Math 541, Lecture 002: Modern Algebra

Lectures: Tues/Thurs 11:00 a.m. - 12:15 p.m. in Van Vleck B131.

Instructor: Michael Brown

  • Office: Van Vleck Hall 407
  • Email:

  • Office Hours: Mondays 2:30 p.m. - 4:00 p.m., Thursdays 9:00 a.m. - 10:30 a.m. There is also a tutor for Math 541 this semester. His name is Tom Stone, and his hours are 11:00 a.m. - 2:00 p.m. on Thursdays in Van Vleck B205.

    Textbook: Abstract Algebra, by Dummit and Foote, Third Edition, 2004.

    Description: This is an introductory course in modern algebra. Fundamental objects in modern algebra such as groups, rings, and fields will be introduced. There will also be a focus on learning to write proofs.


    Problem sets will be posted here. They will be collected at the beginning of class on the due date. Late homework will not be accepted. If you have a university-sanctioned excuse for missing a due date, please contact me as soon as possible about this issue.

    While you are encouraged to consult with your classmates on the homework, your final work must be your own. Copying a classmate's work constitutes plagiarism and violates the University of Wisconsin Student Conduct Code. If you collaborate to reach an answer, include the name of your classmate(s) with your solution.

  • Homework 1 (with solutions)

  • Homework 2 (with solutions)

  • Homework 3 (with solutions)

  • Homework 4 (with solutions)

  • Homework 5 (with solutions)

  • Proofs from class

    Here are some write-ups of proofs we discussed in class:

  • The Division Algorithm

  • There will be two midterms given in class and one final exam. All exams are closed book and closed notes. No make-up exams will be given. If you have a university-sanctioned excuse for missing an exam, it is your responsibility to contact me as soon as possible about this issue (at least two weeks before the exam date). In the case of a last-minute medical or family emergency, you should first contact the dean of students.

    Outline of Course

    My current plan is to cover the following sections of the textbook: 0.1 - 0.3, 1.1, 1.3, 1.6, 1.7, 2.1 - 2.4, 3.1 - 3.3, 3.5, 4.1, 4.2, 5.1, 5.5, 7.1 - 7.4, and a selection of topics from Chapters 8 and 13. But this is subject to change.

    Honors Students

    This course has an optional honors component consisting of:
    1. Additional reading: Sections 4.5 and 6.1 of the text.

    2. Two additional problem sets based on these sections:

      Honors Problem Set 1 (due November 21)

      The second problem set will be due on the last day of class, December 12.

    Course policies


    Course grades will be determined as follows: Work must be neat, legible, and clearly organized in order to receive consideration. The logic of a proof must be completely clear in order to receive full credit.
    Academic Integrity:

    Students in this class have the right to expect that their fellow students are upholding the academic integrity of this university. Academic dishonesty is a serious offense, because it undermines the bonds of trust and honesty between members of the community. On homework assignments, academic dishonesty includes, but is not limited to: copying other students' homework or copying homework answers from the internet. On exams, academic dishonestly includes, but is not limited to: looking at another students' work, making use of a disallowed reference during an exam, or looking at a cellphone for any reason (even if it's just to check the time) during an exam.

    Members of the math department treat all incidents of academic dishonesty very seriously. For instance, the consequences for cheating on an exam may range from automatically failing the course to suspension or expulsion. We will not hesitate to initiate disciplinary procedures should such a case arise.


    I wish to fully include persons with disabilities in this course. I encourage you to inform me as soon as possible regarding any special accommodations in the curriculum, instruction, or assessments of this course that may be necessary to enable you to fully participate in this course. Special accommodations for individuals with documented disabilities require two weeks advance notice. I will try to maintain confidentiality of the information you share with me.