Math 321 - Foundations of Abstract Algebra

Books and Online Resources

There is no required textbook. I will produce course notes throughout the semester and post them here: Current notes.

If you are looking for other sources to supplement the notes from class, here are some recommendations:

  • A First Course in Abstract Algebra by John Fraleigh.
  • Algebra by Michael Artin.
  • Abstract Algebra by David Dummit and Richard Foote.
  • Abstract Algebra: Theory and Applications by Thomas Judson. Available Online.

    If you would like a book that teaches the fundamentals of reading and writing proofs, I recommend the following:

  • How to Prove It by Daniel Velleman.
  • How to Think Like a Mathematician by Kevin Houston.
  • Mathematical Reasoning: Writing and Proof by Ted Sundstrom. Available Online.
  • Book of Proof by Richard Hammack. Available Online.

    If you would find it helpful to review some of the material from Linear Algebra, please consult my Linear Algebra book.

  • Administrative Information
    Instructor Joe Mileti
    Email miletijo ~at~ grinnell ~dot~ edu
    Office Noyce 2514
    Office Hours Monday 3:00 - 4:00
    Tuesday 10:00 - 11:00
    Wednesday 11:00 - 12:00
    Thursday 3:00 - 4:00
    Also By Appointment
    Class Time MWF 2:00 - 2:50
    Classroom Noyce 2245

    Course Objectives


    Homework assignments will be due on Wednesdays at 5:00pm, and will be posted to the course webpage. You should submit you solutions as one pdf file to the corresponding homework folder within your course OneDrive folder (that I will share with you). Throughout the semester, you may extend the deadline of at most two homework assignments by (up to) two days. If you choose to extend the deadline of an assignment, you should send me an email by the usual due date. Beyond these two extensions, late homework will not be accepted for credit, unless there is an emergency that you bring to my attention before the due date. Your lowest homework score will be dropped.

    Although there will certainly be some "computational" problems in the course, most of the homework involves writing proofs and/or detailed explanations. As a result, there are often many correct answers. Moreover, the clarity of exposition and the proper use of mathematical terminology are as vital to your solutions as having the correct idea. A major goal of this course is to learn how to express your mathematical ideas correctly and to write convincing, detailed, and clear proofs. One of my core responsibilities is provide helpful feedback for how to improve your writing. Do not be alarmed if your homework has many comments and suggestions!

    Reading Responses

    One of the most difficult aspects of many people's people mathematical journey is learning how to read mathematics. To get the most out of books and papers, it is essential to work out examples while reading, to constantly ask questions, to isolate what aspects of the material are unclear, and to make conjectures. To help develop these skills, I will give you a few prompts for the assigned reading for Monday and Friday classes. Your responses to the prompts will be due on Gradescope by 10:00am on the corresponding class day. These will be graded for completeness and thoughtfulness, rather than for correctness.


    In addition to reading and homework assignments, I expect each of you to engage in the learning process other ways. You should regularly attend class, contribute to class discussions, and ask questions in office hours or via email.


    There will be two in-class exams and a scheduled three hour final exam, each of which will focus on conceptual problems and proofs.

    In-class exams dates: March 8 and April 28.
    Final exam date: Tuesday, May 16 at 9:00am.


    Homework 25%
    Reading Responses 10%
    Engagement 5%
    Lower of Two In-class Exams 15%
    Higher of Two In-class Exams 20%
    Final 25%


    If you want to learn how to present your work professionally, as well as keep digital records, I recommend learning how to typeset your solutions. LaTeX is a wonderful free typesetting system which produces high-quality documents at the cost of only a small amount of additional effort (beyond the nontrivial start-up cost of learning the fundamentals). If you plan to do any kind of mathematical or scientific writing in the future, you will likely use LaTeX, so it is worth your time to familiarize yourself with it. See Jim Hefferon's LaTeX for Undergraduates and his LaTeX Cheat Sheet for the basics. Also, feel free to ask me questions about how to use LaTeX, and/or to send you the LaTeX file for homework assignments.

    Academic Honesty

    Consult the general Grinnell College policy on Academic Honesty and the associated booklet for general information.

    Homework: If you enjoy working in groups, I strongly encourage you to work with others in the class to solve the homework problems. If you do collaborative work or receive help form somebody in the course, you must acknowledge this on the corresponding problem(s). Writing "I worked with Sam on this problem" or "Mary helped me with this problem" suffices. You may ask students outside the course for help, but you need to make sure they understand the academic honesty policies for the course and you need to cite their assistance as well. Failure to acknowledge such collaboration or assistance is a violation of academic honesty.

    If you work with others, your homework must be written up independently in your own words. You cannot write a communal solution and all copy it down. You cannot read one person's solution and alter it slightly in notation/exposition. Discussing ideas and/or writing parts of computations together on whiteboards or scratch paper is perfectly fine, but you need to take those ideas and write the problem up on your own. Under no circumstances should you look at another student's completed written work.

    I encourage you to look to other books or online sources for additional help in understanding concepts and ideas, but you must cite other books or online sources if they provide you with an idea that helps you solve a problem. However, you may not specifically look for solutions to homework problems, and you may not solicit help for homework problems from online forums.

    Exams and Final: You may neither give nor receive help. Books, written notes, computers, phones, and calculators are not permitted at any time during a testing period.


    I encourage students with documented disabilities to discuss appropriate accommodations with me. You will also need to have a conversation with, and provide documentation of your disability to, the Coordinator for Disability Resources, located on the ground level floor of Steiner Hall (641-269-3124).

    Religious Observations

    I encourage students who plan to observe holy days that coincide with class meetings or assignment due dates to consult with me as soon as possible so that we may reach a mutual understanding of how you can meet the terms of your religious observance and also the requirements for this course.

    Unsolicited Advice