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

Finally, whoever put the class notes on the front page should probably move them to the appropriate class page.

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.