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Week of...
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Notes and Links
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| 1
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Sep 10
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About This Class, Tuesday, Thursday
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| 2
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Sep 17
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HW1, Tuesday, Thursday, HW1 Solutions
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| 3
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Sep 24
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HW2, Tuesday, Class Photo, Thursday
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| 4
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Oct 1
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HW3, Tuesday, Thursday
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| 5
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Oct 8
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HW4, Tuesday, Thursday
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| 6
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Oct 15
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Tuesday, Thursday
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| 7
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Oct 22
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HW5, Tuesday, Term Test was on Thursday. HW5 Solutions
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| 8
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Oct 29
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Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class
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| 9
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Nov 5
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Tuesday, Thursday
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| 10
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Nov 12
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Monday-Tuesday is UofT November break, HW7, Thursday
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| 11
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Nov 19
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HW8, Tuesday,Thursday
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| 12
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Nov 26
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HW9, Tuesday , Thursday
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| 13
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Dec 3
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Tuesday UofT Fall Semester ends Wednesday
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| F
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Dec 10
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The Final Exam (time, place, style, office hours times)
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| Register of Good Deeds
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Add your name / see who's in!
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Various properties of fields
Thrm: In a field F:
1. a+b = c+b ⇒ a=c
2. b≠0, a∙b=c∙b ⇒ a=c
3. 0 is unique.
4. 1 is unique.
5. -a is unique.
6. a^-1 is unique (a≠0)
7. -(-a)=a
8. (a^-1)^-1 =a
9. a∙0=0 **Surprisingly difficult, required distributivity.
10. ∄ 0^-1, aka, ∄ b∈F s.t 0∙b=1
11. (-a)∙(-b)=a∙b
12. a∙b=0 iff a=0 or b=0
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16. (a+b)∙(a-b)= a^2 - b^2
[Define a^2 = a∙a]
Hint: Use distributive law
Thrm 2: Given a field F, there exists a map Ɩ: Z → F with the properties:
1) Ɩ(0) =0, Ɩ(1)=1
2) Ɩ(m+n) = Ɩ(m) +Ɩ(n)
3) Ɩ(mn) = Ɩ(m)∙Ɩ(n)
Furthermore, Ɩ is unique.
