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user:tarafife:tara_s_outline [2014/01/01 08:44]
tarafife 		user:tarafife:tara_s_outline [2014/01/01 09:30] (current)
tarafife
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 {{pabe>Problem:Show that $Q\[\alpha\]$ is a Field}} {{pabe>Problem:Show that $Q\[\alpha\]$ is a Field}}
  
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 +[[Problem:Binomial Theorem]]
 +{{pabe>Problem:Binomial Theorem}}
  
 =====Introduction to Galois Theory===== =====Introduction to Galois Theory=====
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 We've seen in Group Theory how we can add, subtract, multiply, and sometimes divide things that aren't numbers. In other words Group Theory has let to us being able to add apples and oranges. Category Theory goes one step further, and lets us get an apple from an orange tree. Or in other words, Category Theory lets us get groups from rings, or fields, or topological spaces. Or it lets us get topological spaces from groups or rings and so forth. Category Theory uses functions to map from one object to another. And the objects can be from different categories (ie. one could be a ring, and the other a group.) Several common categories are the category or rings, the category of groups, the category of fields, the category of sets and the category of topological spaces. We've seen in Group Theory how we can add, subtract, multiply, and sometimes divide things that aren't numbers. In other words Group Theory has let to us being able to add apples and oranges. Category Theory goes one step further, and lets us get an apple from an orange tree. Or in other words, Category Theory lets us get groups from rings, or fields, or topological spaces. Or it lets us get topological spaces from groups or rings and so forth. Category Theory uses functions to map from one object to another. And the objects can be from different categories (ie. one could be a ring, and the other a group.) Several common categories are the category or rings, the category of groups, the category of fields, the category of sets and the category of topological spaces.
  
 +[[Problem:Endomorphisms]]
 +{{pabe>Problem:Endomorphisms}}
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 +[[Problem:Group Ring of G over R]]
 +{{pabe>Problem:Group Ring of G over R}}
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 +[[Problem:Real Quaternions]]
 +{{pabe>Problem:Real Quaternions}}
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 +[[Problem:Endomorphisms]]
 +{{pabe>Problem:Endomorphisms}}
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 +[[Problem:Endomorphisms]]
 +{{pabe>Problem:Endomorphisms}}
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 +[[Problem:Endomorphisms]]
 +{{pabe>Problem:Endomorphisms}}
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 +[[Problem:Endomorphisms]]
 +{{pabe>Problem:Endomorphisms}}
  
 =====Review===== =====Review=====
  
 {{tag>tarafife}}  {{tag>tarafife}} 
user/tarafife/tara_s_outline.1388583885.txt.gz ยท Last modified: 2014/01/01 08:44 by tarafife

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