced topics



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