Math 31: Topics in Algebra
Fall 2007

## Textbook

 Contemporary Abstract Algebra, Sixth Edition by Joseph A. Gallian Published by Houghton Mifflin Company

## Instructor

Martino Arkowitz
Office: 207 Kemeny Hall
E-mail: martin arkowitz@dartmouth.edu

## Office Hours

Tuesdays 1:30pm - 3pm
Thursdays 1:30pm - 3pm
and by appointment.

## Lecture Information

Location: Haldeman Center 028
Time: MWF, 12:30 - 1:35
X-hour: Tues, 1:00 - 1:50

Grades are based on homework, a midterm exam, a quiz and a final.

Grades will be calculated as follows:
 homework: 15% takehome midterm: 32% quiz: 8% takehome final: 45%

## Homework

Homework will be assigned weekly. The due date will appear below in the Current Homework Assignment Section. Late homework will NOT be accepted, except in extreme circumstances.

You are to individually write up your homework solutions by yourself, but you are encouraged to work with other people or to seek help on the homework.

## Current Homework Assignments and Exam Information

Assignment 1 (due Wednesday, October 3): Read Chapter 2 (pp. 42--53), Do pp. 54--56: 3, 5, 7, 13, 14, 23, 25, 29, 33, 34.

Assignment 2 (due Wednesday, October 10): Read Chapter 3, Chapter 4 (up to Corollary, bottom p. 80), Chapter 5 (up to Example 6), Do pp. 67--70: 4, 8, 15, 29, 31, 49; pp. 82--84: 9, 18, 19, 29, 42; pp. 111--114: 3ae, 4b, 9ce, 24, 25.

Assignment 3 (due Wednesday, October 17): Read Chapter 6 (up to and including Theorem 6.4), Chapter 7 (up to Lagrange's Theorem p. 140), Do pp. 114: 26, 28, 36, 41, 45; pp. 132--134: 1--4, 5 (sketch proof), 10, 24, 25, 33, 36.

Assignment 4 (due Wednesday, October 24): Read Chapter 7 (up to Theorem 7.2), Chapter 8 (up to Theorem 8.2). Do pp. 148 -- 150: 1, 2, 7, 12, 15, 25, 26, 36; pp. 165 -- 166: 2, 4, 5, 13, 15, 20.

Assignment 5 (due Monday, October 29): Read Chapter 9 (up to Theorem 9.3), Chapter 10 (up to Example 14), Chapter 12. Do pp. 191 -- 193: 7, 8, 10, 19, 24, 40; pp. 210 -- 212: 3, 7, 16, 18, 21, 31.

MONDAY, OCTOBER 29: TAKE HOME MIDTERM WILL BE HANDED OUT IN CLASS.

Assignment 6 (due Monday, November 12): Read Chapter 13, Chapter 14. Do pp. 240 -- 242: 9, 15, 17, 22, 26; pp. 254 -- 256: 5, 10, 13, 16, 20, 41.

TUESDAY, NOVEMBER 13: IN CLASS QUIZ DURING X-HOUR.

Assigment 7 (due Tuesday, November 20 at noon): Read Chapter 15 (up to Cor. 1, p. 283), Chapter 16, Chapter 17 (pp. 303 -- 304, middle p. 309 -- 311). Do pp. 268 -- 270: 2, 6, 17, 25, 34; pp. 286 -- 287: 7, 12, 21, 28, 30; pp. 299 -- 300: 13, 19, 20, 23, 31.

Assigment 8 (due Friday, November 30): Read Chapter 18, pp. 326 -- 329 (up to Euclidean Domains), Chapter 19, Chapter 20, pp. 352 -- 354 (up to Splitting Fields), pp. 357 -- 359 (from Theorem 20.3 up to Lemma p. 359), Chapter 21, pp. 369 -- 374. Do pp. 347 -- 348: 3, 5, 8, 11, 18; pp. 365 -- 366: 2, 7, 8, 10, 14, 17, 20, 29.

FRIDAY, NOVEMBER 30: TAKE HOME FINAL EXAM WILL BE HANDED OUT IN CLASS.

## Honor Principle

On Exams: On all exams you are to do your own work without help from others. No collaboration is permitted. The precise rules regarding an exam will be stated when the exam is given.

## Disabilities

Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see the instructor before the end of the second week of the term. All discussions will remain confidential, although the Student Disability Services office may be consulted to discuss appropriate implementation of any accommodation requested.