Math 541: Modern Algebra

Math 541 Section 004, Fall 2020

Lectures: MWF 3:30 -4:20 pm, VV B102 until Nov 25. Online from Nov 30 to Dec 10. Update: from 9/14 until at least 9/25, class will be held online over Zoom, at the usual time. See Canvas for the meeting room ID.

Instructor: Daniel Corey, VV 321, dcorey[at]

Office Hours: Tuesday 1-2:30 pm, Thursday 2:30-4 pm, over Zoom (see Canvas for the meeting room ID).

Textbook: Abstract Algebra, by Dummit and Foote, Third Edition, 2004. The plan is to cover the following sections: 1.1-1.7, 2.1-2.4, 3.1-3.3, 3.5, 4.1-4.3, 5.1, 5.2, 7.1-7.4, 7.6. Here are my Lecture Notes.



Canvas URL:

Piazza: All discussions outside of the classroom will take place on Piazza, accessible through Canvas.

Course assistant: Shourya Mohaniya will have office hours 7-10 pm on Fridays. These will be held over Zoom, see Canvas for the link.

Homework: All references to problems are from Dummit and Foote. Please turn in your homework on Canvas.

  • Homework 1: 1.3: 2, 6 (do all elements, not just those of order 4), 9a, 10 (ignore the last sentence), 12, 16, 1.4 10 (replace the phrase "subgroup of GL_2(R)" with "matrix group"), 11ab (let F=R). Due Friday, Sept 18.

  • Homework 2: 0.3 12, 13, 14; 1.1 8, 13, 22, 31; 1.3 4b; 1.4 11e. Due Friday, Sept 25.

  • Homework 3: 1.2 4; 1.5 1; 1.6 2, 4, 23; 2.1 1, 6, 15; 2.4 14. Due Friday, Oct 2.

  • Homework 4: 2.3 4, 11, 19; 3.1 1, 26, 32 (only the first sentence); 3.2 8, 16. Due Friday Oct 16.

  • Homework 5: 3.1 22, 33, 36; 3.2 4, 11; 3.3 3, 4, 9. Due Friday Oct 23.

  • Homework 6: 1.7 5, 15; 2.2 5, 6, 8, 12; 3.5 1 (just the first and last sentences), 9. Due Friday Oct 30.

  • Homework 7: 1.1 30; 4.2 2, 7; 4.3 2, 6, 13, 27, 30; 5.2 4. Due Friday Nov 6.

  • Homework 8: 7.1 3, 5, 14, 26, 27; 7.2 1, 3, 10. Due Friday Nov 20.

  • Homework 9: 7.3 6, 10, 19, 24, 29, 31, 33, 35; 7.4 12 Due Wednesday Dec 2.

  • Homework 10: 7.4 8, 11, 13, 15, 30, 37, 39 Due Wednesday Dec 9.

Honors Problem Set: If you are signed up to take this class with Honors, please complete the following assignment. Read sections 4.4 and 4.5 in the book and complete exercises 4.4 1, 6, 7; 4.5 3, 16, 23, 24, 30, 45. Please email your solutions to me by 8 am Dec. 15 CT (early submissions are welcome).

Midterm exam 1: Monday Oct 5, in class.

Midterm exam 2: Monday Nov 9, in class.

Final Exam:

Wednesday, Dec 16. The "official" time for the exam is 10:05am - 12:05pm. However, the exam will be take-home, open-notes, open-book, however it must be completed by yourself and without use of the internet. I will write an exam as if it were a 2-hour in-class exam, but you will have 24 hours to complete it.

I will send you the exam on Dec 15 at 12:05 pm Madison time (CT). You must send me your solutions by Dec 16 12:05 pm CT. Solutions may be either typed or handwritten, as you prefer, but please use a separate sheet of paper for each full problem.

Face Coverings During In-person Instruction Statement (COVID-19)

Individuals are expected to wear a face covering while inside any university building. Face coverings must be worn correctly (i.e., covering both your mouth and nose) in the building if you are attending class in person. If any student is unable to wear a face-covering, an accommodation may be provided due to disability, medical condition, or other legitimate reason.

Students with disabilities or medical conditions who are unable to wear a face covering should contact the McBurney Disability Resource Center or their Access Consultant if they are already affiliated. Students requesting an accommodation unrelated to disability or medical condition, should contact the Dean of Students Office.

Students who choose not to wear a face covering may not attend in-person classes, unless they are approved for an accommodation or exemption. All other students not wearing a face covering will be asked to put one on or leave the classroom. Students who refuse to wear face coverings appropriately or adhere to other stated requirements will be reported to the Office of Student Conduct and Community Standards and will not be allowed to return to the classroom until they agree to comply with the face covering policy. An instructor may cancel or suspend a course in-person meeting if a person is in the classroom without an approved face covering in position over their nose and mouth and refuses to immediately comply.

Quarantine or Isolation Due to COVID-19

Student should continually monitor themselves for COVID-19 symptoms and get tested for the virus if they have symptoms or have been in close contact with someone with COVID-19. Student should reach out to instructors as soon as possible if they become ill or need to isolate or quarantine, in order to make alternate plans for how to proceed with the course. Students are strongly encouraged to communicate with their instructor concerning their illness and the anticipated extent of their absence from the course (either in-person or remote). The instructor will work with the student to provide alternative ways to complete the course work.

Digital Course Evaluation (AEFIS)

UW-Madison now uses an online course evaluation survey tool, AEFIS. You will receive an official email two weeks prior to the end of the semester when your course evaluation is available. You will receive a link to log into the course evaluation with your NetID where you can complete the evaluation and submit it, anonymously. Your participation is an integral component of this course, and your feedback is important to me. I strongly encourage you to participate in the course evaluation.




Instructors should discuss academic integrity with students early and often. For suggested ways to engage students in these discussions, see the College of Letters and Science Remote Teaching Toolkit.

By virtue of enrollment, each student agrees to uphold the high academic standards of the University of Wisconsin-Madison; academic misconduct is behavior that negatively impacts the integrity of the institution. Cheating, fabrication, plagiarism, unauthorized collaboration, and helping others commit these previously listed acts are examples of misconduct which may result in disciplinary action. Examples of disciplinary action include, but is not limited to, failure on the assignment/course, written reprimand, disciplinary probation, suspension, or expulsion.


The University of Wisconsin-Madison supports the right of all enrolled students to a full and equal educational opportunity. The Americans with Disabilities Act (ADA), Wisconsin State Statute (36.12), and UW-Madison policy (Faculty Document 1071) require that students with disabilities be reasonably accommodated in instruction and campus life. Reasonable accommodations for students with disabilities is a shared faculty and student responsibility. Students are expected to inform faculty [me] of their need for instructional accommodations by the end of the third week of the semester, or as soon as possible after a disability has been incurred or recognized. Faculty [I], will work either directly with the student [you] or in coordination with the McBurney Center to identify and provide reasonable instructional accommodations. Disability information, including instructional accommodations as part of a student's educational record, is confidential and protected under FERPA. (See: McBurney Disability Resource Center)


Diversity is a source of strength, creativity, and innovation for UW-Madison. We value the contributions of each person and respect the profound ways their identity, culture, background, experience, status, abilities, and opinion enrich the university community. We commit ourselves to the pursuit of excellence in teaching, research, outreach, and diversity as inextricably linked goals.

The University of Wisconsin-Madison fulfills its public mission by creating a welcoming and inclusive community for people from every background – people who as students, faculty, and staff serve Wisconsin and the world.