12-240/Classnotes for Thursday September 13: Difference between revisions

Revision as of 16:42, 13 September 2012

#	Week of...	Notes and Links
Additions to this web site no longer count towards good deed points.
1	Sep 10	About This Class, Tuesday, Thursday
2	Sep 17	HW1, Tuesday, Thursday, HW1 Solutions
3	Sep 24	HW2, Tuesday, Class Photo, Thursday
4	Oct 1	HW3, Tuesday, Thursday
5	Oct 8	HW4, Tuesday, Thursday
6	Oct 15	Tuesday, Thursday
7	Oct 22	HW5, Tuesday, Term Test was on Thursday. HW5 Solutions
8	Oct 29	Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class
9	Nov 5	Tuesday, Thursday
10	Nov 12	Monday-Tuesday is UofT November break, HW7, Thursday
11	Nov 19	HW8, Tuesday,Thursday
12	Nov 26	HW9, Tuesday , Thursday
13	Dec 3	Tuesday UofT Fall Semester ends Wednesday
F	Dec 10	The Final Exam (time, place, style, office hours times)
Register of Good Deeds
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In the second day of the class, the professor continues on the definition of a field.

Combined with a part from the first class, we have a complete definition as follow:

A field is a set "F' with two binary operations +,x defind on it, and two special elements 0 ≠ 1 such that

F1: commutative law

$\forall \!\,$ a, b $\in \!\,$ F: a+b=b+a and a.b=b.a

F2: associative law

$\forall \!\,$ a, b, c $\in \!\,$ F: (a+b)+c=a+(b+c) and (a.b).c= a.(b.c)

F3: the existence of identity elements

$\forall \!\,$ a $\in \!\,$ Fa+o=a and a.1=a

F4: existence of inverses

$\forall \!\,$ 0≠a $\in \!\ F,\exists \!\,c,d\in \!\ F,$ such that a+c=o and a.d=1

@@ Line 17: / Line 17: @@
-'''F3:''' the existence of identity element
+'''F3:''' the existence of identity elements
-a+o=a and a.1=a
+<math>\forall \!\,</math> a <math>\in \!\,</math> Fa+o=a and a.1=a
+'''F4:''' existence of inverses
+<math>\forall \!\,</math> 0≠a <math>\in \!\ F, \exists \!\, c, d \in \!\ F,</math> such that a+c=o and a.d=1