Welcome to Abstract Algebra!

Welcome to Abstract Algebra!  Since Linear Algebra is a prerequisite, you have already done some abstract algebra, by working with the definition of a vector space, along with many examples satisfying that definition.  In this course, we will examine other algebraic structures, most notably groups, rings, and fields.  There are some interesting (and perhaps surprising) applications of these concepts, but of course I think they’re beautiful in their own right.

Instructor:  Priscilla Bremser Warner 307, ext. 5555 bremser@middlebury.edu

Office Hours:  Monday 2:00 – 4:00 Tuesday 2:00 – 3:00 Friday 1:30 – 2:30

Learning Objectives:  Through this course, you will develop a working knowledge of several algebraic structures, starting with groups. You will explore the concepts of homomorphisms and isomorphisms to establish when two groups are related or essentially the same, and then learn the beautiful and powerful theory of factor groups. We’ll only have time for an introduction to rings and fields, but by the end of the course you will have developed a strong foundation for further study. Along the way, you will further develop your ability to communicate mathematical ideas, both orally and in writing.

About Inquiry-Based Learning

Grounded in a simple idea – that we learn better by doing than by watching – Inquiry-Based Learning (IBL) takes a variety of forms in classrooms. All of them include in-class activities and discussion, providing immediate feedback. There is a growing body of evidence that IBL and other active learning methods are more effective than lectures, particularly in going beyond computational skills and developing students’ conceptual understanding of mathematics. (See the course website for references.)

In this course, students will work in small groups on worksheets for much of the time. The worksheets will contain all of the necessary definitions and provide illustrative examples and guiding questions. We will also have full-class discussions, in which students will present their work.


So that everyone can get the most out of the course, I expect you to

• come to each class on time and ready to participate;
• serve as scribe when your turn comes;
• be ready to ask your classmates to explain things to you; • be willing to explain things to your classmates;
• be willing to present your work to the whole class;
• come see me if you have questions or concerns.

As much as the rest of us will appreciate your contributions to class, please don’t come if you are ill. In that event, send me an email before class if possible.

Academic Honesty

My job, as I see it, is to offer you ample opportunity to learn for twelve short weeks. There will be more and better learning if everyone embraces academic honesty in the most general sense. You will benefit by engaging your brain appropriately, both in discussions and on your own, and I do my best to set up guidelines to make that happen:

  • You may consult only the course handouts, your class notes, your own written work, and the course website (including direct links from there). You may not consult textbooks or mathematics content websites.
  • You may discuss regular homework assignments with classmates; in fact, I encourage that. The final writeup must be your own.
  • The midterm and final exams will be strictly individual efforts.
    If you have questions or concerns about those guidelines, please let me know.


Problem sets are generally due at the start of class on Thursdays; you’ll find them on the website. Reflections (ungraded, but required) are due Sundays at 7:00 pm; again, see the website for details.

There will be a take-home exam due Thursday, March 24 at the start of class. There will also be a take-home final exam, due Wednesday, May 18 at noon.
Your grade will be computed roughly as follows:
Participation: 15%

Problem sets: 45%

Midterm exam: 20%

Final exam: 20%

SPECIAL THANKS to Professor Margaret Morrow of the State University of New York, Plattsburgh, for sharing her course materials with me.