diff options
author | bryan newbold <bnewbold@snark.mit.edu> | 2008-06-10 10:48:24 -0400 |
---|---|---|
committer | bryan newbold <bnewbold@snark.mit.edu> | 2008-06-10 10:48:24 -0400 |
commit | 397cefef7929e6cd49959db1d891f5b0654ebd05 (patch) | |
tree | ec197475d62c9149288863f89c97e26131959815 /math/algebra | |
parent | 80b4628e5a94dfedd2c6ee91bdb608c531a78598 (diff) | |
download | knowledge-397cefef7929e6cd49959db1d891f5b0654ebd05.tar.gz knowledge-397cefef7929e6cd49959db1d891f5b0654ebd05.zip |
added a bunch of math content based on alaska notes. added more ethernet content
Diffstat (limited to 'math/algebra')
-rw-r--r-- | math/algebra | 71 |
1 files changed, 71 insertions, 0 deletions
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. |