Drorbn - User contributions [en]

14-1100/Class Photo

2014-10-06T02:40:40Z

Travis.russell: /* Who We Are... */

Our class on September 25, 2014:

[[Image:14-1100-ClassPhoto.jpg|thumb|centre|800px|Class Photo: click to enlarge]]
{{14-1100/Navigation}}

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...===

{| align=center border=1 cellspacing=0
|-
!First name
!Last name
!UserID
!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. For better line-breaking, leave a space next to the "@" in email addresses.}}


{{Photo Entry|last=Alboiu|first=Mihai|userid=Malboiu|email=malboiu@ math. toronto. edu|location=Front row, 2nd person from left (in black t-shirt)|comments=}}

{{Photo Entry|last=Barakatain|first=Masoud|userid=masoud88b|email=masoud88b@ gmail.com|location=Back row, fifth person from left|comments=}}

{{Photo Entry|last=Iorgulescu|first=Ana|userid=Anai|email=ana.iorgulescu@ mail. utoronto. ca|location=Back row, third person from the left, in red.|comments=}}

{{Photo Entry|last=Qi|first=Xin (Jessica)|userid=Jqi|email=jxin.qi@ math. toronto. edu|location=First row, third from right|comments=}}

{{Photo Entry|last=Russell|first=Travis|userid=Travis.russell|email=travis.russell@ mail.utoronto.ca|location=Back row, fourth from right, wearing watch, denim shirt|comments=}}

14-1100/Class Photo

2014-10-06T02:39:30Z

Travis.russell: /* Who We Are... */

Our class on September 25, 2014:

[[Image:14-1100-ClassPhoto.jpg|thumb|centre|800px|Class Photo: click to enlarge]]
{{14-1100/Navigation}}

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...===

{| align=center border=1 cellspacing=0
|-
!First name
!Last name
!UserID
!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. For better line-breaking, leave a space next to the "@" in email addresses.}}


{{Photo Entry|last=Alboiu|first=Mihai|userid=Malboiu|email=malboiu@ math. toronto. edu|location=Front row, 2nd person from left (in black t-shirt)|comments=}}

{{Photo Entry|last=Barakatain|first=Masoud|userid=masoud88b|email=masoud88b@ gmail.com|location=Back row, fifth person from left|comments=}}

{{Photo Entry|last=Iorgulescu|first=Ana|userid=Anai|email=ana.iorgulescu@ mail. utoronto. ca|location=Back row, third person from the left, in red.|comments=}}

{{Photo Entry|last=Qi|first=Xin (Jessica)|userid=Jqi|email=jxin.qi@ math. toronto. edu|location=First row, third from right|comments=}}
|}

{{Photo Entry|last=Russell|first=Travis|userid=Travis.russell|email=travis.russell@ mail.utoronto.ca|location=Back row, fourth from right, wearing watch|comments=}}
|}

14-1100

2014-10-06T00:18:55Z

Travis.russell:

__NOEDITSECTION__
__NOTOC__
{{14-1100/Navigation}}
==Core Algebra I==
===Department of Mathematics, University of Toronto, Fall 2014===

{{14-1100/Crucial Information}}

===Texts===
Lang's ''Algebra'', Selick's [http://www.math.toronto.edu/mat1100/ lecture notes for this class], Dummit and Foote's ''Abstract Algebra'', Hungerford's ''Abstract Algebra''. My son Assaf (a math student in another university) recommends also [http://hpmor.com/ Harry Potter and the Methods of Rationality].

===Further Resources===

* [http://www.math.utoronto.ca/cms/graduate-program/ Graduate Studies] at the [http://www.math.toronto.edu/ UofT Math Department]. In particular, [http://www.math.utoronto.ca/cms/tentative-2010-2011-graduate-course-descriptions/ Graduate Course Descriptions].

* My {{Pensieve Link|Classes/14-1100/|14-1100 notebook}}.

* My [[11-1100|2011 Class]].

* My [[10-1100|2010 Class]].

* Paul Selick's [http://www.math.toronto.edu/mat1100/ 2007 class] ([[11-1100/Errata_to_Prof._Selick's_Notes|Errata]]).

* Some (mostly complete) notes from last year's class: [[10-1100-Notes]].

* Some [http://drorbn.net/bbs/show?prefix=14_1100 blackboard shots].

{{Template:14-1100:Dror/Students Divider}}

14-1100

2014-10-05T23:30:49Z

Travis.russell:

14-1100/tower cube

2014-10-05T23:27:02Z

Travis.russell: Combinations of the Tower Cube (HW1-Travis Russell)

== The Tower Cube - Homework 1, Travis Russell ==

The Tower Cube is a combination puzzle reminiscent of the Rubik's Cube. While the normal Rubik's Cube is a 3x3x3 cube, the Tower Cube is 2x2x3, giving it a distinct tower shape. The 2x2 faces of the Tower Cube are able to make 90 degree turns, (or quarter-turns), while the 2x3 faces of the Tower Cube can only make 180 degree turns (or half-turns). Here is a diagram of the Tower Cube with its vertices labelled:

[[File:Tower_cube.png]]

In order to generate the possible combinations of the Tower Cube, I used the following seven generators:

[[File:Tower_cube_generators.png]]

Where <math>g_1</math> is the generator that fixes the yellow face and makes a quarter-turn about the blue face, <math>g_2</math> is the generator that makes a quarter-turn about the middle tier of blocks, <math>g_3</math> is the generator that fixes the blue face and makes a quarter-turn about the yellow face, <math>g_4</math> is the generator that fixes the red face and makes a half-turn about the blue face, <math>g_5</math> is the generator that fixes the orange face and makes a half turn about the red face, <math>g_6</math> is the generator that fixes the green face and makes a half-turn about the white face, and <math>g_7</math> is the generator that fixes the white face and makes a half-turn about the green face.

In order to compute the number of possible combinations of the Tower Cube, I used the code given in class by Professor Bar-Natan:

[[File:Tower_cube_program.png]]

I attempted to write my own program using Java, but I encountered some stack overflow errors. Perhaps in the future I will update this page with my own solution.

After running the program, the following output was generated:

[[File:Tower_cube_output.png]]

Analyzing the output, it seems apparent that only one of the half-turn generators is necessary; combining the three quarter-turn generators with one of the half-turn generators will give all possible combinations.
Checking our solution with other sources online, (such as [http://www.jaapsch.net/puzzles/cube223.htm this one]), we see that the correct solution is 241920, or exactly one eighth of the combinations we generated. In the classic version of the puzzle, the 8 corner pieces are not oriented, however using our generators they are, and this accounts for the factor of eight in the difference between solutions.

File:Tower cube generators.png

2014-10-05T23:02:44Z

Travis.russell: The generators used for generating the combinations of the power cube.

The generators used for generating the combinations of the power cube.

File:Tower cube program.png

2014-10-05T23:02:16Z

Travis.russell: The program used to compute the number of combinations of the tower cube.

The program used to compute the number of combinations of the tower cube.

File:Tower cube output.png

2014-10-05T23:01:38Z

Travis.russell: Output for the tower cube program which computes the number of possible combinations for the tower cube.

Output for the tower cube program which computes the number of possible combinations for the tower cube.

File:Tower cube.png

2014-10-05T23:00:02Z

Travis.russell: Labelling of the tower cube.

Labelling of the tower cube.