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josh_s_outline [2013/08/09 05:41]
joshuawiscons 		josh_s_outline [2013/08/21 10:17] (current)
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 ====== Josh's outline ====== ====== Josh's outline ======
  
-==== Introduction ====+===== Introduction =====
 The goal is to produce a set of IBL notes that works from the definition of a [[Definition:Group|group]] to [[Theorem:Sylow's Theorem]]. The primary point of view will be that of [[Definition:Permutation Group|permutation groups]] with the abstract definition of a [[Definition:Group|group]] being preceded by exploring concrete examples of [[Definition:Automorphism Group|automorphism groups]]. The goal is to produce a set of IBL notes that works from the definition of a [[Definition:Group|group]] to [[Theorem:Sylow's Theorem]]. The primary point of view will be that of [[Definition:Permutation Group|permutation groups]] with the abstract definition of a [[Definition:Group|group]] being preceded by exploring concrete examples of [[Definition:Automorphism Group|automorphism groups]].
  
 ---- ----
  
-==== Prerequisites ====+===== Prerequisites =====
   * Linear algebra   * Linear algebra
 +
  
 ---- ----
  
-==== The outline ====+===== The outline =====
  
-=== First definitions and examples ===+==== First definitions and examples ====
  
-  * [[problem:Aut-square|Problem: automorphisms of a square]]+{{page>problem:Simple Matrix Encryption#problem&link&noeditbutton&nofooter&inline}}
  
-----+{{page>definition:Symmetric group#definition&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>problem:Diagramatic representation of Sn#problem&link&noeditbutton&nofooter&inline}}  
 + 
 +{{page>definition:Automorphism of a graph#definition&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>problem:Aut-square#problem&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>definition:Group#definition&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>problem:Explicit examples of abstract groups#problem&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>definition:Order (for groups)#definition&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>definition:Abelian group#definition&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>definition:Subgroup#definition&link&noeditbutton&nofooter&inline}} 
 + 
 +{{page>problem:Examples of abstract groups#problem&link&noeditbutton&nofooter&inline}}
  
 +{{page>theorem:Intersection of subgroups is a subgroup#theorem&link&noeditbutton&nofooter&inline}}
josh_s_outline.1376041264.txt.gz · Last modified: 2013/08/09 05:41 by joshuawiscons

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