MATH 6140 (Algebra 2)

MATH 6140, Spring 2020
Instructor: Dr Green
Venue: MWF 9, MATH 220
Office: MATH 313
Email: rmg [AT]
Office Hours: M 10, W 10, F 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 will be held during class on Wednesday, February 12, and Wednesday, March 18, 2020.
The first midterm might be something like this.
Update: Midterm 2
Despite what was said earlier, midterm 2 will be a take-home exam. You will be allowed to use notes and books, but you will not be allowed to use other people or the internet as resources. The exam will cover the expected material and will be of the expected level of difficulty, but the questions will be more detailed or longer than for an in-class exam. There will be an online class as usual on March 18, and the exam will take place after that.
The second midterm might be something like this.
Update: Final
Despite what was said earlier, the final will be a take-home exam. The exam will be distributed by email before 9am on the "reading day", Friday, May 1. I will be available at 9am that day to discuss the exam, and to answer questions about it. The final will be due at 4pm on Tuesday, May 5. As usual, the final should be submitted by email to me, as a single pdf with a helpful filename.
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.
Update: Homework
Online homework must be submitted by email as a single pdf. Please give your file a useful name: Chris_HW10.pdf is helpful, but myhomework.pdf is not.
Students With Disabilities
If you qualify for accommodations because of a disability, please submit to your professor a letter from Disability Services in a timely manner (for exam accommodations provide your letter at least two classes prior to the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities. Contact Disability Services at 303-492-8671 or by e-mail at dsinfo [AT]
If you have a temporary medical condition or injury, see Temporary Medical Conditions: Injuries, Surgeries, and Illnesses guidelines under Quick Links at the Disability Services website and discuss your needs with your professor.
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 classes in advance. If you miss a midterm exam for any acceptable reason (e.g. religious obligation, documented 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 exam after the exam has started.
In order to be excused from an exam for medical reasons, you must either produce a note from a doctor, or you must obtain prior permission from the instructor to miss the exam. Self-diagnosis and self-medication are not acceptable for this purpose.
Religious Obligations
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 notify your instructor of any conflict immediately.
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.
Student Classroom and Course-Related Behavior
Students and faculty each have responsibility for maintaining an appropriate learning environment. 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 differences of race, color, culture, religion, creed, politics, veteran's status, sexual orientation, gender, gender identity and gender expression, age, disability, and nationalities. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. Please, no open yawning or sleeping in class!
Sexual Misconduct, Discrimination, Harassment and/or Related Retaliation
The University of Colorado Boulder (CU Boulder) is committed to maintaining a positive learning, working, and living environment. CU Boulder will not tolerate acts of sexual misconduct, discrimination, harassment or related retaliation against or by any employee or student. CU's Sexual Misconduct Policy prohibits sexual assault, sexual exploitation, sexual harassment, intimate partner abuse (dating or domestic violence), stalking or related retaliation. CU Boulder's Discrimination and Harassment Policy prohibits discrimination, harassment or related retaliation based on race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. Individuals who believe they have been subject to misconduct under either policy should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127. Information about the OIEC, the above referenced policies, and the campus resources available to assist individuals regarding sexual misconduct, discrimination, harassment or related retaliation can be found at the OIEC website.
Honor Code
All students enrolled in a University of Colorado Boulder course are responsible for knowing and adhering to the academic integrity policy of the institution. Violations of the policy may include: plagiarism, cheating, fabrication, lying, bribery, threat, unauthorized access, clicker fraud, resubmission, and aiding academic dishonesty. Any incident of academic misconduct may be reported to the Honor Code Council (; 303-735-2273). Students who are found responsible for violating the academic integrity policy will be subject to nonacademic sanctions from the Honor Code Council as well as academic sanctions from the faculty member. Additional information regarding the academic integrity policy can be found at

Homework assignments

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