Math 31 Fall 2009
Blackboard Content
Syllabus:
Course Overview
Daily Content
Office Hours (updated)
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Assignments:
Written Homework 1
Written Homework 2
Written Homework 3
Written Homework 4
Written Homework 5 (part 1)
Written Homework 5 (part 2)
Written Homework 6
Written Homework 7
Written Homework 8
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Exams & Quizzes:
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Take-home Midterm
In-class Midterm
Quiz 5
Quiz 6
Quiz 7
Quiz 8
Take-home Final
In-class Final
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Documents & Links:
Cayley Tables from 10/9/2009 Lecture
Here
you'll find a copy of the Cayley tables for S_3 (the permutation group
on the set {1,2,3}) and D_3 (the symmetries of an equilateral triagle) which demonstrate the isomorphism
between these groups.
X-hour Proofs with Comments
I
transcribed the comments other groups made on each proof and scanned
the original proofs each group submitted during the first two x-hour periods.
As always, if you have questions, please feel free to send them my
way.
Group Theory Q&A
Here
are answers to some of the questions that have been sent in. If
you feel that your questions haven't been answered, please let me
know! It wasn't intentional.
X-hour Factor Group Examples
X-hour Venn Diagrams
Examples of Splitting Fields
I really only expect you to know what a splitting
field is; I will not expect you to be able to find a splitting field or
to verify that a certain field is the splitting field for a given polynomial. But,
to further illustrate the point that a splitting field for a polynomial
of degree n does NOT necessarily have degree n over the base
field (in fact, all we can guarantee is that its degree is at most n!,
but that's another story), here are some examples borrowed from
Dummit and Foote's Abstract Algebra, 3rd Ed.
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