Math 31: Abstract Algebra

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Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them.
  --Henri Poincaré


Through this course, you will

  • gain fluency with the structure of groups and rings, and the notion of mapping and homomorphism;
  • write clear, concise, and correct mathematical proofs;
  • develop mathematical maturity through brainstorming with others on homework, reading your textbook, and proof writing.

  • class meeting structure

    Class will be a mixture of interactive lecture and active learning. Active learning will be mostly in the form of activities and guided worksheets, which you will work on either individually or in groups.

    We will be using most of our x-hours over the quarter. Our first three x-hours will be proof workshops. Later x-hours will be used to develop your facility with important and prevalent topics that are not tied to any particular section of the course.


    The more interactive our lectures are, the better class will be. I will regularly be asking you questions, and I anticipate answers. To this end, I expect you to attend class and participate. On the other hand, I don't want a few students to dominate the discussion. If you've already spoken several times during a class, consider refraining from answering until others have had a chance to share. Participation will count in a small way to your final grade. Please resist the temptation to use your phone during class. In general, you are not as stealthy as you may think.

    I also encourage you to ask questions. If you are unsure about something, it is likely that other students are equally confused. Ask a question, for everyone's benefit.


    After each class, you will have a reading assignment to complete before the next class. Your reading will serve several purposes. Often the reading will give you a preview of the next class. Occasionally, the reading will not be covered in detail in class, and your knowledge of it will be assumed. In general, it is much easier to learn an abstract idea if you've already had some prior exposure to it. Independent reading will allow class time to be spent on activities which complement your reading, instead of lecture imitating the textbook. Finally, you will develop the ability to learn math from a textbook, a necessary task for learning higher mathematics and furthering your mathematical maturity.


    Weekly problem sets will be posted every Wednesday, and due the following Wednesday (unless otherwise noted) before the start of class. Problems sets are a primary vehicle for learning the course material and preparing for exams. Problem sets will generally contain a few problems designed to check your understanding of material covered that week, as well as several problems requiring a synthesis of different ideas, some of which you may not have seen in class. They will generally contain a mix of both proofs and computations. It is a good idea to be thinking about the problems before Tuesday night.

    In addition to weekly problem sets, you will also be working on challenge problems over the quarter. These problems will generally be more difficult than those on problem sets, and a new problem will be posted to the website every few days. You don't have to solve every challenge problem; you will hand in solutions to ten such problems before the end of the quarter.


    You will have one midterm and one final exam in this course. The midterm will consist of an in-class portion and a take-home portion, whereas the final exam will be entirely take-home. See the exams page for further details.


    Your final grade will be based on your homework and exam scores as follows.

    problem sets 25%
    challenge problems 10%
    in-class participation 5%
    midterm exam 30%
    final exam 30%


    We are using I.N. Herstein's Abstract Algebra (third edition). The book is paperback and has a domestic cover. It will be available at Wheelock Books. This text was also used for Math 31 over the Summer quarter.

    honor principle

    In-class exams are closed book, with no notes or textbooks allowed. No help will be given or received. On take-home exams, collaboration is not permitted in any form, and no help will be given or received. The use of your textbook and lecture notes on take-home exams will be allowed at the instructor's discretion. The use of the internet will be forbidden.

    You are welcome to discuss your homework assignments with your peers and instructor, but the final result should be your own work. You are encouraged to collaborate with your classmates, but in the end you should always write up your own solutions. That is, you are free to brainstorm with each other, but you should write up your final solutions by yourself. You should also credit the classmates with whom you worked (put a note in your homework solutions). See the homework page for more details on collaboration.

    disabilities and religious observances

    Students with disabilities who may need disability-related classroom accommodations are encouraged to meet with your instructor before the end of the second week of the quarter. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested.

    Some students may wish to take part in religious observances that occur during the academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.