From 397cefef7929e6cd49959db1d891f5b0654ebd05 Mon Sep 17 00:00:00 2001 From: bryan newbold Date: Tue, 10 Jun 2008 10:48:24 -0400 Subject: added a bunch of math content based on alaska notes. added more ethernet content --- math/algebra | 71 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 math/algebra (limited to 'math/algebra') diff --git a/math/algebra b/math/algebra new file mode 100644 index 0000000..b337a2e --- /dev/null +++ b/math/algebra @@ -0,0 +1,71 @@ +==================== +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. -- cgit v1.2.3