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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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Course Overview

Daily Content

Office Hours (updated)

Back to top

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

Back to top

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

Back to top

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.

Back to top