Abstract Algebra
MA312 Fall 2020: Northern Michigan University

This is the syllabus for Math 312. Here are links for Lecture Notes and Assignments


  • Dr. Josh Thompson | Campus Office - JAMR 2226 | Virtual Office | email
  • Course

  • Where: West Science 2905
  • When: 11:00-11:50 p.m., Mon-Wed-Fri
  • Online: [Virtual Classroom]
  • Office Hours

  • Tuesday: 2pm - 3pm
  • Thursday: 12pm - 2pm
  • Friday: 12pm - 1pm
  • Office hours will be held outside Jamrich near the Wildcat on nice days and online always.

    Course Description

    Math 312 is an introduction to modern abstract algebraic systems and their applications. The course will focus on a rigorous treatment of the basic theory of groups (subgroups, quotient groups, homomorphisms, isomorphisms, group actions) and their applications.


    C or better in Math 211 and Math 163.


    The textbook we will use for this course Contemporary Abstract Algebra by Joseph Gallian. I will use the Ninth Edition, which is available at the University Bookstore or online

    Other editions will be very similar, but the exercises will occasionally differ. If you have a different edition, find a friend with the ninth edition to make sure the exercises you work match your friend's.


    Regular attendance is expected. Important dates can be found here.

    Drop Date

    If you need to drop the course, look here.


  • Weekly homework collected and graded, see the Assignments page for details.
  • Submit your work in Educat.
  • Grading

  • Homework 30%
  • Midterm 25%
  • Final 25%
  • Project 20%
  • Project

    You are to complete a class project. Here is list of topics. The end of each chapter of the text lists some ideas or you may suggest your own.


  • Midterm: October 6
  • Final - Friday, November 20 :: 11 am - 12:50 pm
  • Final Exam Schedule
  • Technology

    I first learned Abstract Algebra about 15 years ago and I would have loved to have some of the computer generated graphics and computing power available today. Check out the Group Explorer for starters.

    On the Take-Home Midterms and Exams, you are NOT allowed to use the internet.

    Other Resources

    Some popular video lectures on Abstract Algebra: [Socratica, Math Doctor Bob]

    Both free and paid tutoring is available, in the tutoring lab in JMR 2nd floor.

    Outcomes and Assesment

    Upon successful completion of this course students will be able to:

  • Select and correctly apply standard proof writing techniques.
  • Describe various properties of groups, such as its subgroups, its order and isomorphisms.
  • Apply group theory to analyze symmetry and motion of common objects.
  • Evaluation of these learning outcomes will be done through a mix of assignments, class exercises, projects, research papers, group work, written & oral quizzes and tests.

    Course Description

    This course will cover most of Parts 1 and 2 text. We will study groups, subgroups and various classes such as cyclic and permutation groups. We will construct homomorphisms and isomorphisms of groups and use these to classify finite abelian groups.

  • Preliminaries and Intro to Groups - 3 weeks
  • Subgroups - 1 week
  • Cyclic Subgroups - 1 week
  • Permuatation Groups - 1 week
  • Isomorphisms - 1 week
  • Cosets and Lagrange's Theorem - 2 weeks
  • Products, Normal Subgroups and Factor Groups - 2 weeks
  • Homomorphisms - 1 week
  • The Fundamental Theorem of Finite Abelian Groups - 1 week
  • Academic Honesty: Cheating is not only unethical and pathetic, but is a violation of the Northern Michigan University Student Code and University Policy and grounds for your dismissal from the University.

    Discrimination & Harassment: Northern Michigan University does not unlawfully discriminate on the basis of race, color, religion, national origin, gender, age, height, weight, martial status, handicap/disability, sexual orientation or veteran status. If you have a civil rights inquiry, contact the Affirmative Action Office at 906-227-2420.

    Americans with Disabilities Act Statement: If you have a need for disability-related accommodations or services, please inform the Coordinator of Disability Services in the Dean of Students Office at 2001 C. B. Hedgcock Building (227-1737 or disserv@nmu.edu). Reasonable and effective accommodations and services will be provided to students if requests are made in a timely manner, with appropriate documentation, in accordance with federal, state, and University guidelines.

    The Registrar: Withdrawing from any course or any matters relating to registration are the responsibility of the student. For more information regarding this topic, check out the Registrars Website.