Abstract Algebra II
MA412 Winter 2015: Northern Michigan University

This is the syllabus for Math 412. See the links to the right for updated information. Here you'll find information on prerequisites, grading policy, homework, study resources and a tentative course calender.


  • Where: LRC 235B
  • When: 11:00-11:50 a.m., Mon-Wed-Fri
  • Office Hours

    I am often in my office JXJ 2226, you are encouraged to stop by and see if I am available. My official office hours are

  • Monday: 10am - 11am
  • Tuesday: 1pm - 3pm
  • Thursday: 1pm - 2pm
  • Course Description

    Math 412 is continuation of Math 312. We will study the algebraic properties of rings, ideals, quotient rings, integral domains extension fields, and splitting fields. We will also study the Sylow theorems and Galois theory.


    C- or better in Math 312.


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

    Abstract Algebra Textbook

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


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


    You will have weekly homework assignments that will be collected and graded. The problems will range in difficulty and you are encouraged to work together. You must, however, write up your own solutions and acknowledge your collaborators and sources, and staple (or neatly package) your work.


  • Homework 40%
  • Quizzes 20%
  • Midterm 20%
  • Final 20%
  • Quizzes

    Quizzes will be given frequently. Some quizzes will be group/team quizzes.


  • Midterm: Feb. 27
  • Final: Thursday, April 30, 10am - 11:50am
  • Make sure that you will be able to attend the exams at the given dates and times. Exceptions can only be accepted in case of time conflicts with other courses, or serious illness with a physician's certification.
  • Final Exam Schedule
  • Technology

    I do not expect that you will be able to easily do all the homework on your own. You will need to work with others, and you should ask your professor for help. You should not quickly resort to the internet when you are stuck. Being stuck is an important part of the learning process.

    If you find hints or solutions on the internet and use them in your solutions, I want you to also include the work you have done on your own up to this point.

    Laptops and Cellphones

    Do not use your laptop in class unless instructed to do so and please put your phone away while in class. I often find that my most creative thoughts arrive while sitting through a boring lecture. I'll do my best to not be boring, but if I fail give daydreaming a try.

    Other Resources

    These Abstract Algebra Videos are pretty good.

    Both free and paid tutoring is available, in the tutoring lab in NSF 3810.

    Outcomes & Assesment

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

  • Select and correctly apply standard proof writing techniques.
  • Describe various properties of rings, fields and integral domains.
  • Apply the theory of rings and fields in the solution of algebraic equations.
  • 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.

  • Introduction to Rings - 1 week
  • Integral Domains - 1 week
  • Ideals and Factor Rings - 1 week
  • Permuatation Groups - 1 week
  • Ring Homomorphisms - 1 week
  • Polynomial Rings - 1 weeks
  • Factorization of Polynomials - 1 week
  • Extension Fields - 1 week
  • Algebraic Extensions- 1 week
  • Finite Fields 1 week
  • Geometric Constructions 1 week
  • Sylow Theorems 1 week
  • Introduction to Galois Theory 1 week
  • University Policies

    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: The University seeks to provide equal access to its programs, services and activities for people with disabilities. 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 (227-1700). at 906-227-1700 as soon as possible. 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.