Math 281: Modern Algebra II
All notes, homework, and the exam review sheet from Math 280 are still online
- they may be useful.
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
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.
- 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.
- 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.
- 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
- Midterm Exam: Friday, March 18th
- 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:
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.
|Feb 3||Class Introduction, Review|
|Feb 8||Polynomial Rings|
|Feb 22||Sylow Theorems|
|Feb 24||Sylow Theorems|
|Feb 26||Sylow Theorems|
|Feb 29||Finite Simple Groups|
|Mar 2||Finite Simple Groups|
|Mar 4||Finite Simple Groups|
|Mar 7||Extension Fields|
|Mar 9||Algebraic Extensions|
|Mar 11||Galois Theory|
|Mar 14||Galois Theory|
|Mar 18||Midterm Exam|
|Mar 21-25||Easter Break|
|Mar 28||Easter Break|
|Mar 30||Symmetry Groups|
|Apr 1||Symmetry Groups||MAA Section Meeting (April 1-2, Gannon U)|
|Apr 4||Symmetry Groups|
|Apr 6||Symmetry Groups|
|Apr 8||Wallpaper Group Hunt|
|Apr 15||Duality||Abstracts Due|
|Apr 18||Knots and Braids|
|Apr 20||Knots and Braids|
|Apr 25||Representation Theory|
|Apr 27||Representation Theory|
|Apr 29||Representation Theory|
|May 2||Representation Theory|
|May 6|| ||Conference|
|May 9|| ||Conference|
|May 11|| ||Conference|
|May 13|| ||Review|
|May 16|| ||Reading Day|
|May 18|| ||Final Exam 10:30-12:30|
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.