Math 171 Home | Homework | Syllabus | Lecture Notes

Math 171 Homework

Prof. Dagan Karp
Spring 2012

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. Karp, located at 1267 Olin.

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Current Assignments

The following is a list of assigned homework problems.

TeX and pdf versions of assigned problems are provided via Kevin Black. Please inform the community of any typo's.

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1. Due Mon 1/23.

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

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2. Due Th. 1/26 : Basic Properties of Groups and the Dihedral Group

Reading: (1.2,1.3)
Problems: (1.1) 2, 3. (2.1) 5,6
hw2.tex || hw2.pdf

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3. Due Mon. Mon 1/30 : Symmetric Groups and Matrix Groups

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

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4. Due Th. 2/2 : Homomorphisms and Isomorphisms

Reading -- (1.6, 3.1).
Problems -- (1.6) 7, 13, 14, 23.
hw4.tex || hw4.pdf

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Due Mon. 2/6 : Writing Assignment

Write a brief note (one or two paragraphs) describing your impression of the Algebra as a subject. For example, how does it compare to previous courses? Do you like it? How does it compare to non-mathematics courses? Does it stir any emotions? etc.

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Wed. 2/8-2/13: Exam 1

Take home exam.
Distributed Wed. 2/8.
Due Mon. 2/13.

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5. Due Th. 2/9: 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 Th. 2/16: 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. 2/20: 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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8. Due Th. 2/23: 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 Mon. 2/27: Rings

Reading -- (7.1)
Problems -- (7.1) 14, 15, 16, 17.
Rewrites Due -- HW 5.
hw9.tex || hw9.pdf

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10. Due Th. 3/1: Examples of Rings

Reading -- (7.2)
Problems -- (7.2) 3,7,10,13
Rewrites Due -- HW 6
hw10.tex || hw10.pdf

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11. Due Mon. 3/5 : Homomorphisms and Quotients

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

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12. Due Th. 3/8: Properties of Ideals

Reading -- (7.3), (7.4)
Problems -- (7.3), 17, 24. (7.4) 8.
Rewrites Due
hw12.tex || hw12.pdf

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13. Due Th. 3/22: Properties of Ideals

Reading -- (7.4)
Problems -- (7.4) 24, 30, 31, 32.
Rewrites Due -- HW 5.
hw13.tex || hw13.pdf

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Wed. 3/21-3/26

Take home exam.
Distributed Wed. 3/21
Due Mon. 3/26

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14. Due Th. 3/29: Euclidean Domains

Reading -- (8.1)
Problems -- (8.1) 3, 11, Two extra problems that are not in the book. They are in the pdf and tex below.
Rewrites Due -- TBA
hw14.tex || hw14.pdf

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15. Due Mon 4/2 : PID's

Reading -- (8.2)
Problems -- (8.2) 3, 4, 5
Rewrites Due -- HW 6 and HW 7
hw15.tex || hw15.pdf

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16. Due Thu 4/5: UFD's

Reading -- (8.3)
Problems -- 1, 2, 8, 11.
Rewrites Due -- HW 12 and HW 13
hw16.tex || hw16.pdf

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17. Due Mon 4/9: Categories and Morphisms

Reading -- Grillet (17.1) via Sakai
Problems -- Below
Rewrites Due -- None
hw17.tex || hw17.pdf

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18. Due Thu 4/12: Functors.

Reading -- Grillet (17.2)
Problems -- Below
Rewrites Due -- HW 10 and HW 11.
hw18.tex || hw18.pdf

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19. Due Mon 4/16: Functors Continued

Reading -- Grillet
Problems -- Below
Rewrites Due -- 14 and 15.
hw19.tex || hw19.pdf

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20. Due Thu 4/19: Group Actions.

Reading -- 4.1-4.2
Problems -- See links below
Rewrites -- HW 8 and HW 9.
hw20.tex || hw20.pdf

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21. Due Mon 4/23: Cayley Graphs.

Reading -- Terry Tao's Blog
Problems -- See links below
Rewrites -- HW 16
hw21.tex || hw21.pdf

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22. Due Thu 4/26: 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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Mon. 5/7: Exam 3

Take home exam.
Distributed Wed. 4/25.
Due Mon. May 7 at 5pm.

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Tentative Assignments

The following is a list of problems which are likely to be assigned.

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