MATH 6140 (Algebra 2)

MATH 6140, Spring 2021
Instructor: Dr Green
Venue: MWF 9.10, ECCR 200
Office: MATH 313
Office: Zoom Meeting ID 977 9848 5789; see me for the password.
Email: rmg [AT]
Office Hours: MWF 10.20-11.10, or by appointment
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 Friday, February 19, and Wednesday, March 31, 2021.
The final examination is on Saturday, May 1, 2021 from 4.30pm to 7pm 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, except that it will be (a) closed book, (b) shorter, and (c) easier.
The final might be something like this, except that it will be (a) closed book, and (b) shorter.
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. When classes are online, homework should be submitted via Canvas at
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Students who fail to adhere to these 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 policies on COVID-19 Health and Safety and classroom behavior and the Student Code of Conduct. If you require accommodation because a disability prevents you from fulfilling these safety measures, please see the "Accommodation for Disabilities" statement on this syllabus.
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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.
See the campus policy regarding religious observances for full details.
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, unless you think you may have COVID-19.

Homework assignments

Assignment 1 (assigned Fri 15 Jan, due Mon 25 Jan)
10.1: 1, 3, 4, 5, 6, 8 (a, c), 9, 15, 18, 19, 20, 21
Assignment 2 (assigned Mon 25 Jan, due Mon 1 Feb)
10.2: 1, 2, 4, 5, 6, 7, 9, 10, 11
Assignment 3 (assigned Mon 1 Feb, due Mon 8 Feb)
10.3: 1, 3, 4, 5, 6, 7, 8, 9, 10, 11
Assignment 4 (assigned Mon 8 Feb, due Mon 15 Feb)
11.1: 4, 5, 6
11.2: 9, 11, 12, 38
Assignment 5 (assigned Mon 15 Feb, due Mon 22 Feb)
11.3: 2, 3 (except part (b)), 4
Assignment 6 (assigned Mon 22 Feb, due Mon 1 Mar)
11.4: 3
12.1: 1, 2, 5, 6, 7, 9, 13, 15
Assignment 7 (assigned Mon 1 Mar, due Mon 8 Mar)
12.2: 1, 3, 4, 5, 6, 8, 11, 17, 18
Assignment 8 (assigned Mon 8 Mar, due Mon 15 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 Wed 24 Mar)
13.2: 3, 4, 5, 10, 12, 13, 14, 16, 19
13.3: 4, 5
Assignment 10 (assigned Mon 22 Mar, due Fri 2 Apr)
13.4: 1, 2, 3, 4
13.5: 3, 6, 9
Assignment 11 (assigned Mon 29 Mar, due Wed 7 Apr)
13.6: 1, 2, 3, 4, 6, 9, 10
14.1: 2, 3, 4, 6, 7, 10
Assignment 12 (assigned Mon 5 Apr, due Wed 14 Apr)
14.2: 1, 4 [over Q], 5, 8, 11, 13
14.3: 1, 3, 7, 8, 9, 10
Assignment 13 (assigned Mon 12 Apr, due Wed 21 Apr)
14.4: 1, 3
14.5: 4, 5, 7, 10, 12
Assignment 14 (assigned Mon 19 Apr, due Mon 26 Apr)
14.6: 2 [over Q], 3, 4 [over Q], 11, 17, 44, 46
14.7: 10, 12