Talk:06-240: Difference between revisions
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If anyone is interested in typesetting the lectures I think they should follow these Wikipedia guidelines: http://en.wikipedia.org/wiki/WP:MSM |
If anyone is interested in typesetting the lectures I think they should follow these Wikipedia guidelines: http://en.wikipedia.org/wiki/WP:MSM |
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==Exam Forum== |
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I hope you will excuse my intrusion onto the front page, but I thought the link might help increase participation. It will be removed right after the final exam. |
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Also, my use of "help", leaving it ambiguous as to whether the person clicking on the link would be receiving or giving help, is intentional. |
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== Modular Arithmetic == |
== Modular Arithmetic == |
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Latest revision as of 18:42, 15 June 2007
If anyone is interested in typesetting the lectures I think they should follow these Wikipedia guidelines: http://en.wikipedia.org/wiki/WP:MSM
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.
Mistake in the timetable in the main page of 06-240?
In the timetable in the main page of 06-240,i.e. http://katlas.math.toronto.edu/drorbn/index.php?title=06-240 , I think there's a mistake about the date of the first test. There, it's written Oct 23th, but we have no class on Oct 23 which is a Monday. I guess the correct date should be Oct 24th as written in the course outline.
-Yanshuai
The dates on the time table are the dates of the Mondays in each week; the header says "week of...". --Drorbn 17:46, 9 October 2006 (EDT)
TA Office Hours?
Do they have any?
