MATH 6140 (Algebra 2)

MATH 6140, Spring 2023
Instructor: Dr Green
Venue: MWF 9.05am, ECCR 108
Office: MATH 313
Online classes: Zoom Meeting ID 958 6741 2737; see me for the password.
Email: rmg [AT]
Office Hours: M 12.20, W 12.20, F 10.10
Abstract Algebra by David S. Dummit and Richard M. Foote (third edition)
MATH 6130
Course Contents
Modules, vector spaces, modules over principal ideal domains, field theory, Galois theory. This is chapters 10--14 of the book, except sections 10.4, 10.5 and 11.5.
Homework will be worth 100 points in total and will be based on your best 10 homework scores. Usually, three or more of the assigned problems will be graded, and late work will ordinarily not be graded.
The two midterms will be worth 100 points each, and the final will be worth 200 points. These three examinations may be individually curved to produce an appropriate profile.
The two midterms are scheduled to be held during class on Wednesday, February 15, and Wednesday, March 22, 2023.
The final examination is on Tuesday, May 9, 2023 from 1.30pm to 4pm in the usual classroom. (Check that this agrees with your other sources of information!)
The first midterm might be something like this.
The second midterm might be something like this.
The final might be something like this.
Homework is due at the beginning of class. Some, but not all of the problems will be graded. Justify all your answers. You should assume that late work will not be graded.
Students With Disabilities
If you qualify for accommodations because of a disability, please submit your accommodation letter from Disability Services to your faculty member in a timely manner so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities in the academic environment. Information on requesting accommodations is located on the Disability Services website. Contact Disability Services at 303-492-8671 or for further assistance. If you have a temporary medical condition, see Temporary Medical Conditions on the Disability Services website.
Missed Exams
If you know that you are going to miss an exam or cannot take the final exam at the scheduled time, please notify your instructor at least two weeks in advance. If you miss a midterm exam for any acceptable reason (e.g. religious obligation, illness), that midterm exam score will be replaced by an estimated score based on your performance on the other midterm. If you miss both exams for acceptable reasons, your midterm scores will be replaced by estimated scores based on your performance on the final. If you miss the final exam and have not rescheduled it in advance, you will score zero on the final or receive an incomplete in the course, depending on the circumstances. You may not reschedule a final after the final has started.
Classroom Behavior
Both students and faculty are responsible for maintaining an appropriate learning environment in all instructional settings, whether in person, remote or online. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. For more information, see the classroom behavior policy, the Student Code of Conduct, and the Office of Institutional Equity and Compliance.
Please, no open yawning or sleeping in class!
CU Boulder recognizes that students' legal information doesn't always align with how they identify. Students may update their preferred names and pronouns via the student portal; those preferred names and pronouns are listed on instructors' class rosters. In the absence of such updates, the name that appears on the class roster is the student's legal name.
Requirements for COVID-19
As a matter of public health and safety, all members of the CU Boulder community and all visitors to campus must follow university, department and building requirements and all public health orders in place to reduce the risk of spreading infectious disease. CU Boulder currently requires COVID-19 vaccination and boosters for all faculty, staff and students. Students, faculty and staff must upload proof of vaccination and boosters or file for an exemption based on medical, ethical or moral grounds through the MyCUHealth portal.
The CU Boulder campus is currently mask-optional. However, if public health conditions change and masks are again required in classrooms, students who fail to adhere to masking requirements will be asked to leave class, and students who do not leave class when asked or who refuse to comply with these requirements will be referred to Student Conduct and Conflict Resolution. For more information, see the policy on classroom behavior and the Student Code of Conduct. If you require accommodation because a disability prevents you from fulfilling these safety measures, please follow the steps in the "Accommodation for Disabilities" statement on this syllabus.
If you feel ill and think you might have COVID-19, if you have tested positive for COVID-19, or if you are unvaccinated or partially vaccinated and have been in close contact with someone who has COVID-19, you should stay home and follow the further guidance of the Public Health Office ( If you are fully vaccinated and have been in close contact with someone who has COVID-19, you do not need to stay home; rather, you should self-monitor for symptoms and follow the further guidance of the Public Health Office (
Honor Code
All students enrolled in a University of Colorado Boulder course are responsible for knowing and adhering to the Honor Code. Violations of the Honor Code may include, but are not limited to: plagiarism, cheating, fabrication, lying, bribery, threat, unauthorized access to academic materials, clicker fraud, submitting the same or similar work in more than one course without permission from all course instructors involved, and aiding academic dishonesty. Any incident of academic misconduct may be reported to Student Conduct & Conflict Resolution (; 303-492-5550). Students found responsible for violating the Honor Code will be assigned resolution outcomes from the Student Conduct & Conflict Resolution as well as be subject to academic sanctions from the faculty member. Additional information regarding the Honor Code academic integrity policy can be found on the Honor Code website.
Sexual Misconduct, Discrimination, Harassment and/or Related Retaliation
CU Boulder is committed to fostering an inclusive and welcoming learning, working, and living environment. University policy prohibits sexual misconduct (harassment, exploitation, and assault), intimate partner violence (dating or domestic violence), stalking, protected-class discrimination and harassment, and related retaliation by or against members of our community on- and off-campus. These behaviors harm individuals and our community. The Office of Institutional Equity and Compliance (OIEC) addresses these policies, and individuals who believe they have been subjected to misconduct can contact OIEC at 303-492-2127 or email Information about university policies, reporting options, and support resources can be found on the OIEC website.
Please know that faculty and graduate instructors have a responsibility to inform OIEC when they are made aware of any issues related to these policies regardless of when or where they occurred to ensure that individuals impacted receive information about their rights, support resources, and resolution options. To learn more about reporting and support options for a variety of concerns, visit Don't Ignore It.
Religious Holidays
Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance.
In this class, you should inform your professor of any conflict as soon as possible. In the case of conflicts with exams, if you do not inform your instructor of the conflict at least two classes in advance of the exam, you must provide documentary evidence of the religious obligation.
See the campus policy regarding religious observances for full details.

Homework assignments

Assignment 1 (assigned Wed 18 Jan, due Wed 25 Jan)
10.1: 1, 3, 4, 5, 6, 8 (a, c), 9, 15, 18, 19, 20, 21
Assignment 2 (assigned Mon 23 Jan, due Mon 30 Jan)
10.2: 1, 2, 4, 5, 6, 7, 9, 10, 11
Assignment 3 (assigned Mon 30 Jan, due Mon 6 Feb)
10.3: 1, 3, 4, 5, 6, 7, 8, 9, 10, 11
Assignment 4 (assigned Mon 6 Feb, due Mon 13 Feb)
11.1: 4, 5, 6
11.2: 9, 11, 12, 38
Assignment 5 (assigned Mon 13 Feb, due Mon 20 Feb)
11.3: 2, 3 (except part (b)), 4
Assignment 6 (assigned Mon 20 Feb, due Wed 1 Mar)
11.4: 3
12.1: 1(a), 2(a), 5, 6, 7, 9, 13, 15
Assignment 7 (assigned Mon 27 Feb, due Mon 6 Mar)
12.2: 1, 3, 4, 5, 6, 8, 11, 17, 18
Assignment 8 (assigned Mon 6 Mar, due Mon 13 Mar)
12.3: 2, 17, 18, 20, 21, 22, 23, 25, 26, 31, 32, 34
13.1: 3, 5, 7 [over Z]
Assignment 9 (assigned Mon 15 Mar, due Mon 20 Mar)
13.2: 3, 4, 5, 10, 12, 13, 14, 16, 19
13.3: 4, 5
Assignment 10 (assigned Mon 20 Mar, due Mon 3 Apr)
13.4: 1, 2, 3, 4
13.5: 3, 6, 9
Assignment 11 (assigned Mon 3 Apr, due Mon 10 Apr)
13.6: 1, 2, 3, 4, 6, 9, 10
14.1: 2, 3, 4, 6, 7, 10
Assignment 12 (assigned Mon 10 Apr, due Mon 17 Apr)
14.2: 1, 4 [over Q], 5, 8, 11, 13
14.3: 1, 3, 7, 8, 9, 10
Assignment 13 (assigned Mon 17 Apr, due Mon 24 Apr)
14.4: 1, 3
14.5: 4, 5, 7, 10, 12
Assignment 14 (assigned Mon 24 Apr, due Mon 1 May)
14.6: 2 [over Q], 3, 4 [over Q], 11, 17, 44, 46
14.7: 10, 12