Talk:06-240
I think this page needs to list the course textbook. I do not have it on me right now, however, so someone will have to add it.
Also, if anyone is interested in typesetting the lectures I think they should follow these Wikipedia guidelines: http://en.wikipedia.org/wiki/WP:MSM
I attempted to typeset the Sept 12 notes, but it takes way too long to do. If we really want to have typesetted notes, it would probably be much more efficient to make a Word document and then upload it, although it's not as "official" looking.
I doubt it is eaiser to type with Word; typing is typing; you just have to get used to the different interface. And if you type in word others can view and edit it only if they have word too, and even then, fixing a typo becomes way harder. --Drorbn 03:27, 23 September 2006 (EDT)
title of the Textbook
the title of the textbook is:
LINEAR ALGEBRA by Friedberf, Insel and Spence. 4th edition. Publisher: Prentice Hall.
-nicole =)
Modular Arithmetic
This was particularly interesting after being introduced to Modular Multiplication tables and seeing some visual patterns with the numbers, such as the in the '1' column where the elements go from 1 to n-1 in Zn and backwards in the 'n-1' column.
After searching around, it seems that people had been able to discover other, more interesting patterns!
Make sure to analyze the tables since they begin from the bottom left corner instead of top left which we saw in class.
http://whistleralley.com/mod/mod25.htm
The following site allows you to see tables up to mod 30.
http://www.cut-the-knot.org/blue/Modulo.shtml
-Richard
Also, notice how in modular multiplication tables for prime numbers, in specific for modulo 5 in the columns and rows for 0 and 5 only 0s appear. The 0s create a sort of frame around a 4x4 square of elements. Specifically all elements within the frame of 0s are between 1 and n-1 and all are non-zero. In the case of the mod 4 table there was a 0 which, as proved in class causes Z4 to fail as a field. There must be something deeper about all those 0s.
