Math 280: Modern Algebra

Course Information

Instructor: Dr. Lauren Williams
Class Days: Monday, Wednesday, Friday
Class Time: 9:15 - 10:20
Class Location: Hirt 209
My Office: Old Main 404 (Tower)
My Office Hours: Mon 10:30-12, Tues 12-1, Wed 2:15-3:15, Thurs 11-12, Fri 10:30-12

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.

Course Description

This is the first semester of a year long sequence on the study of algebraic structures. Course topics include the properties of numbers, equivalence relations, groups, rings, fields, direct products, homomorphisms and isomorphisms, and the natural development of various number systems.

Course Objectives

On successful completion of the course, students should be able to:
  • provide the definitions of algebraic objects, and know some examples of each.
  • develop abstract and critical reasoning by studying and writing mathematical proofs.
  • understand the connection between modern algebra and other branches of mathematics.
  • relate the material learned in this course to prerequisite courses.
  • recognize algebraic structures and objects in everyday situations.
  • learn about the historical development of modern algebra.

Lectures and Notes

Partial notes for each lecture, including definitions and theorem statements, will be available on this website (see the schedule or course resources). You should read the relevant course notes for each topic before class, and you're encouraged to come to class with questions. By seeing the definitions and theorems ahead of time, you'll be able to focus on understanding them in class, rather than concentrating on writing.
The notes you'll be given are not complete, but will complement the examples and proofs of important theorems we'll cover in class. How you choose to use these notes is up to you. One suggestion for studying is to recopy all notes (handouts and those you take in class) in a way that's clear to {\it you}. As you're doing so, you're likely to uncover questions you hadn't thought of before.
If you miss a class, make sure you get the additional notes from a classmate. Attendance is not required nor part of your grade, but coming to class regularly is in your best interest.


You will have several assignment due throughout the semester (generally every Friday). You should expect to spend a fair amount of time on each assignment - don't wait until the night before it's due to get started! You are free to work together on your assignments, but everyone must submit their own work, in their own words. The lowest homework grade will be dropped. Late homework will not be accepted, unless you talk to me before it's due.


We will have a midterm exam and a final exam. The midterm exam will have a take home portion, followed by an in class portion. Unlike the homework assignments, you are not permitted to work together on the take home portion of the midterm exam. The in class portion will be comprised of shorter questions based on definitions, while the take home will include some proofs. The final exam will be a cumulative exam with no take home portion.

Exam Dates:
Midterm Exam (In Class and Take Home Portion Due): Monday, October 19
Final Exam: Friday, December 11, 8:00-10:00 am


Your final grade will be calculated as follows:
  • Assignments: 60% (lowest assignment grade is dropped)
  • Midterm Exam: 20%
  • Final Exam: 20%
Your letter grade will be determined according to the department grading scale:

Want to know how you'll need to do on the final exam to earn the grade you want? Use the calculator below:
Assignment Average: Midterm Grade:
Desired Grade:DD+CC+BB+A
Needed on Final Exam:

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.

Course Calendar

DateTopicAssignment Due