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] euclid.colorado.edu
Office Hours: MWF 10.20-11.10, or by appointment
Text
Abstract Algebra by David S. Dummit and Richard M. Foote (third edition)
Prerequisites
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.
Grading
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.
Tests
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
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 https://canvas.colorado.edu/courses/71830.
Student Classroom and Course-Related 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 University's policies on classroom behavior and the Student Code of Conduct. Please, no open yawning or sleeping in class!
Requirements for COVID-19
As a matter of public health and safety due to the pandemic, all members of the CU Boulder community and all visitors to campus must follow university, department and building requirements, and public health orders in place to reduce the risk of spreading infectious disease. Required safety measures at CU Boulder relevant to the classroom setting include:
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.
Before returning to campus, all students must complete the COVID-19 Student Health and Expectations Course. Before coming on to campus each day, all students are required to complete the Buff Pass.
Students who have tested positive for COVID-19, have symptoms of COVID-19, or have had close contact with someone who has tested positive for or had symptoms of COVID-19 must stay home.
Accommodation for 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 dsinfo@colorado.edu for further assistance. If you have a temporary medical condition, see Temporary Medical Conditions on the Disability Services website.
Preferred Student Names and Pronouns
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.
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 policy may include: 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. Incidents of academic misconduct may be reported to the Honor Code (honor@colorado.edu; 303-492-5550). Students found responsible for violating the academic integrity policy will be subject to nonacademic sanctions from the Honor Code as well as academic sanctions from the faculty member. Additional information regarding the Honor Code academic integrity policy can be found at the Honor Code Office website.
Sexual Misconduct, Discrimination, Harassment and/or Related Retaliation
The University of Colorado Boulder (CU Boulder) is committed to fostering a positive and welcoming learning, working, and living environment. CU Boulder will not tolerate acts of sexual misconduct intimate partner abuse (including dating or domestic violence), stalking, protected-class discrimination or harassment by members of our community. Individuals who believe they have been subject to misconduct or retaliatory actions for reporting a concern should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127 or cureport@colorado.edu. Information about the OIEC, university policies, anonymous reporting, and the campus resources can be found on the OIEC website.
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