### Math 171 Homework

Prof.'s Dagan Karp and Matt Davis
Fall 2010

## 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.

## 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.
1. Due 9/6.
Problems: (1.1) 8, 22, 25, 26, 27, 31.
hw1.tex || hw1.pdf

2. Due 9/9 : Dihedral and Symmetric Groups
Problems: (1.1) 2, 3. (2.1) 5,6
hw2.tex || hw2.pdf

3. Due Mon. 9/13 : Matrix and Quaternion Groups
Problems -- (1.3) 10, 14. (1.4) 10. (1.5) 2
hw3.tex || hw3.pdf

Due Wed. 9/15 : 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.

4. Due Th. 9/16 : Homomorphisms and Isomorphisms
Problems -- (1.6) 7, 13, 14, 23.
hw4.tex || hw4.pdf

5. Due Mon. 9/20: Quotient Groups
Problems -- (3.1) 1, 6, 7, 9.
Rewrite Due -- HW 1
hw5.tex || hw5.pdf

6. Due Thu. 9/23: More Quotient Groups
Problems -- (3.1) 14, 24, 40, 41.
Rewrite Due -- HW 2
hw6.tex || hw6.pdf

7. Due Mon. 9/27: Lagrange's Theorem
Problems -- (3.2) 16, 18, 19, 22.
Rewrites Due -- HW 3
hw7.tex || hw7.pdf

Wed. 9/29-10/4: Exam 1
Take home exam.
Distributed Wed. 9/29.
Due Mon. 10/4.
Rewrites Due on 10/4 -- HW 5

8. Due Thu. 9/30: The Isomorphism Theorems
Problems -- (3.3) 3, 7, 8, 9.
Rewrites Due -- HW 4 .
hw8.tex || hw8.pdf

9. Due Thu. 10/7: Rings
Problems -- (7.1) 14, 15, 16, 17.
Rewrites Due -- HW 6.
hw9.tex || hw9.pdf

10. Due Mon 10/11: Examples of Rings
Problems -- (7.2) 3,7,10,13
Rewrites Due -- HW 7
hw10.tex || hw10.pdf

11. Due Thu 10/14 : Homomorphisms and Quotients
Problems -- (7.3) 10, 13, 26, 29.
Rewrites Due -- None
hw11.tex || hw11.pdf

12. Due Thu 10/21: Properties of Ideals
Problems -- (7.3), 17, 24. (7.4) 8.
Rewrites Due -- HW 8
hw12.tex || hw12.pdf

13. Due Mon 10/25: Properties of Ideals

14. Due Thu 10/28: Euclidean Domains
Problems -- (8.1) 3, 11, Two extra problems that are not in the book. They are in the pdf and tex below.
Rewrites Due --
hw14.tex || hw14.pdf

15. Due Mon 11/1: PID's
Problems -- (8.2) 3, 4, 5
Rewrites Due -- HW 9, 11
hw15.tex || hw15.pdf

16. Due Thu 11/4: UFD's (EXAM OUT 11/3)
Problems -- 1, 2, 8, 11.
Rewrites Due -- HW 10
hw16.tex || hw16.pdf

17. Due Thu 11/11: Categories and Morphisms
Reading -- Grillet (17.1) via Sakai
Problems -- Below
Rewrites Due -- None
hw17.tex || hw17.pdf

18. Due Mon 11/15: Functors.
Problems -- Below
Rewrites Due -- HW 13.
hw18.tex || hw18.pdf

19. Due Thu 11/18: Functors Continued
Problems -- Below
Rewrites Due -- HW 12.
hw19.tex || hw19.pdf

Due Wed 11/24: Rewrites only
Rewrites Due: HW 15
20. Due Thurs 12/2: Group Actions.
Rewrites -- HW 14.
hw20.tex || hw20.pdf

21. Due Mon 12/6: Sylow theorems.

22. Due Thurs 12/9: Modules.
Problems -- 10.1 1,9, one extra problem - see below.
hw22.tex || hw22.pdf

20-something. Due Mon 12/6: 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.

## Tentative Assignments

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

Wed. 12/8-12/13: Exam 3

Take home exam.
Distributed Wed. 12/10.
Due Mon. 12/13.