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--- ben_s_outline [2013/08/08 23:25]
bmwoodruff
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-I plan to have multiple threads running simultaneously through the semester.  However, for development purposes, it will probably be easiest to organize them into sections.  I'm hoping to grab a lot of ideas about combinatorial games from Dana.  I'm not sure what you are planning Josh, but I hope to see it soon.
-=== Cryptography ===
-We'll start with a simple cryptosystem that involves shifting. Then advance to matrix encryption, then matrix modular encryption.  This gets to GL(n,m) really fast, and introduces homomorphisms via the determinant map, and isomorphisms between U(p-1) and Z(p) for prime p. I want to get to homomorphisms quickly, as I want to introduce the concepts of factor groups, normal groups, cosets, and more, from the context of homomorphisms.
-  *[[Problem:Simple Shift on 26 letters]] - Introduces Modular arithmetic
-  *[[Problem:The Order of a Simple Shift ]] - Introduces the fact that the order of an element divides the order of a group.  This comes from
-  *[[Theorem:The Order of an Element Divides the Order of the Group]]
-=== Cayley Graphs ===
-=== Combinatorial Games ===
-=== Fundamental Theorems ===
-=== Definitions ===
-  *[[Definition:Group]]

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