Drorbn - User contributions [en]

File:07-401 hm9.pdf

2007-04-18T14:07:40Z

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07-401 Solutions

2007-04-18T14:07:21Z

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[[Image:07-401 hm9.pdf]]

07-401 Solutions

2007-04-18T14:06:48Z

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07-401/Homework Assignment 9

2007-04-18T14:06:36Z

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{{07-401/Navigation}}

===Reading===
Read chapter 32 of Gallian's book three times:
* First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
* And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.

===Doing===
Solve problems 22#, 23, 24#, 25, 26# and 27# in Chapter 32 of Gallian's book but submit only the solutions of the problems marked with a sharp (#).

===Due Date===
This assignment is due in class on Wednesday April 4, 2007.

[[07-401 Solutions|Solutions]]

===Just for Fun===

# Explain how the group <math>O(3</math>) of rigid rotations of <math>{\mathbb R}^3</math> can be identified with the subgroup <math>\{A\in M_{3\times 3}({\mathbb R}):\, A^TA=I\}</math> of the group of invertible <math>3\times 3</math> matrices.
# Prove that <math>O(3)</math> is not solvable (though note that the similarly-defined group <math>O(2)</math> is solvable).

07-401/Homework Assignment 9

2007-04-18T14:06:28Z

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{{07-401/Navigation}}

===Reading===
Read chapter 32 of Gallian's book three times:
* First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
* And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.

===Doing===
Solve problems 22#, 23, 24#, 25, 26# and 27# in Chapter 32 of Gallian's book but submit only the solutions of the problems marked with a sharp (#).

===Due Date===
This assignment is due in class on Wednesday April 4, 2007.

===Just for Fun===

# Explain how the group <math>O(3</math>) of rigid rotations of <math>{\mathbb R}^3</math> can be identified with the subgroup <math>\{A\in M_{3\times 3}({\mathbb R}):\, A^TA=I\}</math> of the group of invertible <math>3\times 3</math> matrices.
# Prove that <math>O(3)</math> is not solvable (though note that the similarly-defined group <math>O(2)</math> is solvable).

Template:07-401/Navigation

2007-04-07T15:34:50Z

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{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
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{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
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!#
!Week of...
!Links
|- align=left
|align=center|1
|Jan 10
|[[07-401/About This Class|About]], [[07-401/Class Notes for January 10|Notes]], [[07-401/Homework Assignment 1|HW1]]
|- align=left
|align=center|2
|Jan 17
|[[07-401/Homework Assignment 2|HW2]], [[07-401/Class Notes for January 17|Notes]]
|- align=left
|align=center|3
|Jan 24
|[[07-401/Homework Assignment 3|HW3]], [[07-401/Class Photo|Photo]], [[07-401/Class Notes for January 24|Notes]]
|- align=left
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|Jan 31
|[[07-401/Homework Assignment 4|HW4]], [[07-401/Class Notes for January 31|Notes]]
|- align=left
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|Feb 7
|[[07-401/Homework Assignment 5|HW5]], [[07-401/Class Notes for February 7|Notes]]
|- align=left
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|Feb 14
|[[07-401/On the Term Test|On TT]], [[07-401/Class Notes for February 14|Notes]]
|- align=left
|align=center|R
|Feb 21
|Reading week
|- align=left
|align=center|7
|Feb 28
|[[07-401/Term Test|Term Test]]
|- align=left
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|Mar 7
|[[07-401/Homework Assignment 6|HW6]], [[07-401/Class Notes for March 7|Notes]]
|- align=left
|align=center|9
|Mar 14
|[[07-401/Homework Assignment 7|HW7]], [[07-401/Class Notes for March 14|Notes]]
|- align=left
|align=center|10
|Mar 21
|[[07-401/Homework Assignment 8|HW8]], [[07-401/G&M Article|E8]], [[07-401/Class Notes for March 21|Notes]]
|- align=left
|align=center|11
|Mar 28
|[[07-401/Homework Assignment 9|HW9]], [[07-401/Class Notes for March 28|Notes]]
|- align=left
|align=center|12
|Apr 4
|[[07-401/Homework Assignment 10 (and last!)|HW10]], [[07-401/Class Notes for April 4|Notes]]
|- align=left
|align=center|13
|Apr 11
|[[07-401/Class Notes for April 11|Notes]], [[07-401/Class Evaluation|Eval]]
|- align=left
|align=center|S
|Apr 16-20
|Study Period
|- align=left
|align=center|F
|Apr 24
|[[07-401/The Final Exam|Final]]
|-
|colspan=3 align=center|[[Image:07-401 Class Photo.jpg|180px]]<br>[[07-401/Class Photo|Add your name / see who's in!]]
|-
|colspan=3 align=center|[[07-401/Register of Good Deeds|Register of Good Deeds]]
|}
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|}

Template:07-401/Navigation

2007-04-07T15:25:31Z

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{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
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{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|- align=center
!#
!Week of...
!Links
|- align=left
|align=center|1
|Jan 10
|[[07-401/About This Class|About]], [[07-401/Class Notes for January 10|Notes]], [[07-401/Homework Assignment 1|HW1]]
|- align=left
|align=center|2
|Jan 17
|[[07-401/Homework Assignment 2|HW2]], [[07-401/Class Notes for January 17|Notes]]
|- align=left
|align=center|3
|Jan 24
|[[07-401/Homework Assignment 3|HW3]], [[07-401/Class Photo|Photo]], [[07-401/Class Notes for January 24|Notes]]
|- align=left
|align=center|4
|Jan 31
|[[07-401/Homework Assignment 4|HW4]], [[07-401/Class Notes for January 31|Notes]]
|- align=left
|align=center|5
|Feb 7
|[[07-401/Homework Assignment 5|HW5]], [[07-401/Class Notes for February 7|Notes]]
|- align=left
|align=center|6
|Feb 14
|[[07-401/On the Term Test|On TT]], [[07-401/Class Notes for February 14|Notes]]
|- align=left
|align=center|R
|Feb 21
|Reading week
|- align=left
|align=center|7
|Feb 28
|[[07-401/Term Test|Term Test]]
|- align=left
|align=center|8
|Mar 7
|[[07-401/Homework Assignment 6|HW6]], [[07-401/Class Notes for March 7|Notes]]
|- align=left
|align=center|9
|Mar 14
|[[07-401/Homework Assignment 7|HW7]], [[07-401/Class Notes for March 14|Notes]]
|- align=left
|align=center|10
|Mar 21
|[[07-401/Homework Assignment 8|HW8]], [[07-401/G&M Article|E8]], [[07-401/Class Notes for March 21|Notes]]
|- align=left
|align=center|11
|Mar 28
|[[07-401/Homework Assignment 9|HW9]], [[07-401/Class Notes for March 28|Notes]]
|- align=left
|align=center|12
|Apr 4
|[[07-401/Homework Assignment 10 (and last!)|HW10]], [[07-401/Class Notes for April 4|Notes]]
|- align=left
|align=center|13
|Apr 11
|[[07-401/Class Notes for April 11|Notes]], [[07-401/Class Evaluation|Eval]]
|- align=left
|align=center|S
|Apr 16-20
|Study Period
|- align=left
|align=center|F
|Apr 24
|[[07-401/The Final Exam|Final]], [[07-401/Book Review|Review Notes]]
|-
|colspan=3 align=center|[[Image:07-401 Class Photo.jpg|180px]]<br>[[07-401/Class Photo|Add your name / see who's in!]]
|-
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07-401/G&M Article

2007-03-21T21:22:31Z

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{{07-401/Navigation}}

I found this today on the Globe and Mail newspaper website.
Thought it might interest some of you.
Here is the link to the article:
http://www.theglobeandmail.com/servlet/story/RTGAM.20070320.wmathpuz0320/BNStory/Science/home

07-401/G&M Article

2007-03-21T15:23:10Z

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I found this today on the Globe and Mail newspaper website.
Thought it might interest some of you.

-----------------------------------
'''120-year-old math puzzle solved'''
Associated Press

PALO ALTO, Calif. — An international team of mathematicians has cracked a 120-year-old puzzle that researchers say is so complicated its handwritten solution would cover the island of Manhattan.

The 18-member group of mathematicians and computer scientists was convened by the American Institute of Mathematics in Palo Alto to map a theoretical object known as the “Lie group E8.”

Lie (pronounced Lee) groups were invented by 19th-century Norwegian mathematician Sophus Lie in his study of symmetrical objects, especially spheres, and differential calculus.

The E8 group, which dates to 1887, is the most complicated Lie group, with 248 dimensions, and was long considered impossible to solve.

“To say what precisely it is is something even many mathematicians can't understand,” said Jeffrey Adams, the project's leader and a math professor at the University of Maryland.

The problem's proof, announced at the Massachusetts Institute of Technology, took the researchers four years to find. It involves about 60 times as much data as the Human Genome Project.

When stored in highly compressed form on a computer hard drive, the solution takes up as much space as 45 days of continuous music in MP3 format.

“It's like a Mount Everest of mathematical structures they've climbed now,” said Brian Conrey, director of the institute.

The calculation does not have any obvious practical applications but could help advance theoretical physics and geometry, researchers said.

Template:07-401/Navigation

2007-03-21T15:19:46Z

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{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[07-401]]/[[Template:07-401/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=center
!#
!Week of...
!Links
|- align=left
|align=center|1
|Jan 10
|[[07-401/About This Class|About]], [[07-401/Class Notes for January 10|Notes]], [[07-401/Homework Assignment 1|HW1]]
|- align=left
|align=center|2
|Jan 17
|[[07-401/Homework Assignment 2|HW2]], [[07-401/Class Notes for January 17|Notes]]
|- align=left
|align=center|3
|Jan 24
|[[07-401/Homework Assignment 3|HW3]], [[07-401/Class Photo|Photo]], [[07-401/Class Notes for January 24|Notes]]
|- align=left
|align=center|4
|Jan 31
|[[07-401/Homework Assignment 4|HW4]], [[07-401/Class Notes for January 31|Notes]]
|- align=left
|align=center|5
|Feb 7
|[[07-401/Homework Assignment 5|HW5]], [[07-401/Class Notes for February 7|Notes]]
|- align=left
|align=center|6
|Feb 14
|[[07-401/On the Term Test|On TT]], [[07-401/Class Notes for February 14|Notes]]
|- align=left
|align=center|R
|Feb 21
|Reading week
|- align=left
|align=center|7
|Feb 28
|[[07-401/Term Test|Term Test]]
|- align=left
|align=center|8
|Mar 7
|[[07-401/Homework Assignment 6|HW6]], [[07-401/Class Notes for March 7|Notes]]
|- align=left
|align=center|9
|Mar 14
|[[07-401/Homework Assignment 7|HW7]], [[07-401/Class Notes for March 14|Notes]]
|- align=left
|align=center|10
|Mar 21
|[[07-401/Homework Assignment 8|HW8]], [[07-401/G&M Article|E8]]
|- align=left
|align=center|11
|Mar 28
|HW9
|- align=left
|align=center|12
|Apr 4
|HW10
|- align=left
|align=center|13
|Apr 11
|[[07-401/Class Evaluation|Eval]]
|- align=left
|align=center|S
|Apr 16-20
|Study Period
|- align=left
|align=center|F
|Apr 24
|[[07-401/The Final Exam|Final]]
|-
|colspan=3 align=center|[[Image:07-401 Class Photo.jpg|180px]]<br>[[07-401/Class Photo|Add your name / see who's in!]]
|-
|colspan=3 align=center|[[07-401/Register of Good Deeds|Register of Good Deeds]]
|}
</div></div>
|}

07-401/Notes

2007-03-08T05:08:25Z

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==Page 1==

[[Image:07-401 page1.jpg]]

[[Image:07-401 page2.jpg]]

[[Image:07-401 page3.jpg]]

[[Image:07-401 page4.jpg]]

[[Image:07-401 page5.jpg]]

[[Image:07-401 page6.jpg]]

[[Image:07-401 page7.jpg]]

[[Image:07-401 page8.jpg]]

[[Image:07-401 page9.jpg]]

File:07-401 page9.jpg

2007-03-08T05:07:03Z

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File:07-401 page8.jpg

2007-03-08T05:06:36Z

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File:07-401 page7.jpg

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File:07-401 page6.jpg

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File:07-401 page5.jpg

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File:07-401 page4.jpg

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File:07-401 page3.jpg

2007-03-08T05:04:22Z

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2007-03-08T05:03:57Z

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07-401/Notes

2007-03-08T05:03:41Z

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==Page 1==

[[Image:07-401 page1.jpg]]
[[Image:07-401 page2.jpg]]
[[Image:07-401 page3.jpg]]
[[Image:07-401 page4.jpg]]
[[Image:07-401 page5.jpg]]
[[Image:07-401 page6.jpg]]
[[Image:07-401 page7.jpg]]
[[Image:07-401 page8.jpg]]
[[Image:07-401 page9.jpg]]

File:07-401 page1.jpg

2007-03-08T05:02:29Z

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07-401/Notes

2007-03-08T05:02:13Z

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==Page 1==

[[Image:07-401 page1.jpg]]

07-401/Notes

2007-03-08T04:57:23Z

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== Page 1 ==

Lecture notes from week 8

[[Page 1]]

07-401/Notes

2007-03-08T03:20:47Z

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== Page 1 ==

Lecture notes from week 8

[[Image:07-401_lecture_wk8.tif]]

07-401/Notes

2007-03-08T03:18:00Z

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== Page 1 ==

Lecture notes from week 8

07-401/Class Notes for March 7

2007-03-08T03:17:37Z

Sm: /* Class Plan */

{{07-401/Navigation}}

==Class Plan==

Some discussion of the [[07-401/Term Test|term test]] and [[07-401/Homework Assignment 6|HW6]].

Some discussion of our general plan.

Lecture [[07-401/Notes|notes]]

===Extension Fields===

'''Definition.''' An extension field <math>E</math> of <math>F</math>.

'''Theorem.''' For every non-constant polynomial <math>f</math> in <math>F[x]</math> there is an extension <math>E</math> of <math>F</math> in which <math>f</math> has a zero.

'''Example''' <math>x^2+1</math> over <math>{\mathbb R}</math>.

'''Example''' <math>x^5+2x^2+2x+2=(x^2+1)(x^3+2x+2)</math> over <math>{\mathbb Z}/3</math>.

'''Definition.''' <math>F(a_1,\ldots,a_n)</math>.

'''Theorem.''' If <math>a</math> is a root of an irreducible polynomial <math>p\in F[x]</math>, within some extension field <math>E</math> of <math>F</math>, then <math>F(a)\cong F[x]/\langle p\rangle</math>, and <math>\{1,a,a^2,\ldots,a^{n-1}\}</math> (here <math>n=\deg p</math>) is a basis for <math>F(a)</math> over <math>F</math>.

'''Corollary.''' In this case, <math>F(a)</math> depends only on <math>p</math>.

===Splitting Fields===

'''Definition.''' <math>f\in F[x]</math> splits in <math>E/F</math>, a splitting field for <math>f</math> over <math>F</math>.

'''Theorem.''' A splitting field always exists.

'''Example.''' <math>x^4-x^2-2=(x^2-2)(x^2+1)</math> over <math>{\mathbb Q}</math>.

'''Example.''' Factor <math>x^2+x+2\in{\mathbb Z}_3[x]</math> within its splitting field <math>{\mathbb Z}_3[x]/\langle x^2+x+2\rangle</math>.

'''Theorem.''' Any two splitting fields for <math>f\in F[x]</math> over <math>F</math> are isomorphic.

'''Lemma 1.''' If <math>p\in F[x]</math> irreducible over <math>F</math>, <math>\phi:F\to F'</math> an isomorphism, <math>a</math> a root of <math>p</math> (in some <math>E/F</math>), <math>a'</math> a root of <math>\phi(p)</math> in some <math>E'/F'</math>, then <math>F(a)\cong F'(a')</math>.

'''Lemma 2.''' Isomorphisms can be extended to splitting fields.

===Zeros of Irreducible Polynomials===

'''Definition.''' The derivative of a polynomial.

'''Claim.''' The derivative operation is linear and satisfies Leibnitz's law.

'''Theorem.''' <math>f\in F[x]</math> has a multiple zero in some extension field of <math>F</math> iff <math>f</math> and <math>f'</math> have a common factor of positive degree.

'''Lemma.''' The property of "being relatively prime" is preserved under extensions.

'''Theorem.''' Let <math>f\in F[x]</math> be irreducible. If <math>\operatorname{char}F=0</math>, then <math>f</math> has no multiple zeros in any extension of <math>F</math>. If <math>\operatorname{char}F=p>0</math>, then <math>f</math> has multiple zeros (in some extension) iff it is of the form <math>g(x^p)</math> for some <math>g\in F[x]</math>.

'''Definition.''' A perfect field.

'''Theorem.''' A finite field is perfect.

'''Theorem.''' An irreducible polynomial over a perfect field has no multiple zeros (in any extension).

'''Theorem.''' Let <math>f\in F[x]</math> be irreducible and let <math>E</math> be the splitting field of <math>f</math> over <math>F</math>. Then in <math>E</math> all zeros of <math>f</math> have the same multiplicity.

'''Corollary.''' <math>f</math> as above must have the form <math>a(x-a_1)^n\cdots(x-a_k)^n</math> for some <math>a\in F</math> and <math>a_1,\ldots,a_k\in E</math>.

'''Example.''' <math>x^2-t\in{\mathbb Z}_2(t)[x]</math> is irreducible and has a single zero of multiplicity 2 within its splitting field over <math>{\mathbb Z}_2(t)[x]</math>.

07-401/Class Notes for March 7

2007-03-08T03:15:04Z

Sm: /* Class Plan */

{{07-401/Navigation}}

==Class Plan==

Some discussion of the [[07-401/Term Test|term test]] and [[07-401/Homework Assignment 6|HW6]].

Some discussion of our general plan.

Lecture notes [[07-401/Notes|notes]]

===Extension Fields===

'''Definition.''' An extension field <math>E</math> of <math>F</math>.

'''Theorem.''' For every non-constant polynomial <math>f</math> in <math>F[x]</math> there is an extension <math>E</math> of <math>F</math> in which <math>f</math> has a zero.

'''Example''' <math>x^2+1</math> over <math>{\mathbb R}</math>.

'''Example''' <math>x^5+2x^2+2x+2=(x^2+1)(x^3+2x+2)</math> over <math>{\mathbb Z}/3</math>.

'''Definition.''' <math>F(a_1,\ldots,a_n)</math>.

'''Theorem.''' If <math>a</math> is a root of an irreducible polynomial <math>p\in F[x]</math>, within some extension field <math>E</math> of <math>F</math>, then <math>F(a)\cong F[x]/\langle p\rangle</math>, and <math>\{1,a,a^2,\ldots,a^{n-1}\}</math> (here <math>n=\deg p</math>) is a basis for <math>F(a)</math> over <math>F</math>.

'''Corollary.''' In this case, <math>F(a)</math> depends only on <math>p</math>.

===Splitting Fields===

'''Definition.''' <math>f\in F[x]</math> splits in <math>E/F</math>, a splitting field for <math>f</math> over <math>F</math>.

'''Theorem.''' A splitting field always exists.

'''Example.''' <math>x^4-x^2-2=(x^2-2)(x^2+1)</math> over <math>{\mathbb Q}</math>.

'''Example.''' Factor <math>x^2+x+2\in{\mathbb Z}_3[x]</math> within its splitting field <math>{\mathbb Z}_3[x]/\langle x^2+x+2\rangle</math>.

'''Theorem.''' Any two splitting fields for <math>f\in F[x]</math> over <math>F</math> are isomorphic.

'''Lemma 1.''' If <math>p\in F[x]</math> irreducible over <math>F</math>, <math>\phi:F\to F'</math> an isomorphism, <math>a</math> a root of <math>p</math> (in some <math>E/F</math>), <math>a'</math> a root of <math>\phi(p)</math> in some <math>E'/F'</math>, then <math>F(a)\cong F'(a')</math>.

'''Lemma 2.''' Isomorphisms can be extended to splitting fields.

===Zeros of Irreducible Polynomials===

'''Definition.''' The derivative of a polynomial.

'''Claim.''' The derivative operation is linear and satisfies Leibnitz's law.

'''Theorem.''' <math>f\in F[x]</math> has a multiple zero in some extension field of <math>F</math> iff <math>f</math> and <math>f'</math> have a common factor of positive degree.

'''Lemma.''' The property of "being relatively prime" is preserved under extensions.

'''Theorem.''' Let <math>f\in F[x]</math> be irreducible. If <math>\operatorname{char}F=0</math>, then <math>f</math> has no multiple zeros in any extension of <math>F</math>. If <math>\operatorname{char}F=p>0</math>, then <math>f</math> has multiple zeros (in some extension) iff it is of the form <math>g(x^p)</math> for some <math>g\in F[x]</math>.

'''Definition.''' A perfect field.

'''Theorem.''' A finite field is perfect.

'''Theorem.''' An irreducible polynomial over a perfect field has no multiple zeros (in any extension).

'''Theorem.''' Let <math>f\in F[x]</math> be irreducible and let <math>E</math> be the splitting field of <math>f</math> over <math>F</math>. Then in <math>E</math> all zeros of <math>f</math> have the same multiplicity.

'''Corollary.''' <math>f</math> as above must have the form <math>a(x-a_1)^n\cdots(x-a_k)^n</math> for some <math>a\in F</math> and <math>a_1,\ldots,a_k\in E</math>.

'''Example.''' <math>x^2-t\in{\mathbb Z}_2(t)[x]</math> is irreducible and has a single zero of multiplicity 2 within its splitting field over <math>{\mathbb Z}_2(t)[x]</math>.

07-401/Class Notes for February 14

2007-02-15T00:09:13Z

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{{07-401/Navigation}}

==Page 1==

[[Image:07-401-Feb14-1.jpg|600px]]

==Page 2==

[[Image:07-401-Feb14-2.jpg|600px]]

Template:07-401/Navigation

2007-02-15T00:07:58Z

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{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[07-401]]/[[Template:07-401/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=center
!#
!Week of...
!Links
|- align=left
|align=center|1
|Jan 10
|[[07-401/About This Class|About]], [[07-401/Class Notes for January 10|Notes]], [[07-401/Homework Assignment 1|HW1]]
|- align=left
|align=center|2
|Jan 17
|[[07-401/Homework Assignment 2|HW2]], [[07-401/Class Notes for January 17|Notes]]
|- align=left
|align=center|3
|Jan 24
|[[07-401/Homework Assignment 3|HW3]], [[07-401/Class Photo|Photo]], [[07-401/Class Notes for January 24|Notes]]
|- align=left
|align=center|4
|Jan 31
|[[07-401/Homework Assignment 4|HW4]]
|- align=left
|align=center|5
|Feb 7
|[[07-401/Homework Assignment 5|HW5]]
|- align=left
|align=center|6
|Feb 14
|[[07-401/On the Term Test|On TT]], [[07-401/Class Notes for February 14|Notes]]
|- align=left
|align=center|R
|Feb 21
|Reading week
|- align=left
|align=center|7
|Feb 28
|TT
|- align=left
|align=center|8
|Mar 7
|HW6
|- align=left
|align=center|9
|Mar 14
|HW7
|- align=left
|align=center|10
|Mar 21
|HW8
|- align=left
|align=center|11
|Mar 28
|HW9
|- align=left
|align=center|12
|Apr 4
|HW10
|- align=left
|align=center|13
|Apr 11
|
|-
|colspan=3 align=center|[[Image:07-401 Class Photo.jpg|180px]]<br>[[07-401/Class Photo|Add your name / see who's in!]]
|-
|colspan=3 align=center|[[07-401/Register of Good Deeds|Register of Good Deeds]]
|}
</div></div>
|}
<div align=center>Our <font color=red>'''Term Test'''</font> is on February 28 at 6:20PM at <font color=red>'''Galbraith (GB) 120'''</font>. [[07-401/On the Term Test|Read more.]]</div>

Talk:07-401/About This Class

2007-02-01T01:10:53Z

Sm:

Prof, May you please clarify the date for our midterm. Is it February 28th or March 7th?
Thanks!!!

07-401/Class Photo

2007-01-25T23:42:31Z

Sm: /* Who We Are... */

{{07-401/Navigation}}

Our class on Janury 24, 2007:

[[Image:07-401 Class Photo.jpg|thumb|centre|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=Castro|first=Caroline|userid=Carrot|email=caroline.castro@utoronto.ca|
location=the tall person at the very top of the stairs with the grey hat|comments=no comment.}}
{{Photo Entry|last=Henderson|first=Sean|userid=sean_henderson|email=sean.henderson[at]utoronto.ca|location=front row, far left|comments=no comment.}}
{{Photo Entry|last=Maniak|first=Sylvia|userid=sm|email=sylvia.maniak[at]gmail.com|location=front row, the blonde wearing a black shirt|comments=no comment.}}

07-401/Class Photo

2007-01-25T23:40:07Z

Sm: /* Who We Are... */

{{07-401/Navigation}}

Our class on Janury 24, 2007:

[[Image:07-401 Class Photo.jpg|thumb|centre|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 Sylvia
!Last name Maniak
!UserID sm
!Email sylvia.maniak@gmail.com
!In the photo blonde in the black shirt, first row
!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=Castro|first=Caroline|userid=Carrot|email=caroline.castro@utoronto.ca|
location=the tall person at the very top of the stairs with the grey hat|comments=no comment.}}
{{Photo Entry|last=Henderson|first=Sean|userid=sean_henderson|email=sean.henderson[at]utoronto.ca|location=front row, far left|comments=no comment.}}