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.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.
1. Due 9/8.
2. Due 9/11.
3. Due Mon. 9/15 : Symmetric, Matrix, and Quaternion Groups
4. Due Th. 9/18 : Homomorphisms and Isomorphisms
5. Due Mon. 9/22: Quotient Groups
6. Due Thu. 9/25: More Quotient Groups
7. Due Mon. 9/29: Lagrange's Theorem
Wed. 10/1: Exam 1
- Take home exam.
Distributed Wed. 10/1.
Due Mon. 10/6.
Rewrites Due on 10/6 -- HW 5
8. Due Thu. 10/2: The Isomorphism Theorems
9. Due Thu. 10/9: Rings
10. Due Mon 10/13: Examples of Rings
11. Due Thu 10/16 : Homomorphisms and Quotients
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
13. Due Mon 10/27: Properties of Ideals
14. Due Thu 10/30: Euclidean Domains
15. Due Mon 11/3: PID's
16. Due Thu 11/6: UFD's
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
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
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
20. Due Wed 11/26: Sylow Theorems continued.
-
Reading -- (4.5)
Problems -- (4.5) 13, 19, 24, 26.
Tentative Future Problems
The following is a list of problems which may be assigned in the future. Due Thu. 10/9 : Group Actions-
Reading -- (1.7).
Problems -- (1.7) 4, 6, 12, 17, 18, 19.
Rewrites Due .
Due . : Centralizers and Normalizers, Stabilizers and Kernels
-
Reading -- (2.2).
Problems -- (2.2) 2, 3, 6, 9, 10, 14.
Rewrites Due --.
Due: Quotient Groups and Lagrange's Theorem
-
Reading -- (3.2).
Problems -- (3.1) 40, 42. (3.2) 12, 16, 22.
Rewrites Due -- .
Due : Composition Series
-
Reading -- (3.4).
Problems -- (3.4) 1, 2, 5, 6, 7.
Rewrites Due -- .
Due: Finitely Generated Abelian Groups
-
Reading -- (5.2-5.3).
Problems -- (4.5) 18, 30. (5.2) 2, 4, 14.
Rewrites Due -- .
Due: Applications of Algebra (10 points)
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.
You should also, on a separate sheet of paper, provide the location in Dummit and Foote's book at which you believe your piece would best fit, as well as a justification (one paragraph) for why your piece would be appropriate.
For consistency and convenience, your piece should be written using LaTeX and the template found here. Your completed piece will eventually be posted on the class website unless otherwise requested.
Please feel free to look at some of the applied algebra papers written by a previous class.