From 397cefef7929e6cd49959db1d891f5b0654ebd05 Mon Sep 17 00:00:00 2001
From: bryan newbold <bnewbold@snark.mit.edu>
Date: Tue, 10 Jun 2008 10:48:24 -0400
Subject: added a bunch of math content based on alaska notes. added more
ethernet content
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+====================
+Algebra
+====================
+
+.. note:: Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
+
+.. list-table:: Closure of binary operators on given sets of numbers
+ * Operation
+ - :latex:`$+$`
+ - :latex:`$\times$`
+ - :latex:`$-$`
+ - :latex:`$\divide$`
+ - :latex:`$^$`
+ - :latex:`$\sqrt{\text{ }}$`
+ * Positive Integers
+ - Y
+ - Y
+ - N
+ - N
+ - Y
+ - N
+ * Positive rationals
+ - Y
+ - Y
+ - N
+ - Y
+ - Y
+ - N
+ * Rationals (and zero)
+ - Y
+ - Y
+ - Y
+ - Y
+ - Y
+ - N
+ * Reals wrt positive integers
+ - Y
+ - Y
+ - Y
+ - Y
+ - Y
+ - Y
+ * Complex numbers
+ - Y
+ - Y
+ - Y
+ - Y
+ - Y
+ - Y
+
+Definitions
+=============
+
+*involution*
+ to raise a number to a given power
+
+*evolution*
+ to take a given root of a number
+
+*associative*
+ :latex:`$(a+b)+c=a+(b+c)$`
+
+*comutative*
+ :latex:`$a+b=b+c$`
+
+*distributive*
+ :latex:`$(a+b)c=ac+bc$`
+
+.. [rudin] `Principles of Mathematical Analysis (3rd ed)`:title:, by Walter Rudin. McGraw-Hill, 1976
+
+.. [meserve] `Fundamental Concepts of Algebra`:title:, by Bruce Meserve.
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