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Math 171 Homework

Prof.'s Dagan Karp and Mike Orrison
Fall 2008

General information.

Homework is due every Monday and Thursday. Monday's work is due in class, and Thursday's should be deposited by 5 PM to the in-box of Prof. Orrison, located at 1280 Olin.

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Current and past assignments

The following is a list of assigned homework problems.

TeX and pdf versions of assigned problems are provided via Martijn van Schaardenburg. Please inform the community of any typo's.

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1. Due 9/8.

Reading: 1.1, 2.1
Problems: (1.1) 8, 22, 25, 26, 27, 31.
hw1.tex || hw1.pdf

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2. Due 9/11.

Reading: (1.2,2.1)
Problems: (1.1) 2, 3. (2.1) 5,6
hw2.tex || hw2.pdf

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3. Due Mon. 9/15 : Symmetric, Matrix, and Quaternion Groups

Reading -- (1.3-1.5).
Problems -- (1.3) 10, 14. (1.4) 10. (1.5) 2
hw3.tex || hw3.pdf

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4. Due Th. 9/18 : Homomorphisms and Isomorphisms

Reading -- (1.6).
Problems -- (1.6) 7, 13, 14, 23.
hw4.tex || hw4.pdf

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5. Due Mon. 9/22: Quotient Groups

Reading -- (3.1).
Problems -- (3.1) 1, 6, 7, 9.
Rewrite Due -- HW 1
hw5.tex || hw5.pdf

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6. Due Thu. 9/25: More Quotient Groups

Reading -- (3.1)
Problems -- (3.1) 14, 24, 40, 41.
Rewrite Due -- HW 2
hw6.tex || hw6.pdf

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7. Due Mon. 9/29: Lagrange's Theorem

Reading -- (3.2)
Problems -- (3.2) 16, 18, 19, 22.
Rewrites Due -- HW 3
hw7.tex || hw7.pdf

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Wed. 10/1: Exam 1

Take home exam.
Distributed Wed. 10/1.
Due Mon. 10/6.
Rewrites Due on 10/6 -- HW 5

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8. Due Thu. 10/2: The Isomorphism Theorems

Reading -- (3.3).
Problems -- (3.3) 3, 7, 8, 9.
Rewrites Due -- HW 4 .
hw8.tex || hw8.pdf

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9. Due Thu. 10/9: Rings

Reading -- (7.1)
Problems -- (7.1) 14, 15, 16, 17.
Rewrites Due -- HW 6.
hw9.tex || hw9.pdf

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10. Due Mon 10/13: Examples of Rings

Reading -- (7.2)
Problems -- (7.2) 7,8,10,13
Rewrites Due -- HW 7
hw10.tex || hw10.pdf

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11. Due Thu 10/16 : Homomorphisms and Quotients

Reading -- (7.3)
Problems -- (7.3) 10, 13, 26, 29.
Rewrites Due -- HW 8.
hw11.tex || hw11.pdf

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12. Due Thu 10/23: Properties of Ideals

Reading -- (7.3), (7.4)
Problems -- (7.3), 20, 24. (7.4) 7, 8.
Rewrites Due -- HW 9.
hw12.tex || hw12.pdf

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13. Due Mon 10/27: Properties of Ideals

Reading -- (7.4)
Problems -- (7.4) 24, 30, 31, 32.
hw13.tex || hw13.pdf

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14. Due Thu 10/30: Euclidean Domains

Reading -- (8.1)
Problems -- (8.1) 3, 5, 11, 12.
hw14.tex || hw14.pdf

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15. Due Mon 11/3: PID's

Reading -- (8.2)
Problems -- (8.2) 3, 4, 5, 8.
Rewrites Due -- HW 10.
hw15.tex || hw15.pdf

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16. Due Thu 11/6: UFD's

Reading -- (8.3)
Problems -- 1, 2, 8, 11.
Rewrites Due -- HW 11 and 12.
hw16.tex || hw16.pdf

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17. Due Fri 11/14: Group actions

Reading -- (1.7), (2.2), (4.1)
Problems -- (4.1) 1, 7, 8, 10.
Rewrites Due -- HW 13 and 14.
hw17.tex || hw17.pdf

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18. Due Mon 11/17: Groups acting on themselves.

Reading -- (4.2), (4.3)
Problems -- (4.2) 8, 9; (4.3) 2, 5.
Rewrites Due -- HW 15. (tentative)
hw18.tex || hw18.pdf

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19. Due Thu 11/20: Sylow Theorems.

Reading -- (4.5)
Problems -- (4.5) 1, 4, 5, 17.
Rewrites Due -- HW 16. (tentative)
hw19.tex || hw19.pdf

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20. Due Wed 11/26: Sylow Theorems continued.

Reading -- (4.5)
Problems -- (4.5) 13, 19, 24, 26.
hw20.tex || hw20.pdf

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21. Due Mon 12/8: Applications of Algebra

Write 2-3 paragraphs on a particular application of abstract algebra in another field of mathematics (e.g., topology) or another discipline (e.g., chemistry). Your piece should be written as though it could be included seamlessly in a future edition of Dummit and Foote's book, and you must use at least one outside source.

For consistency and convenience, your piece should be written using LaTeX and the template found here. Lastly, please feel free to look at some of the applied algebra papers written by a previous class.

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Wed. 12/10-12/15: Exam 3

Take home exam.
Distributed Wed. 12/10.
Due Mon. 12/15.
Note: We suggest that you at least skim the first ten problems in Section 10.1 and Section 10.2. Working through some of these problems should help build some confidence and momentum when it comes to grappling with the basics of modules.