Drorbn - User contributions [en]

06-240/Linear Algebra - Why We Care

2006-10-19T01:16:37Z

John.koziar: /* Extra Class Time */

{{06-240/Navigation}}

==Linear Algebra is the Small Scale Theory of ''Everything''==

* '''To study the large, start with the small.'''

* '''In small scales, every space is a vector space.'''
** Indeed if you walk a mile east, a mile north, a mile west and a mile south, you're back were you started, but if you fly a 1,000 miles east, a 1,000 miles north, a 1,000 miles west and a 1,000 miles south, you're not back were you started (where will you be?).

* '''In small scales, every function is a linear function.'''
{| align=center
|- align=center
|[[Image:06-240-QuiltBeforeMap.png|200px]]
|<math>\longrightarrow</math>
|[[Image:06-240-QuiltAfterMap.png|200px]]
|
|- align=center
|<math>z</math>
|<math>\mapsto</math>
|<math>z^2</math>
|([[06-240/QuiltPlot|code]])
|}

* '''The world doesn't come with coordinates.'''
** Hence whenever we can we work without a basis, and when we do study bases, we study all of them.

==Some Technical Remarks==

===The Term Test===

Our one and only Term Test is coming up. It will take place in class on Tuesday October 24 2006, starting promptly at 1:10PM and ending at 3:00PM sharp. It will consist of 4-5 questions (each may have several parts) on everything that we will have covered in class by October 18: the axiomatic definition of fields and vector spaces, <math>{\mathbb Z}/p</math> and other examples, spans, linear combinations and linear equations, linear dependence and independence, bases, the replacement lemma and its consequences, a bit about linear transformations and a few smaller topics that we touched but don't deserve their own headers.

Note my comments from [[06-240/Homework Assignment 5]]:

;Will there be "proof questions"?
:Sure. What else have we done so far?
;Do we need to know the proofs from class?
:Sure. There's a reason why these proofs are in class to start with; if they weren't valuable, we wouldn't have covered them.

Note also that there may be some computations, but nothing that will require a calculator. Note also that I may include some questions from the homework assignments verbatim or nearly verbatim.

No electronic devices capable of displaying text or sounding speech will be allowed.

===Extra Class Time===

On Thursday, October 26th, we will have a 2-hour class (1-3PM) to make up for the class time lost on the Term Test, and just one hour of tutorials (3-4PM) as no HW assignment is due on that week anyway.

User talk:Drorbn

2006-10-06T03:23:46Z

John.koziar:

Is the grammar intentional on the user page?
-John

User talk:Drorbn

2006-10-06T03:23:25Z

John.koziar:

User talk:Drorbn

2006-10-06T03:23:14Z

John.koziar:

Is the grammar intentional?
-John

06-240/Class Photo

2006-10-05T21:34:31Z

John.koziar: /* Who We Are... */

Our class on September 28, 2006:

[[Image:06-240-ClassPhoto.jpg|thumb|centre|500px|Class Photo: click to enlarge]]
{{06-240/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
|-
!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}}
{{Photo Entry|last=Beach|first=Laura|userid=Beacher|email=laura.beach@ utoronto.ca|location=3rd row from front, far right in light shirt, in front of guy in hat.|comments=Lookin' good, everybody!}}
{{Photo Entry|last=Bumagin|first=Mark|userid=Bumaginm|email=mark.bumagin@ utoronto.ca|location=Guy in light blue collar shirt, second row, third on the right|comments= }}
{{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=Dong|first=Qi (Tom)|userid=houseofglass|email=tom_dongqi@ hotmail.com|location= The only chinese blonde guy with glasses located on the second row in the main picture|comments=testing 1 2 3 4 5 6 7 8 9 }}
{{Photo Entry|last=Dzamba|first=Michael|userid=dzambami|email=michael.dzamba@ utoronto.ca|location=In the middle, sort of, have a bit of extra hair on my head, forms sort of a spherical volume, sometimes visible from a distance|comments="The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers." - Bill Gates , The Road Ahead (his book), P265, This is not a typo on my behalf ;) }}
{{Photo Entry|last=Gokmen|first=Murat|userid=Gokmen|email=uoftmurat@ gmail.com|location=the guy second row @second from the right:with the shining jacket & blue hat|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=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=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= }}
{{Photo Entry|last=Soreanu|first=Alla|userid=Alla|email=alla.soreanu@ utoronto.ca|location=mini-picture, first from the left|comments= }}
{{Photo Entry|last=SUN|first=LUYANG|userid=Luyang|email=luyang.sun@ utoronto.ca|location=the guy in the middle, wearing a white coat row3 col4|comments=Hello World}}
{{Photo Entry|last=Tai|first=Johnathan|userid=Zapyre|email=zapyre_1@ hotmail.com|location= At the very back, left hand corner (all blue) |comments= >.<}}
{{Photo Entry|last=Veytsman|first=Maxim|userid=Mveytsman|email=|location=small picture in the bottom left corner. Second one from the right.|comments=}}
{{Photo Entry|last=Wong|first=Pak|userid=wongpak|email=plwong@ utoronto.ca|location=Third row from the back, left most, black shirt|comments= }}

06-240/Homework Assignment 4

2006-10-05T21:11:44Z

John.koziar: Added bit about honorificabilitudinitatibus.

{{06-240/Navigation}}

* '''Read''' sections 1.5 through 1.7 in our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read.

* '''Solve''' problems 3, 8, 9, 10 and 11 on pages 41-42, but submit only your solutions of problems 8 and 9.

* '''Solve''' problems 1, 2, 4, 5, 9 and 16 on page 53-56, but submit only your solutions of problems 4, 5 and 9.

{|
|-
|'''Just for Fun.'''
* Take a large integer and write it in base 10. Cut away the "singles" digit, double it and subtract the result from the remaining digits. Repeat the process until the number you have left is small. Prove that the number you started from is divisible by 7 iff the resulting number is divisible by 7. Thus the example on the right shows that 86415 is divisible by 7 as 0 is divisible by 7. (I learned this trick a few days ago from [http://www.math.toronto.edu/hovinen/ Bradford Hovinen]).
* Find a similar criterion for divisibility by 17 and for all other divisibilities and indivisibilities.
* Note that the word "indivisibilities" has the largest number of repetitions of a single letter among all words in the English language (7 i's). I've known this fact for years but this is the first time that I'm finding a semi-legitimate use for that word! (It is tied with the word honorificabilitudinitatibus for seven 'i's. You can read more about it here: http://en.wikipedia.org/wiki/Honorificabilitudinitatibus)
|
8641<s>5</s>
10
----
863<s>1</s>
2
---
86<s>1</s>
2
--
8<s>4</s>
8
-
0
|}

Template:06-240/Crucial Information

2006-10-05T04:24:43Z

John.koziar: Reworded tutorial room division to make it simpler and shorter; added "are covered" to the Hidden Agenda to make the second clause dependent.

'''Agenda:''' Understand linear algebra, the simplest algebra there is, and come to appreciate that simplest is also the most fundamental.

'''Hidden Agenda:''' Learn (by example) how "real" math is done; abstraction and generalization, definitions, theorems and proofs are covered.

'''Instructor:''' [http://www.math.toronto.edu/~drorbn/ Dror Bar-Natan], drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: {{Office Hours}}.

'''Classes:''' Tuesdays 1-3 and Thursdays 1-2 at [http://www.osm.utoronto.ca/cgi-bin/class_spec/spec03?bldg=MP&room=203 MP 203].

{|
|-
|[[Image:06-240-DoninAndLee.jpg|100px|center|Dmitry, Paul]]
|'''Teaching Assistants:''' Dmitry Donin, donin@math.toronto.edu, Bahen 6191, 416-978-2095 and Paul Lee, plee@math.toronto.edu, Bahen 6135, 416-978-4794.

'''Tutorials:''' Thursdays 2-4 at [http://www.osm.utoronto.ca/cgi-bin/class_spec/spec03?bldg=MP&room=203 MP 203] if the last digit of your student number is even, and at [http://www.osm.utoronto.ca/cgi-bin/class_spec/spec03?bldg=MP&room=118 MP 118] if it is odd.
|}

06-1350/Class Photo

2006-10-05T04:19:05Z

John.koziar: Made same questionable edit as on MAT240 picture page.

Our class on September 28, 2006:

[[Image:06-1350-ClassPhoto.jpg|thumb|center|500px|Class Photo: click to enlarge]]
{{06-1350/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
|-
!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}}
{{Photo Entry|last=Dancso|first=Zsuzsi|userid=Zsuzsi|email=zsuzsi@ math.toronto.edu|location=first row, second from the right|comments=}}
{{Photo Entry|last=Ivrii|first=Oleg|userid=Oivrii|email=oleg@math.toronto.edu|location=last row, middle of the sitting |comments=}}
|}

Talk:06-1350

2006-10-05T04:15:08Z

John.koziar:

Guys,

I thought it might be nice to establish a lively discussion board on which we can discuss, develop and clarify any, or all, aspects of material pertaining to the class! I'll try to get things started with something that I had on my mind.

From lectures, we've opted to get our teeth stuck into things from the outset, with the point being that a thorough discussion of the elementary concepts would eat up a substancial amount of time, from which the only outcome would be a rigorous confirmation of what we all already understood knot, and equivalence of knots, to mean.

Being eager, I thought I'd jot down a couple of sentences (having just finished the post, I can say that this is was a gross underestimate of length) indicating what I think the pedantic issues at stake to be, and was hoping that perhaps we could iron out a couple of things I find to be confusing.

As I see it, the first, and main, point that might warrent a discussion, is on the correspondence between smooth and peicewise linear embeddings of the circle in three space.

[Recall from the first lecture that we would like a knot to be an equivalence class of embeddings, where the embeddings can be taken to be peicewise linear or smooth and the equivalence relation is determined by ambient isotopy; namely f and g are said to be ambient isotopic embeddings if and only if we have a smooth/peicewise linear (depending on whether we're talking about smooth or peicewise linear embeddings) map H:S^3x[0,1]->S^3 subject to H(_,t) being a smooth/peicewise linear homeomorphism with H(_,0) the identity and H(f(S^1),1)=g(S^1).]

The first question is: what is the correspondence between the two theories? Clearly any peicewise linear knot may be smoothed at the corners, and any smooth embedding has a linear approximation. However, if we try to talk about isotopies of such knots we're talking about something living in S^3x[0,1]xS^3. I think smooth manifolds, of which the graph of H is one, can be triangulated, though I don't have a good reference for this. Further, if the peicewise linear isotopies could be "smoothed" then we could conclude that thinking of knots as being peicewise linear or smooth is really the same for our purposes. Does anyone know about this or have any good references?

The second question (which is really dependant on the first question) I had in mind was on the connection between representations of knots in the form of quadravalent planar diagrams up to Reidmeister moves, and knots up to ambient isotopy.

Firstly, well defined parallel projections of knots exist

[infact there is a lovely visual argument that show that almost all parallel projections are "nice" in the sence that the inverse image of points of the diagram have at most two preimages and such points are isolated... equate the projections with points on the sphere and observe that two linear segments of the knot project onto each other only on arcs of the sphere, and further that projections having preimage sets of cardinality greater or equal to two are isolated or again lie on an arc. Thus the measure of such a set is zero.]

Now ambient isotopies of peicewise linear isotopies of knots can be broken down into moves where you can either replace one segement of a knot with the other two edges of a triangle containing the fixed segment as an edge as long as the spanning triangle doesn't intersect the knot anywhere else and vica versa (a picture would be very handy here, but I don't really know how to use any such feature yet), and consequently we see the Reidemister moves of planar diagrams all correspond to isotopies. The other direction is Reidemeister's famous theorem (the equivalence that we assumed axiomatically) and is quite a complicated argument. The question that arises in my mind is that if the smooth and peicewise linear theories are not equivalent [see question one], then it would seem that Reidemeister's proof may not carry over!

I'd love to have this put straight in my mind, and hope that someone can help me via a reference or authorative confirmation.

Sorry this was long winded, confused and above all practically irrelevant to the course!

Fionntan

Talk:06-240/Class Photo

2006-10-05T04:11:01Z

John.koziar:

The image being centred caused it to appear below the navigation bar, making for a large white area on my screen. I tried multiple browsers and browser-widths, all with the same problem, so I assume the problem was shared by others. The silly fix was to move the navigation bar below the picture, but this might be against format. Anyone with good knowledge of the editing format should be able to post a better fix, or point out my insanity. -John.koziar.

06-240/Class Photo

2006-10-05T04:09:40Z

John.koziar:

Our class on September 28, 2006:

[[Image:06-240-ClassPhoto.jpg|thumb|centre|500px|Class Photo: click to enlarge]]
{{06-240/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
|-
!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}}
{{Photo Entry|last=Beach|first=Laura|userid=Beacher|email=laura.beach@utoronto.ca|location=3rd row from front, far right in light shirt, in front of guy in hat.|comments=Lookin' good, everybody!}}
{{Photo Entry|last=Bumagin|first=Mark|userid=Bumaginm|email=mark.bumagin@utoronto.ca|location=Guy in light blue collar shirt, second row on the right|comments= }}
{{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=Dong|first=Qi (Tom)|userid=houseofglass|email=tom_dongqi@hotmail.com|location= The only chinese blonde guy with glasses located on the second row in the main picture|comments=testing 1 2 3 4 5 6 7 8 9 }}
{{Photo Entry|last=Gokmen|first=Murat|userid=Gokmen|email=uoftmurat@gmail.com|location=the guy second row @second from the right:with the shining jacket & blue hat|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=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=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= }}
{{Photo Entry|last=Soreanu|first=Alla|userid=Alla|email=alla.soreanu@utoronto.ca|location=mini-picture, first from the left|comments= }}
{{Photo Entry|last=SUN|first=LUYANG|userid=Luyang|email=luyang.sun@utoronto.ca|location=the guy in the middle, wearing a white coat row3 col4|comments=Hello World}}
{{Photo Entry|last=Tai|first=Johnathan|userid=Zapyre|email=zapyre_1@hotmail.com|location= At the very back, left hand corner (all blue) |comments= >.<}}
{{Photo Entry|last=Veytsman|first=Maxim|userid=Mveytsman|email=|location=small picture in the bottom left corner. Second one from the right.|comments=}}
{{Photo Entry|last=Wong|first=Pak|userid=wongpak|email=plwong@utoronto.ca|location=Third row from<nowiki>Insert non-formatted text here</nowiki><nowiki>Insert non-formatted text here</nowiki> the back, left most, black shirt|comments= }}

Talk:06-240/Class Photo

2006-10-05T04:05:38Z

John.koziar:

The image being centred caused it to appear below the navigation bar, making for a large white area on my screen. I tried multiple browsers and browser-widths, all with the same problem, so I assume the problem was shared by others. I changed the word 'centre' to 'left' in the picture-call. Also, in wide-screen, this caused "Who We Are" to appear beside the picture while the actual table appears below it, causing another blank space. The easiest thing to do was to add "..." so it doesn't look as silly. -John.koziar.

06-240/Class Photo

2006-10-05T04:00:31Z

John.koziar:

{{06-240/Navigation}}

Our class on September 28, 2006:

[[Image:06-240-ClassPhoto.jpg|thumb|left|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...===

{| align=center border=1
|-
!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}}
{{Photo Entry|last=Beach|first=Laura|userid=Beacher|email=laura.beach@utoronto.ca|location=3rd row from front, far right in light shirt, in front of guy in hat.|comments=Lookin' good, everybody!}}
{{Photo Entry|last=Bumagin|first=Mark|userid=Bumaginm|email=mark.bumagin@utoronto.ca|location=Guy in light blue collar shirt, second row on the right|comments= }}
{{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=Dong|first=Qi (Tom)|userid=houseofglass|email=tom_dongqi@hotmail.com|location= The only chinese blonde guy with glasses located on the second row in the main picture|comments=testing 1 2 3 4 5 6 7 8 9 }}
{{Photo Entry|last=Gokmen|first=Murat|userid=Gokmen|email=uoftmurat@gmail.com|location=the guy second row @second from the right:with the shining jacket & blue hat|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=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=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= }}
{{Photo Entry|last=Soreanu|first=Alla|userid=Alla|email=alla.soreanu@utoronto.ca|location=mini-picture, first from the left|comments= }}
{{Photo Entry|last=SUN|first=LUYANG|userid=Luyang|email=luyang.sun@utoronto.ca|location=the guy in the middle, wearing a white coat row3 col4|comments=Hello World}}
{{Photo Entry|last=Tai|first=Johnathan|userid=Zapyre|email=zapyre_1@hotmail.com|location= At the very back, left hand corner (all blue) |comments= >.<}}
{{Photo Entry|last=Veytsman|first=Maxim|userid=Mveytsman|email=|location=small picture in the bottom left corner. Second one from the right.|comments=}}
{{Photo Entry|last=Wong|first=Pak|userid=wongpak|email=plwong@utoronto.ca|location=Third row from<nowiki>Insert non-formatted text here</nowiki><nowiki>Insert non-formatted text here</nowiki> the back, left most, black shirt|comments= }}

06-240/Class Photo

2006-10-02T01:08:58Z

John.koziar: /* Who We Are */

{{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===

{| align=center border=1
|-
!First Name
!Last Name
!UserID
!Email
!In 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=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= }}

|}

06-240/Class Photo

2006-10-02T01:07:33Z

John.koziar: /* Who We Are */

{{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===

{| align=center border=1
|-
!First Name
!Last Name
!UserID
!Email
!In 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=Kaifosh|first=Patrick|userid=Pat|email=patrick.kaifosh@utoronto.ca|location=large picture, farthest to the right on sidewalk|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= }}

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