## Math 171: Abstract Algebra, Fall 2011

### Prof. Davis

## 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 Prof. Davis's office (Olin B160). You are encouraged (perhaps expected) to work together on homework problems, since discussing mathematical ideas is an excellent way to gain insight. However, you should turn in your own write-up of the problems. Acknowledging your collaborators is always appropriate.

## Readings and Assignments:

#### Week 1: Chapter 0, Section 1.1.

#### Week 2: Section 1.2-1.3.

HW 1 (Due 9/8): (1.1) 8,22,25, 27; (2.1) 5; Extra Problem 1 - Write out the multiplication table for the group of 6 functions given in class - what patterns do you see in this table?

hw1.tex | hw1.pdf

#### Week 3: Section 1.6, 3.2

HW 2 (Due 9/12): (1.1) 24 (1.2) 3,7; (1.3) 15; (2.1) 6

171hw2.tex | 171hw2.pdf

HW 3 (Due 9/15): (1.6) 5,9,17,23; Extra Problem 2 - Prove that, up to isomorphism, there are exactly two groups of order 4.

171hw3.tex | 171hw3.pdf

#### Week 4: Section 3.1

HW 4 (Due 9/19): (3.2) 7,11,22; Extra Problem 3 - see pdf.

171hw4.tex | 171hw4.pdf

HW 5 (Due 9/22): (3.1) 1,22,24; Extra Problem 4,5 - see pdf.

171hw5.tex | 171hw5.pdf

HW #1 Rewrites due - please include your original assignment with the rewrites.

#### Week 5: Section 3.3

HW 6 (Due 9/26): (3.1) 14, 36, 41; (3.2) 18

171hw6.tex | 171hw6.pdf

HW #2 rewrites due.

HW 7 (Due 9/29): (3.3) 3,7,8,9

171hw7.tex | 171hw7.pdf

HW #3 rewrites due.

Exam 1 out 9/28. Due 10/3 (Monday) at the start of class.

HW #4 rewrites due.

#### Week 6: Sections 1.7, 4.1-4.3

HW #8 (Due 10/6):

171hw8.tex | 171hw8.pdf

HW #5 rewrites due.

HW #9 (Due 10/10):

171hw9.tex | 171hw9.pdf

HW #6 rewrites due.

#### Week 7: Section 4.5.

HW #10 (Due 10/13): (4.5) 1,6,32,35

171hw10.tex | 171hw10.pdf

HW #11 (Due 10/20): (4.5) 16,17,28; Extra Problem 6

171hw11.tex | 171hw11.pdf

HW #7 Rewrites due.

#### Week 8: Section 7.1

HW #12 (Due 10/24): 14,15,17,21 (7.1)

171hw12.tex | 171hw12.pdf

#### Week 9: Section 7.2, 7.3

HW #13 (Due 10/27): (7.2) 7,10,13

171hw13.tex | 171hw13.pdf

HW #8 rewrites due (This homework is due officially "whenever" on Thursday. Feel free to see Prof Orrison from 4:15-5:30 or e-mail Prof. Davis for last-minute questions.)

HW #14 (Due 10/31): (7.3) 10,13,17, Extra Problem 7

171hw14.tex | 171hw14.pdf

HW #9 rewrites due

#### Week 10: Section 7.3, 7.4

HW #14 (Due 11/3): (7.3) 24,26,28; (7.4) 8

171hw15.tex | 171hw15.pdf

HW 10 rewrites due

Exam 2 out 11/2. Due 11/7 (Monday) at the start of class.

#### Week 11: Section 8.1

HW #16 (Due 11/10): (7.4) 10,19,24, Extra Problem 8

171hw16.tex | 171hw16.pdf

HW 11 rewrites due

HW # 17 (Due 11/14): (8.1) 3, Extra Problem 9 + 10

171hw17.tex | 1717hw17.pdf

HW 12 rewrites due

#### Week 12: Section 8.2

HW #18: (8.1) 10, (8.2) 3,4

171hw18.tex | 171hw18.pdf

HW #13 rewrites due Monday (11/21). (No new HW due.)

#### Week 13: Section 10.1,10.2

HW #19: Due (11/28) (10.1) 8,9,10

171hw19.tex | 171hw19.pdf

HW #14 rewrites due.

HW #15 rewrites due Thursday (12/1) (No new HW due.)

(Due 12/5) : Applications of Algebra paper.

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.

## Math 171: Abstract Algebra, Fall 2011

### Prof. Davis

### Overview

The main topics for this course are groups, rings, and fields. Additional topics and interesting tangents will be explored as time allows.
Prerequisites: Math 40 or 30 or 25 or 12 (Calculus or Linear Algebra) AND Math 55 (Discrete).

### Textbook

* Abstract Algebra *, Third Edition, by D. Dummit and R. Foote.

### Grading

There will be three midterms and two homework sets a week. Each exam and your overall homework grade will count as one-fifth of your grade. The highest of those four grades will count again and make up the other fifth of your final grade.

### Homework

Written homework will be due each Monday and Thursday, and is posted on the link above. Please submit Monday's homework in class, and Thursday's homework directly to your instructor (or their mailbox). You are encouraged to discuss the homework with other members of the class, and it is appropriate to acknowledge the assistance of others. You will, however, be expected to write up your solutions on your own. The instructor will reserve the right to refuse to accept late homework for any reason. Graded homework, however, may (in most cases) be rewritten and submitted at a later date. Please consult the HMC mathematics homework format guidelines for helpful tips on homework submission and formatting.

### Rewrites

You are encouraged to correct and re-submit returned homework for additional credit. Any homework assignment which receives a less than perfect score may be resubmitted. Please staple your re-writes to your original assignment. Re-writes should be submitted one week after the original assignment is returned, which should ideally be two weeks after the original due date.

### Exams

There will be three exams, all of which will be take-home. Tentative dates for distributing these exams are Sept. 28, Nov. 2, and Dec. 7.

### LaTeX

Students interested in using LaTeX to type their homework may find the HMC Problem Set Class helpful.

### Disabilities

Students who need disability-related accommodations are encouraged to speak with the instructor as soon as possible.

### Honor Code

The HMC Honor Code applies in all matters of conduct regarding this course. In particular, while students are encouraged to cooperate on homework assignments, they are expected to write up solutions individually, and not to merely copy the work of others. The goal of the homework is comprehension of the solution and the ideas contained therein, so you should understand the solution well enough to write it up yourself.Please acknowledge the assistance of others by including their names on your homework. Tests, as usual, are to be worked on individually and not discussed until after all the exams have been turned in.

###### Aspects of this page's design have been shamelessly and blatantly stolen from Michael Orrison.