Math 281: Modern Algebra II

Course Information

Instructor: Dr. Lauren Williams
Class Days: Monday, Wednesday, Friday
Class Time: 10:30 - 11:35
Class Location: Hirt 209
My Office: Old Main 404 (Tower)
My Office Hours: Mon 2:15 - 3:30, Tues 11:45 - 1, Wed 2:15 - 3:30, Thur 11:30 - 2

Course Description

This is the second semester of a year long sequence on the study of algebraic structures. Course topics include rings, fields, an introduction to Galois theory, symmetry, the Sylow theorems, and finite simple groups.

Textbook and Materials

We will be using Contemporary Abstract Algebra, 8th Edition, by Joseph A. Gallian. An older edition of the text would be fine. No other texts or materials are required.


Homework assignments will be given regularly, and will include three types of problems.
  1. Submit: Several problems will be marked with an 'S'. You will be required to submit your solution to all of these problems for grading. Work must be submitted within one week of the assignment date. Solutions to these problems will be posted after the due date.
  2. Practice: Other problems will be marked with a 'P'. These are practice problems that you do not need to turn in, but please be aware that these problems could appear on a midterm or final exam, so be sure to give them a try. Solutions to these problems will generally not be posted, but I'm happy to check your work.
  3. Challenge: Additional problems will be marked with a 'C'. You are not expected to work on all of these problems on your own. However, over the course of the semester, you will be required to choose two of these problems submit a neatly written solution that will be distributed to the class. After you submit your solution, you'll receive a grade and suggestions for improvement, if any. You'll have an opportunity to resubmit the problem for up to 50% of the lost points back (so if your first attempt earned 6/10, a corrected attempt would earn a final grade of 8/10). Only correct, legible solutions will be given to the rest of the class. You will receive 10% extra credit if you type your solution using LaTeX. Only one student can submit a solution for a particular problem. If one appeals to you, notify me by email, and I'll confirm if you've claimed it.

The First Biennial Math 281 Conference

The end of the semester is reserved for an in-class "conference". Details can be found here. An updated conference schedule will be posted by the end of April.


We will have a midterm and a final exam. These will both be taken in class, and will be cumulative and may include material from Math 280.
  1. Midterm Exam: Friday, March 18th
  2. Final Exam: Wednesday, May 18th, 10:30-12:30


Your final grade will be calculated as follows:
  • Graded Homework Problem Average: 30%
  • Challenge Problem Average: 10%
  • Conference Grade: 20%
  • Midterm Exam: 20%
  • Final Exam: 20%
Your letter grade will be determined according to the department grading scale:

Course Schedule

This schedule will be kept up to date as assignments are given, or if we get behind schedule. Exam and "conference" dates will not be changed as long as the University is open on those days.

DateTopicNoteworthy Events
Week 1
Feb 3Class Introduction, Review
Feb 5Rings
Week 2
Feb 8Polynomial Rings
Feb 10Divisibility
Feb 12Divisibility
Week 3
Feb 15Factorization
Feb 17Factorization
Feb 19Factorization
Week 4
Feb 22Sylow Theorems
Feb 24Sylow Theorems
Feb 26Sylow Theorems
Week 5
Feb 29Finite Simple Groups
Mar 2Finite Simple Groups
Mar 4Finite Simple Groups
Week 6
Mar 7Extension Fields
Mar 9Algebraic Extensions
Mar 11Galois Theory
Week 7
Mar 14Galois Theory
Mar 16Review
Mar 18Midterm Exam
Week 8
Mar 21-25Easter Break
Week 9
Mar 28Easter Break
Mar 30Symmetry Groups
Apr 1Symmetry GroupsMAA Section Meeting (April 1-2, Gannon U)
Week 10
Apr 4Symmetry Groups
Apr 6Symmetry Groups
Apr 8Wallpaper Group Hunt
Week 11
Apr 11Symmetry
Apr 13Symmetry
Apr 15DualityAbstracts Due
Week 12
Apr 18Knots and Braids
Apr 20Knots and Braids
Apr 22Break
Week 13
Apr 25Representation Theory
Apr 27Representation Theory
Apr 29Representation Theory
Week 14
May 2Representation Theory
May 4Conference
May 6 Conference
Week 15
May 9 Conference
May 11 Conference
May 13 Review
Week 16
May 16 Reading Day
May 18 Final Exam 10:30-12:30

Learning Differences

In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 824-3017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.

Support of the Mercy Mission

This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.