Drorbn - User contributions [en]

Template:09-240/Navigation

2009-12-03T22:30:25Z

Sknad:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
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{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|- align=left
!#
!Week of...
!Notes and Links
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|Sep 7
|<s>Tue</s>, [[09-240/About This Class|About]], [[09-240/Classnotes for Thursday September 10|Thu]]
|- align=left
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|Sep 14
|[[09-240/Classnotes for Tuesday September 15|Tue]], [[09-240:HW1|HW1]], [[09-240:HW1 Solution|HW1 Solution]], [[09-240/Classnotes for Thursday September 17|Thu]]
|- align=left
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|Sep 21
|[[09-240/Classnotes for Tuesday September 22|Tue]], [[09-240:HW2|HW2]], [[09-240:HW2 Solution|HW2 Solution]], [[09-240/Classnotes for Thursday September 24|Thu]], [[09-240/Class Photo|Photo]]
|- align=left
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|Sep 28
|[[09-240/Classnotes for Tuesday September 29|Tue]], [[09-240:HW3|HW3]], [[09-240:HW3 Solution|HW3 Solution]], [[09-240/Classnotes for Thursday October 1|Thu]]
|- align=left
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|Oct 5
|[[09-240/Classnotes for Tuesday October 6|Tue]], [[09-240:HW4|HW4]], [[09-240:HW4 Solution|HW4 Solution]], [[09-240/Classnotes for Thursday October 8|Thu]],
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|Oct 12
|[[09-240/Classnotes for Tuesday October 13|Tue]], [[09-240/Classnotes for Thursday October 15|Thu]]
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|Oct 19
|[[09-240/Classnotes for Tuesday October 20|Tue]], [[09-240:HW5|HW5]], [[09-240:HW5 Solution|HW5 Solution]], [[09-240/Term Test|Term Test on Thu]]
|- align=left
|align=center|8
|Oct 26
|[[09-240/Classnotes for Tuesday October 27|Tue]], [[09-240/Linear Algebra - Why We Care|Why LinAlg?]], [[09-240:HW6|HW6]], [[09-240/Classnotes for Thursday October 29|Thu]]
|- align=left
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|Nov 2
|[[09-240/Classnotes for Tuesday November 3|Tue]], [[09-240/Useful links to the MIT linear algebra course|MIT LinAlg]], [[09-240/Classnotes for Thursday November 5|Thu]]
|- align=left
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|Nov 9
|[[09-240/Classnotes for Tuesday November 10|Tue]], [[09-240:HW7|HW7]], [[09-240:HW7 Solution|HW7 Solution]] <s>Thu</s>
|- align=left
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|Nov 16
|[[09-240/Classnotes for Tuesday November 17|Tue]], [[09-240:HW8|HW8]], [[09-240/Classnotes for Thursday November 19|Thu]], [[09-240:HW8 Solution|HW8 Solution]]
|- align=left
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|Nov 23
|[[09-240/Classnotes for Tuesday November 24|Tue]], [[09-240:HW9|HW9]], [[09-240/Classnotes for Tuesday November 26|Thu]]
|- align=left
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|Nov 30
|[[09-240/Classnotes for Tuesday December 1|Tue]], [[09-240/On The Final Exam|On the final]], [[09-240/Classnotes for Tuesday December 3|Thu]]
|- align=left
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|Dec 7
|[[09-240/Final Exam Preparation Forum|Forum]], [[09-240/On The Final Exam|Office Hours]]
|- align=left
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|Dec 14
|[[09-240/The Final Exam|Final on Dec 16]]
|- align=left
|colspan=3 align=center|[[09-240/To do|To Do List]]
|- align=left
|colspan=3 align=center|[http://www.youtube.com/watch?v=UTby_e4-Rhg The Algebra Song!]
|- align=left
|colspan=3 align=center|[[09-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:09-240-ClassPhoto.jpg|180px]]<br>[[09-240/Class Photo|Add your name / see who's in!]]
|}
</div></div>
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09-240

2009-11-27T03:39:17Z

Sknad: Added some useful links to the homepage.

__NOEDITSECTION__
{{09-240/Navigation}}

==Algebra I==
===Department of Mathematics, University of Toronto, Fall 2009===

{{09-240/Crucial Information}}

===Text===
Freidberg, Insel, Spence. <u>Linear Algebra, 4e</u>. New Jersy: Pearson Education Inc, 2003.<br>

===Further Resources===

* [http://www.math.toronto.edu/undergrad/ Undergraduate Information] at the [http://www.math.toronto.edu/ UofT Math Department]
* [http://www.artsandscience.utoronto.ca/ofr/calendar/crs_mat.htm Undergraduate Course Descriptions].
* [http://www.math.toronto.edu/murnaghan/courses/mat240/index.html Last year's MAT240 web site].
* [[06-240|My 2006 Math 240 web site]].
* [http://www.math.toronto.edu/~megumi/MAT240/240.html The 2005 MAT240 site].

===Interesting Links===

* [http://aix1.uottawa.ca/~jkhoury/app.htm Interesting Linear Algebra Applications]
* [http://linear.ups.edu/jsmath/latest/fcla-jsmath-latest.html Free Alternative Online Linear Algebra Textbook]

Template:09-240/Navigation

2009-11-26T20:21:07Z

Sknad:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[09-240]]/[[Template:09-240/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 7
|<s>Tue</s>, [[09-240/About This Class|About]], [[09-240/Classnotes for Thursday September 10|Thu]]
|- align=left
|align=center|2
|Sep 14
|[[09-240/Classnotes for Tuesday September 15|Tue]], [[09-240:HW1|HW1]], [[09-240:HW1 Solution|HW1 Solution]], [[09-240/Classnotes for Thursday September 17|Thu]]
|- align=left
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|Sep 21
|[[09-240/Classnotes for Tuesday September 22|Tue]], [[09-240:HW2|HW2]], [[09-240:HW2 Solution|HW2 Solution]], [[09-240/Classnotes for Thursday September 24|Thu]], [[09-240/Class Photo|Photo]]
|- align=left
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|Sep 28
|[[09-240/Classnotes for Tuesday September 29|Tue]], [[09-240:HW3|HW3]], [[09-240:HW3 Solution|HW3 Solution]], [[09-240/Classnotes for Thursday October 1|Thu]]
|- align=left
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|Oct 5
|[[09-240/Classnotes for Tuesday October 6|Tue]], [[09-240:HW4|HW4]], [[09-240:HW4 Solution|HW4 Solution]], [[09-240/Classnotes for Thursday October 8|Thu]],
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|Oct 12
|[[09-240/Classnotes for Tuesday October 13|Tue]], [[09-240/Classnotes for Thursday October 15|Thu]]
|- align=left
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|Oct 19
|[[09-240/Classnotes for Tuesday October 20|Tue]], [[09-240:HW5|HW5]], [[09-240:HW5 Solution|HW5 Solution]], [[09-240/Term Test|Term Test on Thu]]
|- align=left
|align=center|8
|Oct 26
|[[09-240/Classnotes for Tuesday October 27|Tue]], [[09-240/Linear Algebra - Why We Care|Why LinAlg?]], [[09-240:HW6|HW6]], [[09-240/Classnotes for Thursday October 29|Thu]]
|- align=left
|align=center|9
|Nov 2
|[[09-240/Classnotes for Tuesday November 3|Tue]], [[09-240/Useful links to the MIT linear algebra course|MIT LinAlg]], [[09-240/Classnotes for Thursday November 5|Thu]]
|- align=left
|align=center|10
|Nov 9
|[[09-240/Classnotes for Tuesday November 10|Tue]], [[09-240:HW7|HW7]], [[09-240:HW7 Solution|HW7 Solution]] <s>Thu</s>
|- align=left
|align=center|11
|Nov 16
|[[09-240/Classnotes for Tuesday November 17|Tue]], [[09-240:HW8|HW8]], [[09-240/Classnotes for Thursday November 19|Thu]]
|- align=left
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|Nov 23
|[[09-240/Classnotes for Tuesday November 24|Tue]], [[09-240:HW9|HW9]]
|- align=left
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|Nov 30
|[[09-240/On The Final Exam|On the final]]
|- align=left
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|Dec 7
|
|- align=left
|align=center|F
|Dec 14
|[[09-240/The Final Exam|Final on Dec 16]]
|- align=left
|colspan=3 align=center|[[09-240/To do|To Do List]]
|- align=left
|colspan=3 align=center|[[http://www.youtube.com/watch?v=UTby_e4-Rhg The Algebra Song!]]
|- align=left
|colspan=3 align=center|[[09-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:09-240-ClassPhoto.jpg|180px]]<br>[[09-240/Class Photo|Add your name / see who's in!]]
|}
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|}

09-240

2009-11-03T21:21:39Z

Sknad: Changed 2006 to 2009

Template:09-240/Navigation

2009-10-30T02:04:55Z

Sknad: Added a link to a song about Algebra

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[09-240]]/[[Template:09-240/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 7
|<s>Tue</s>, [[09-240/About This Class|About]], [[09-240/Classnotes for Thursday September 10|Thu]]
|- align=left
|align=center|2
|Sep 14
|[[09-240/Classnotes for Tuesday September 15|Tue]], [[09-240:HW1|HW1]], [[09-240:HW1 Solution|HW1 Solution]], [[09-240/Classnotes for Thursday September 17|Thu]]
|- align=left
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|Sep 21
|[[09-240/Classnotes for Tuesday September 22|Tue]], [[09-240:HW2|HW2]], [[09-240:HW2 Solution|HW2 Solution]], [[09-240/Classnotes for Thursday September 24|Thu]], [[09-240/Class Photo|Photo]]
|- align=left
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|Sep 28
|[[09-240/Classnotes for Tuesday September 29|Tue]], [[09-240:HW3|HW3]], [[09-240:HW3 Solution|HW3 Solution]], [[09-240/Classnotes for Thursday October 1|Thu]]
|- align=left
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|Oct 5
|[[09-240/Classnotes for Tuesday October 6|Tue]], [[09-240:HW4|HW4]], [[09-240:HW4 Solution|HW4 Solution]], [[09-240/Classnotes for Thursday October 8|Thu]],
|- align=left
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|Oct 12
|[[09-240/Classnotes for Thursday October 15|Thu]]
|- align=left
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|Oct 19
|[[09-240/Classnotes for Tuesday October 20|Tue]], [[09-240:HW5|HW5]], [[09-240/Term Test|Term Test on Thu]]
|- align=left
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|Oct 26
|[[09-240/Classnotes for Tuesday October 27|Tue]], [[09-240/Linear Algebra - Why We Care|Why LinAlg?]], [[09-240:HW6|HW6]], [[09-240/Classnotes for Thursday October 29|Thu]]
|- align=left
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|Nov 2
|
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|Nov 9
|[[09-240:HW7|HW7]], <s>Thu</s>
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|Nov 16
|[[09-240:HW8|HW8]]
|- align=left
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|Nov 23
|[[09-240:HW9|HW9]]
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|Nov 30
|[[09-240/On The Final Exam|On the final]]
|- align=left
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|Dec 7
|
|- align=left
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|Dec 14
|[[09-240/The Final Exam|Final on Dec 16]]
|- align=left
|colspan=3 align=center|[[09-240/To do|To Do List]]
|- align=left
|colspan=3 align=center|[[http://www.youtube.com/watch?v=UTby_e4-Rhg The Algebra Song!]]
|- align=left
|colspan=3 align=center|[[09-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:09-240-ClassPhoto.jpg|180px]]<br>[[09-240/Class Photo|Add your name / see who's in!]]
|}
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|}

Template:09-240/Navigation

2009-10-29T21:46:13Z

Sknad:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[09-240]]/[[Template:09-240/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 7
|<s>Tue</s>, [[09-240/About This Class|About]], [[09-240/Classnotes for Thursday September 10|Thu]]
|- align=left
|align=center|2
|Sep 14
|[[09-240/Classnotes for Tuesday September 15|Tue]], [[09-240:HW1|HW1]], [[09-240:HW1 Solution|HW1 Solution]], [[09-240/Classnotes for Thursday September 17|Thu]]
|- align=left
|align=center|3
|Sep 21
|[[09-240/Classnotes for Tuesday September 22|Tue]], [[09-240:HW2|HW2]], [[09-240:HW2 Solution|HW2 Solution]], [[09-240/Classnotes for Thursday September 24|Thu]], [[09-240/Class Photo|Photo]]
|- align=left
|align=center|4
|Sep 28
|[[09-240/Classnotes for Tuesday September 29|Tue]], [[09-240:HW3|HW3]], [[09-240:HW3 Solution|HW3 Solution]], [[09-240/Classnotes for Thursday October 1|Thu]]
|- align=left
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|Oct 5
|[[09-240/Classnotes for Tuesday October 6|Tue]], [[09-240:HW4|HW4]], [[09-240:HW4 Solution|HW4 Solution]], [[09-240/Classnotes for Thursday October 8|Thu]],
|- align=left
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|Oct 12
|[[09-240/Classnotes for Thursday October 15|Thu]]
|- align=left
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|Oct 19
|[[09-240/Classnotes for Tuesday October 20|Tue]], [[09-240:HW5|HW5]], [[09-240/Term Test|Term Test on Thu]]
|- align=left
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|Oct 26
|[[09-240/Linear Algebra - Why We Care|Why LinAlg?]], [[09-240:HW6|HW6]]
|- align=left
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|Nov 2
|
|- align=left
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|Nov 9
|[[09-240:HW7|HW7]], <s>Thu</s>
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|Nov 16
|[[09-240:HW8|HW8]]
|- align=left
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|Nov 23
|[[09-240:HW9|HW9]]
|- align=left
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|Nov 30
|[[09-240/On The Final Exam|On the final]]
|- align=left
|align=center|S
|Dec 7
|
|- align=left
|align=center|F
|Dec 14
|[[09-240/The Final Exam|Final on Dec 16]]
|- align=left
|colspan=3 align=center|[[09-240/To do|To Do List]]
|- align=left
|colspan=3 align=center|[[09-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:09-240-ClassPhoto.jpg|180px]]<br>[[09-240/Class Photo|Add your name / see who's in!]]
|}
</div></div>
|}

09-240/Term Test

2009-10-27T19:59:53Z

Sknad: /* Solution Set */

{{09-240/Navigation}}

==Announcement==

Our one and only Term Test is coming up. It will take place in class on Thursday October 22 2009, starting promptly at 1:10PM and ending at 3:00PM sharp, in our normal classroom, MP103. It will consist of 4-5 questions (each may have several parts) on everything that will be covered in class by October 16: the axiomatic definition of fields and some basic properties of fields, <math>{\mathbb C}</math> and other examples, a tiny bit on the field with <math>p</math> elements <math>F_p</math>, the axiomatic definition of vector spaces, basic properties and examples of vector spaces, 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 that do not deserve their own headers.

Note 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.

;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.

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

In style and spirit this exam will not be very different of the one I gave 3 years ago. See [[06-240/Term Test]].

==The Test==

===Front Page===

<center>

'''Do not turn this page until instructed.'''

<font style="font-size:150%">Math 240 Algebra I - Term Test</font>

University of Toronto, October 22, 2009

'''Solve the 5 problems on the other side of this page.'''

Each of the problems is worth 20 points.

You have an hour and 50 minutes.

'''Notes.'''

</center>

* No outside material other than stationary and a basic calculator is allowed.
* We will have an hour of discussion time right after this test.
* The final exam date was posted by the faculty --- it will take place on Wednesday December 16 from 9AM until noon at room BN2S of the Clara Benson Building, 320 Huron Street (south west of Harbord cross Huron, home of the Faculty of Physical Education and Health).

<center> '''Good Luck!''' </center>

===Questions Page===

'''Solve the following 5 problems.''' Each of the problems is worth 20 points. You have an hour and 50 minutes.

'''Problem 1.''' Let <math>V</math> be a vector space over a field <math>F</math>, let <math>c\in F</math> and let <math>v\in V</math>. Prove that if <math>cv=0</math>, then either <math>c=0</math> or <math>v=0</math>.

'''Problem 2.'''
# In the field <math>{\mathbb C}</math> of complex numbers, compute
<center><math>4i(1+i)</math>      and     <math>\frac{4i}{1+i}</math>.</center>
(To be precise, "compute" means "write in the form <math>a+ib</math>, where
<math>a,b\in{\mathbb R}</math>").
# In the field <math>{\mathbb C}</math> of complex numbers, find an element <math>z</math> so that <math>z^2=2i</math>.
# In the 11-element field <math>F_{11}</math> of remainders modulo 11, find
all solutions of the equation <math>x^2=-2</math>.

'''Problem 3.''' Let <math>V</math> be a vector space and let <math>W_1</math> and <math>W_2</math> be subspaces of <math>V</math>. Prove that <math>W_1\cup W_2</math> is a subspace of <math>V</math> iff <math>W_1\subset W_2</math> or <math>W_2\subset W_1</math>.

'''Problem 4.''' Let <math>u_1,\ldots,u_n</math> be vectors in a
vector space over the field with two element <math>F_2</math>. Show that the number of
elements in the set <math>\mbox{Span}\{u_1,\dots,u_n\}</math> is equal to <math>2^n</math> if and only
if <math>u_1,\ldots,u_n</math> are linearly independent..

'''Problem 5.''' Find a polynomial <math>f\in P_3({\mathbb R})</math> that
satisfies <math>f(-1)=5</math>, <math>f(0)=4</math>, <math>f(1)=3</math>, and <math>f(2)=8</math>.

<center> '''Good Luck!''' </center>

{{09-240/Results of the Term Test}}

==Solution Set==
Students are most welcome to post a solution set here.

'''Problem 1'''

If <math>a \cdot b = 0</math> and <math>a \neq 0,</math>

then <math>a^{-1} \cdot (a \cdot b) = 0;</math>

thus <math>(a^{-1} \cdot a) \cdot b = 0;</math>

thus <math>1 \cdot b = 0;</math>

thus <math>b = 0.</math>

It should be remembered that "or" means "one or the other, or both."

'''Problem 2'''

(1)

<math>4i(1 + i) = 4i + 4i^2 = -4 + 4i</math>

<math>\frac{4i}{1+i} = \frac{4i(1 - i)}{(1 + i)(1 - i)} = \frac{4 + 4i}{2} = 2 + 2i</math>

(2)

If <math>z^2 = 2i</math> then <math>z = 1 + i \Rightarrow (1 + i)^2 = 1 + 2i + i^2 = 2i</math>

(3)

<math>x = 8, 3</math>

'''Problem 3'''

'''Problem 4'''

'''Problem 5'''

Recall that<math> f_i(x) = \prod_{k = 0 k \neq i}^{n}{\frac{x - c_k}{c_i - c_k}}</math> and that <math>g(x) = \sum_{i = 0}^{n}{b_if_i}</math>

After tedious computation with the addition of eraser bits covering your paper, you should obtain the following:

<math>f_0(x) = -\frac{1}{6}(x^3 - 3x^2 + 2x)</math>

<math>f_1(x) = \frac{1}{2}(x^3 - 2x^2 - x + 2)</math>

<math>f_2(x) = -\frac{1}{2}(x^3 - x^2 - 2x)</math>

<math>f_3(x) = \frac{1}{6}(x^3 - x)</math>

Therefore,

<math>g(x) = 5 \cdot -\frac{1}{6}(x^3 - 3x^2 + 2x) + 4 \cdot \frac{1}{2}(x^3 - 2x^2 - x + 2) + 3 \cdot -\frac{1}{2}(x^3 - x^2 - 2x) + 8 \cdot \frac{1}{6}(x^3 - x)</math>

Infinitely many eraser bits later...

<math>g(x) = x^3 - 2x + 4</math>

09-240/Term Test

2009-10-27T19:24:55Z

Sknad: /* Solution Set */

09-240/Class Photo

2009-10-21T03:13:30Z

Sknad: /* Who We Are... */

Our class on September 24, 2009:

[[Image:09-240-ClassPhoto.jpg|thumb|centre|500px|Class Photo: click to enlarge]]
{{09-240/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 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=Bahadur|first=Jared|userid=bahadurj|email=jared.bahadur@ utoronto.ca| location=left index fingernail visible on handrail at Bar-Natan's right|comments=}}
{{Photo Entry|last=Barkley|first=Max|userid=SpectralWolf|email=max.barkley@ utoronto.ca|location=fourth guy from the left in the front row, beside the guy with the huge mouth|comments=}}
{{Photo Entry|last=Binder|first=Polina|userid=polyacat|email=polina.binder@ utoronto.ca|location= The girl in blue, to the right of the stairs at the top.|comments=}}
{{Photo Entry|last=Chen|first=Yi Le|userid=AlecC|email=alec.chen@ utoronto.ca|location= the guy in black T-shirt at 2nd to the left, on the 2nd standing row, with glasses|comments=}}
{{Photo Entry|last=Chou|first=Daniel|userid=Danielchou|email=daniel.chou@ utoronto.ca|location=the guy above the guy with the yellow shirt.|comments=Hi People.}}
{{Photo Entry|last=Chung|first=Ha Yoon|userid=babo|email=hayoon.chung@ utoronto.ca|location= the guy above k.ott|comments=I'm hungry.}}
{{Photo Entry|last=Chung|first=Wen-Jian|userid=cwjian90|email=cwjian90@ yahoo.com|location= top right corner, guy with Einstein's face on his shirt.|comments=}}
{{Photo Entry|last=Danks|first=Andrew|userid=Sknad|email=a.danks at utoronto.ca|location=Towards middle; maroon shirt|comments=}}
{{Photo Entry|last=Desmarais|first=Eric|userid=EricD|email=eric.desmarais@ utoronto.ca|location=back row, two to the right of the centre lamp post with the beard and glasses and the "has the picture been taken?" look.|comments=}}
{{Photo Entry|last=Dranovski|first=Anne|userid=anne.d|email=a.dranovski@ utoronto.ca|location=third row, sitting, green and happy.|comments=}}
{{Photo Entry|last=Gafar|first=Jonathan|userid=JG89|email=jonathan.gafar@ utoronto.ca|location=the guy in the last row to the right of the big pole.|comments=}}
{{Photo Entry|last=Gu|first=Hyungmo|userid=Hmgu7|email=moe.gu@ utoronto.ca|location=the guy with brown
shirt in the fifth row, third from the right.|comments=}}
{{Photo Entry|last=Ivanov|first=Vesselin|userid=Gungrave|email=vesselin.ivanov@ utoronto.ca|location=Last row, 7th from the right, with a shiny dog-tag.|comments=}}
{{Photo Entry|last=Jeffery|first=Travis|userid=Travisjeffery|email=t.jeffery@ utoronto.ca|location=Blue sweater, headphones around neck on the left.|comments=Ask her to wait a moment--I am almost done.}}
{{Photo Entry|last=Klambauer|first=Max|userid=Max.k|email=maximilian. klambauer@ utoronto.ca|location=Last row, almost as far right as possible; I'm the guy with long hair hidden behind the other guy with long, black hair.|comments=}}
{{Photo Entry|last=Lee|first=Joonhan|userid=Joonhan86|email=tomko_lee@ hotmail.com|location= one small single picture at top right hand side|comments=}}
{{Photo Entry|last=Li|first=Zhao|userid=lzh8571|email=lzh8571@ live.com|location=at the 4th from right in the top right picture, with glasses and jacket|comments=}}
{{Photo Entry|last=Lindquist|first=Emma|userid=Elindquist|email=emmalindquist@ utoronto.ca|location=Far left of front row|comments=}}
{{Photo Entry|last=Makarov|first=Serhei|userid=Serhei|email=serhei.makarov@ utoronto.ca|location=gray shirt, standing on the step under the guy with fingers on the rail (i.e. bahadurj)|comments=}}
{{Photo Entry|last=Mann|first=Alex|userid=Mannimal|email=alexander.mann@ utoronto.ca|location=last row, third guy to the right of the guy on the rail|comments=240>157}}
{{Photo Entry|last=Mantynen|first=Paul|userid=mantynen|email=paul.mantynen@ utoronto.ca| location= 4th row, third from the right in a black shirt|comments=}}
{{Photo Entry|last=McTaggart|first=Raymond|userid=Raymct|email=raymond.mctaggart@ gmail.com|location=Flying in the top-right sky. The one with the black t-shirt|comments= be <math> \mathbb{R} </math>}}
{{Photo Entry|last=Miao|first=Ying|userid=Miaoying|email=ying.miao@ utoronto.ca|location=girl beside the guy who was wearing blue cap and smiling happily.|comments=}}
{{Photo Entry|last=Michaud|first=Adam|userid=Invariel|email=invariel@ gmail.com|location=Back row, black coat, dark hair, full, dark beard, fifth from the right.|comments=Braaaaaaains...}}
{{Photo Entry|last=Milcak|first=Juraj|userid=Milcak|email=j.milcak@ utoronto.ca|location=2nd row, 1st from the right, green shirt|comments=}}
{{Photo Entry|last=Muthurajah|first=Michael Praveen|userid=Michael.muthurajah|email=michael.muthurajah@ utoronto.ca|location=farthest right but in the middle of the picture,the brown guy with a black cap wearing blue jeans carrying a backpack on my right shoulder|comments=It's a pleasure to be in this class,math answers everything}}
{{Photo Entry|last=Nikitakis|first=George|userid=GeorgeN|email=george.nikitakis@ utoronto.ca|location=Part of the group floating in the top right corner. Second from the left|comments=}}
{{Photo Entry|last=Ott|first=Kristian|userid=k.ott|email=k.ott@ utoronto.ca| location= 4th guy from the right in the second row, wearing a green striped sweater|comments=}}
{{Photo Entry|last=Park|first=Sanghee|userid=SangheeP|email=shee.park@ utoronto.ca|location=glasses, a girl, first row, third from right, holding starbucks."|comments=}}
{{Photo Entry|last=Pistone|first=Jamie|userid=JPistone|email=jamie.pistone@ utoronto.ca|location=Guy in the second row on the outside of the left railing, guarded by the two guys with their arms crossed.|comments=}}
{{Photo Entry|last=Popescu|first=Radu|userid=RPopescu|email=radu.popescu@ utoronto.ca|location=Top left-hand box, second from the right|comments=}}
{{Photo Entry|last=Ramdhayan|first=Dinesh|userid=Dinesh®|email=dinesh.ramdhayan@ utoronto.ca|location=top left corner, 4th from the left|comments=}}
{{Photo Entry|last=Roias|first=Stephen|userid=Sven|email=stephen.roias@ utoronto.ca|location=top right corner, furthest right|comments=}}
{{Photo Entry|last=Simmons|first=Olivia|userid=OSimmons|email=olivia.simmons@ yahoo.ca|location=girl on the second top rown two people from the right|comments=}}
{{Photo Entry|last=Simpson|first=Evan|userid=ESimpson|email=evan.simpson@ utoronto.ca|location=2nd Front Row, 2nd from the left, Green Shirt, Glasses|comments=Math is addictive don't try it.}}
{{Photo Entry|last=Sinn|first=Daniel|userid=c8sd|email=|location=second-last row, fourth from left|comments=}}
{{Photo Entry|last=Valdez|first=Wilbur|userid=Valdez84|email=wilbur.valdez@ utoronto.ca|location= Third row yellow shirt guy :)|comments=}}
{{Photo Entry|last=VanZanten|first=Johan|userid=jvzanten|email=j.vanzanten@ utoronto.ca|location=first guy in blue shirt standing on the left of left railing |comments=}}
{{Photo Entry|last=Wang|first=Yu|userid=Bright|email=bright_wangca@ hotmail.com|location=6th row (i think), 5th person from right, white shirt. Behind the guy with a plaid shirt and glasses.|comments=}}
{{Photo Entry|last=Zapf-Belanger|first=Erik|userid=erikzb|email=erikzb@ gmail.com|location=the guy third from the left in the front with the gigantic mouth|comments=Live long and prosper.}}
{{Photo Entry|last=Zhao|first=Yi|userid=zy861|email=zy861100@ hotmail.com|location=guy at the 6th row and 4th from right, with grey shirt and black glasses|comments=}}

09-240/Class Photo

2009-10-21T03:10:31Z

Sknad: /* Who We Are... */

Our class on September 24, 2009:

[[Image:09-240-ClassPhoto.jpg|thumb|centre|500px|Class Photo: click to enlarge]]
{{09-240/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 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=Bahadur|first=Jared|userid=bahadurj|email=jared.bahadur@ utoronto.ca| location=left index fingernail visible on handrail at Bar-Natan's right|comments=}}
{{Photo Entry|last=Barkley|first=Max|userid=SpectralWolf|email=max.barkley@ utoronto.ca|location=fourth guy from the left in the front row, beside the guy with the huge mouth|comments=}}
{{Photo Entry|last=Binder|first=Polina|userid=polyacat|email=polina.binder@ utoronto.ca|location= The girl in blue, to the right of the stairs at the top.|comments=}}
{{Photo Entry|last=Chen|first=Yi Le|userid=AlecC|email=alec.chen@ utoronto.ca|location= the guy in black T-shirt at 2nd to the left, on the 2nd standing row, with glasses|comments=}}
{{Photo Entry|last=Chou|first=Daniel|userid=Danielchou|email=daniel.chou@ utoronto.ca|location=the guy above the guy with the yellow shirt.|comments=Hi People.}}
{{Photo Entry|last=Chung|first=Ha Yoon|userid=babo|email=hayoon.chung@ utoronto.ca|location= the guy above k.ott|comments=I'm hungry.}}
{{Photo Entry|last=Chung|first=Wen-Jian|userid=cwjian90|email=cwjian90@ yahoo.com|location= top right corner, guy with Einstein's face on his shirt.|comments=}}
{{Photo Entry|last=Danks|first=Andrew|userid=Sknad|email=a.danks at utoronto.ca|location=|comments=}}
{{Photo Entry|last=Desmarais|first=Eric|userid=EricD|email=eric.desmarais@ utoronto.ca|location=back row, two to the right of the centre lamp post with the beard and glasses and the "has the picture been taken?" look.|comments=}}
{{Photo Entry|last=Dranovski|first=Anne|userid=anne.d|email=a.dranovski@ utoronto.ca|location=third row, sitting, green and happy.|comments=}}
{{Photo Entry|last=Gafar|first=Jonathan|userid=JG89|email=jonathan.gafar@ utoronto.ca|location=the guy in the last row to the right of the big pole.|comments=}}
{{Photo Entry|last=Gu|first=Hyungmo|userid=Hmgu7|email=moe.gu@ utoronto.ca|location=the guy with brown
shirt in the fifth row, third from the right.|comments=}}
{{Photo Entry|last=Ivanov|first=Vesselin|userid=Gungrave|email=vesselin.ivanov@ utoronto.ca|location=Last row, 7th from the right, with a shiny dog-tag.|comments=}}
{{Photo Entry|last=Jeffery|first=Travis|userid=Travisjeffery|email=t.jeffery@ utoronto.ca|location=Blue sweater, headphones around neck on the left.|comments=Ask her to wait a moment--I am almost done.}}
{{Photo Entry|last=Klambauer|first=Max|userid=Max.k|email=maximilian. klambauer@ utoronto.ca|location=Last row, almost as far right as possible; I'm the guy with long hair hidden behind the other guy with long, black hair.|comments=}}
{{Photo Entry|last=Lee|first=Joonhan|userid=Joonhan86|email=tomko_lee@ hotmail.com|location= one small single picture at top right hand side|comments=}}
{{Photo Entry|last=Li|first=Zhao|userid=lzh8571|email=lzh8571@ live.com|location=at the 4th from right in the top right picture, with glasses and jacket|comments=}}
{{Photo Entry|last=Lindquist|first=Emma|userid=Elindquist|email=emmalindquist@ utoronto.ca|location=Far left of front row|comments=}}
{{Photo Entry|last=Makarov|first=Serhei|userid=Serhei|email=serhei.makarov@ utoronto.ca|location=gray shirt, standing on the step under the guy with fingers on the rail (i.e. bahadurj)|comments=}}
{{Photo Entry|last=Mann|first=Alex|userid=Mannimal|email=alexander.mann@ utoronto.ca|location=last row, third guy to the right of the guy on the rail|comments=240>157}}
{{Photo Entry|last=Mantynen|first=Paul|userid=mantynen|email=paul.mantynen@ utoronto.ca| location= 4th row, third from the right in a black shirt|comments=}}
{{Photo Entry|last=McTaggart|first=Raymond|userid=Raymct|email=raymond.mctaggart@ gmail.com|location=Flying in the top-right sky. The one with the black t-shirt|comments= be <math> \mathbb{R} </math>}}
{{Photo Entry|last=Miao|first=Ying|userid=Miaoying|email=ying.miao@ utoronto.ca|location=girl beside the guy who was wearing blue cap and smiling happily.|comments=}}
{{Photo Entry|last=Michaud|first=Adam|userid=Invariel|email=invariel@ gmail.com|location=Back row, black coat, dark hair, full, dark beard, fifth from the right.|comments=Braaaaaaains...}}
{{Photo Entry|last=Milcak|first=Juraj|userid=Milcak|email=j.milcak@ utoronto.ca|location=2nd row, 1st from the right, green shirt|comments=}}
{{Photo Entry|last=Muthurajah|first=Michael Praveen|userid=Michael.muthurajah|email=michael.muthurajah@ utoronto.ca|location=farthest right but in the middle of the picture,the brown guy with a black cap wearing blue jeans carrying a backpack on my right shoulder|comments=It's a pleasure to be in this class,math answers everything}}
{{Photo Entry|last=Nikitakis|first=George|userid=GeorgeN|email=george.nikitakis@ utoronto.ca|location=Part of the group floating in the top right corner. Second from the left|comments=}}
{{Photo Entry|last=Ott|first=Kristian|userid=k.ott|email=k.ott@ utoronto.ca| location= 4th guy from the right in the second row, wearing a green striped sweater|comments=}}
{{Photo Entry|last=Park|first=Sanghee|userid=SangheeP|email=shee.park@ utoronto.ca|location=glasses, a girl, first row, third from right, holding starbucks."|comments=}}
{{Photo Entry|last=Pistone|first=Jamie|userid=JPistone|email=jamie.pistone@ utoronto.ca|location=Guy in the second row on the outside of the left railing, guarded by the two guys with their arms crossed.|comments=}}
{{Photo Entry|last=Popescu|first=Radu|userid=RPopescu|email=radu.popescu@ utoronto.ca|location=Top left-hand box, second from the right|comments=}}
{{Photo Entry|last=Ramdhayan|first=Dinesh|userid=Dinesh®|email=dinesh.ramdhayan@ utoronto.ca|location=top left corner, 4th from the left|comments=}}
{{Photo Entry|last=Roias|first=Stephen|userid=Sven|email=stephen.roias@ utoronto.ca|location=top right corner, furthest right|comments=}}
{{Photo Entry|last=Simmons|first=Olivia|userid=OSimmons|email=olivia.simmons@ yahoo.ca|location=girl on the second top rown two people from the right|comments=}}
{{Photo Entry|last=Simpson|first=Evan|userid=ESimpson|email=evan.simpson@ utoronto.ca|location=2nd Front Row, 2nd from the left, Green Shirt, Glasses|comments=Math is addictive don't try it.}}
{{Photo Entry|last=Sinn|first=Daniel|userid=c8sd|email=|location=second-last row, fourth from left|comments=}}
{{Photo Entry|last=Valdez|first=Wilbur|userid=Valdez84|email=wilbur.valdez@ utoronto.ca|location= Third row yellow shirt guy :)|comments=}}
{{Photo Entry|last=VanZanten|first=Johan|userid=jvzanten|email=j.vanzanten@ utoronto.ca|location=first guy in blue shirt standing on the left of left railing |comments=}}
{{Photo Entry|last=Wang|first=Yu|userid=Bright|email=bright_wangca@ hotmail.com|location=6th row (i think), 5th person from right, white shirt. Behind the guy with a plaid shirt and glasses.|comments=}}
{{Photo Entry|last=Zapf-Belanger|first=Erik|userid=erikzb|email=erikzb@ gmail.com|location=the guy third from the left in the front with the gigantic mouth|comments=Live long and prosper.}}
{{Photo Entry|last=Zhao|first=Yi|userid=zy861|email=zy861100@ hotmail.com|location=guy at the 6th row and 4th from right, with grey shirt and black glasses|comments=}}