Drorbn - User contributions [en]

06-240/Class Photo

2006-10-03T11:52:48Z

Cerezo:

{{06-240/Navigation}}

Our class on September 28, 2006:

[[Image:06-240-ClassPhoto.jpg|thumb|center|500px|Class Photo: click to enlarge]]

Please identify yourself in this photo! There are two ways to do that:

* [[Special:Userlogin|Log in]] to this Wiki and edit this page. Put your name, userid, email address and location in the picture in the alphabetical list below.
* Send [[User:Drorbn|Dror]] an email message with this information.

The first option is more fun but less private.

===Who We Are===

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|-
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!Email
!In the photo
!Comments
{{Photo Entry|last=Bar-Natan|first=Dror|userid=Drorbn|email=drorbn@ math.toronto.edu|location=facing everybody, as the photographer|comments=Take this entry as a model and leave it first. Otherwise alphabetize by last name. Feel free to leave some fields blank}}
{{Photo Entry|last=Carberry|first=Mick|userid=MC|email=Mick.Carberry@utoronto.ca|location=long haired, bearded old guy in back|comments= }}
{{Photo Entry|last=Cerezo|first=Richard|userid=Cerezo|email=richard.cerezo@utoronto.ca|location=Guy in black jacket and black hat on far right, second from the bottom. |comments= }}
{{Photo Entry|last=Kaifosh|first=Patrick|userid=Pat|email=patrick.kaifosh@utoronto.ca|location=Front row, rightmost.|comments= }}
{{Photo Entry|last=Koziar|first=John|userid=John.koziar|email=|location=Front row, centre.|comments= }}
{{Photo Entry|last=McIntyre|first=Sean|userid=Smcintyre|email=s.mcintyre@utoronto.ca|location=mini-picture, fourth from the right|comments= }}
{{Photo Entry|last=Soreanu|first=Alla|userid=Alla|email=alla.soreanu@utoronto.ca|location=mini-picture, first from the left|comments= }}
{{Photo Entry|last=Wong|first=Pak|userid=wongpak|email=plwong@utoronto.ca|location=Third row from the back, left most, black shirt|comments= }}
{{Photo Entry|last=Halacheva|first=Iva|userid=Haliv|email=iva.halacheva@utoronto.ca|location=Third row from the front, light brown jacket|comments= }}
{{Photo Entry|last=Ng|first=Gilbert|userid=Gilbert|email=gilbert.ng@utoronto.ca|location=to the right of the pole in the back, last row|comments= }}
{{Photo Entry|last=Qiao|first=Li|userid=joy9999|email=li.qiao@ utoronto.ca|location=behind the guy in black, last row|comments= }}

Talk:06-240

2006-09-20T18:54:14Z

Cerezo: /* Modular Arithmetic */

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.

Talk:06-240

2006-09-20T18:47:46Z

Cerezo: /* Modular Arithmetic */

Talk:06-240

2006-09-20T18:47:23Z

Cerezo: Modular Arithmetic