MATH 665 Topics Abstract Algebra I An introduction to Category - - PDF document

MATH 665 – Topics Abstract Algebra I An introduction to Category Theory and Universal Algebra TuTh 12:30-13:45, MDD 214 Instructor: Arturo Magidin Office Hours: MF 11–12, Tu 3–4, We 2–3

• r by appointment.

Office: MDD 404. Campus Phone: 482-6706. e-mail: magidin@louisiana.edu Course homepage: http://userweb.ucs.louisiana.edu/~avm1260/math665.html Course Moodle page: MATH665-001-202120 PREREQUISITES: Passing the Algebra written comprehensive; or being advanced to candidacy;

• r passing the MATH 565-566 sequence with a grade of A or B in both courses and permission of the

instructor. MAIN SOURCES: The main book will be George M. Bergman’s An Invitation to General Algebra and Universal Constructions, 2nd Edition, Universitext, Springer-Verlag, 2015, ISBN 978-3-310-11477-4 (softcover). The book is not going to be available in the bookstore. You can get a PDF of a very close version of the text from the author’s website, at: https://math.berkeley.edu/~gbergman/245/ COURSE MODE AND COVID-19 RELATED INFORMATION: As of this writing, my plan is for the course to run “HyFlex”1. The precise balance between face-to-face and remote content delivery is yet to be determined. It will depend on the situation “on the ground” (how things look in Maxim Doucet, and how students and instructor feel about the situation), and also on the basis

• f campus, city/parish, state, and national directives. But as indicated in the schedule of classes, the

default will be face-to-face, on-campus. At least our first meeting will be face-to-face, on campus. If you have have concerns about any of the above, please contact me immediately. I understand that the situation is fluid, and that some may have serious concerns. I will try to be as accommodating as possible. See also the University’s Covid-19 syllabus policies and guidelines that are attached to this

• syllabus. I am also including some notes on contingencies, and how “remote” parts of the course might

play out after the University’s policies and guidlines. MY OFFICE AND OFFICE HOURS: My office is in Maxim Doucet Hall Room 404. However, please note that per University directives and the Dean’s instructions, faculty are requested to keep our presence on campus and our offices to a minimum, and to conduct office hours remotely or in larger rooms. As a result of this, I may frequently not be found in my office during this semester. I will do my best to remain remotely available during “regular hours” if I am not. I will have four office hours a week, tentatively set as above. We can also “meet” by appointment if you cannot make the regular office hours. You may e-mail me to set up an appointment, or talk to me right before or right after class. Feel free to ask for an appointment, especially if you cannot make the regular office hours for some reason. Meetings can be carried out through video conference platforms like zoom and/or Microsoft Teams (some rooms may be available in the Math Department to conduct office hours in a well-spaced environment, but there will be some competition for the space so I cannot at present promise that will be possible). If I am not logged in on the platform, reach out via e-mail (I may be distracted with some other stuff and forgot to log on).

1“A course that is usually taught face-to-face that utilizes a combination of online technology and on-campus learning

to deliver the course during emergencies.”

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A QUESTION A DAY: Each class meeting will have an assigned reading, either from the text or from class notes I will make available through Moodle. You are expected to read through the assigned reading before each class meeting. Every student taking the course is required to hand in, by the day of the class, one question concerning the reading for the day. Ideally, you should submit the question by e-mail by 10:00 am on the day of the class (I will be teaching a class immediately prior to ours, so this gives me enough time to look at the questions before the class). If you do, I will do my best to work the answer into the lecture for the day. If you cannot submit it before that time, or you cannot submit it through e-mail, you may submit it in writing at the start of the class. I will generally answer it by e-mail if we do not manage to cover the point in class. The e-mail, or paper with your question, should have the following information on it, in this order: your name, the point in the notes that your question refers to, and whether your question is “urgent”, “important”, “unimportant”, or “pro forma.” The first three indicate how important it is for you to have the question answered, especially as it relates to your understanding of the material. The fourth classification is used when there was nothing in the reading that you feel needs to be

• clarified. In that case, the “pro forma” question can be something that puzzled you initially but that

you worked out on your own. Note: If you submit a “pro forma” question, then you must also provide the answer to the question. You may ask more than one question on the reading. You may also ask questions about prior readings, and you absolutely may ask questions in class. But you must submit at least one question related to the reading assignment of the day. HOMEWORKS: Homework is a major part of this course, and very important. Mathematics is learned almost exclusively by doing, and that is what homework is for: to help you understand the material, and to help you zero in on the material you are finding difficult. Do not be afraid to ask for help from your fellow students, or most especially from me. In fact, that’s mainly what my office hours are for. I cannot assign as much homework as I think you should do, because the volume would be too much for us all to handle. So you should try to do more than the assigned problems. Homework will be assigned almost every week, on Thursday. Assignments are normally due the Thursday after they are assigned. I may change the schedule a bit, but if I do I will give you advance notice of the change. I will give you worked out solutions to the homework problems as you turn them in. Be sure to read them, and compare it with your graded assignments. Homework is due at the beginning of class, as you come in. I will not accept late homeworks for any reason. If you are not attending the live lecture, you may submit the question as a PDF file or as scans of your homework via a Moodle “assignment”, but please contact me and alert me of the situation ahead of time. TESTS: As this is an advanced course, I do not plan to have a midterm or a final written exam. I will decide later whether to assign a final homework due the day of the final (Tuesday November 24) as a “take-home” exam. You will be kept informed. GRADING: Your final grade will be based on your homeworks and class participation. I will drop your lowest two homework scores. (If there is a final homework as outlined above, it cannot be one of the dropped homeworks) I do not have a rigid correspondence between numerical grades and letter grades; this is where consideration for people who have improved (or not) throughout the semester comes in, or for people who did exceedingly well in the final, etc. For your reference, however, the following are good approximations: 2

Letter grade Approximate Range A 900 – 1000 B 775 – 875 C 650 – 750 D 550 – 625 F – 550. TIME REQUIREMENTS: Expect to spend about 9–10 hours a week on this course, in addition to the two lectures. This includes working on homework, reading, and reviewing. If you find yourself regularly spending considerably more time than this, let me know! MAKE-UP WORK: I do not receive late homeworks and will not allow anyone to make up any homeworks not turned in. If you cannot make it to class, you should either have someone drop off the homework for you, or send it to me via e-mail postmarked no later than the beginning of the class. I will also not allow you to make up the “question of the day” 3

COVID-19 SYLLABUS POLICIES AND GUIDELINES Student Code of Conduct, covid-19: The University aims to fulfill its mission while protecting the health and safety of our students and campus community at large. This includes taking steps to minimize the potential spread of COVID-19. The University will adhere to the orders, proclamations, and regulations of the Governor of Louisiana and the Mayor-President of Lafayette, Louisiana, as well as guidelines from the Centers for Disease Control and Prevention (“CDC”) and the Louisiana Department

• f Health (“LDH”) regarding COVID-19. This impacts the expectations of all students as the University

continues to make public health informed decisions to protect health and safety on campus. Students should read and understand the addendum to the Code of Student Conduct regarding COVID-19 and Public Health-Informed Policies, and any updates thereto. COVID-19 Mask policy for academic areas: To assist in decreasing the spread of the COVID- 19 virus, it is the University’s policy that all students, faculty, and staff are required to wear masks

• r face coverings which completely cover the nose and mouth areas while inside any academic building

including classrooms, labs, studios, offices, hallways, and stairways. A face shield is not an acceptable substitute of a face mask. Failure to wear a mask is a violation of the Student Code of Conduct and such violation will be forwarded to the Dean of Students for action. Students who have concerns about wearing masks due to a disability or medical condition may discuss a modification to the University’s mask policy with the Office of Disability Services. In order to discuss a modification for the Fall 2020 semester, students must first register with Disability Services. All registrants will be contacted to arrange a virtual meeting for further discussion. Learn more about Disability Services and accommodations on the Student COVID-19 Response page. Email questions to

• ds@louisiana.edu.

COVID-19 Attendance: If you are experiencing any signs or symptoms associated with COVID-19 (refer to the most recent Centers for Disease Control [CDC], at https://www.cdc.gov/coronavirus/2019-ncov/if-you-are-sick/steps-when-sick.html guidance on possible symptoms), do not come to class or to campus. First, contact Student Health Services (337-482-1293) or your medical provider, then contact your instructors to inform them of your situation and discuss possible arrangements and ways to keep up with the courses. If you do not feel well for any reason and are staying home, including for symptoms of COVID-19, fill out the Anticipated

• r Unplanned Absence Form, available at

https://studentaffairs.louisiana.edu/dean-students/students/ students-report-anticipated-or-unplanned-absence If you are required to self-isolate or self-quarantine because of COVID-19, do not come to class or to campus. All students who are required to self-isolate or self-quarantine because of COVID-19 must complete the Student COVID-19 Quarantine and Isolation Form (the link is available at the address for the Anticipated or Unplanned Absence form above, but in this situation you do not need to complete the Anticipated or Unplanned Absence form) and email their instructors for support and resources. Do not wait until you are behind to reach out to your instructors. Options will vary depending on when during the term you are unable to participate, how much class time and coursework is missed, and the nature of the course. Options may include, but not be limited to, transitioning to learning and testing remotely during your absence; in extreme cases, withdrawing from the course, or receiving a grade of incomplete. Contact your instructor and academic advisor with any questions. For requests to move from on-campus to remote learning for reasons related to COVID-19, a student initiates a written request to the faculty member. The faculty member considers the students request, learning objectives of the course, and educational technology available to determine if an arrangement for remote instruction is feasible. If a resolution within the course is not possible, the student may contact the department head over the course, and then the academic Dean, to see what other resolutions may be available. Learn more on the Student COVID-19 Response page on the University’s website. If you have any questions or concerns, email deanofstudents@louisiana.edu. 4

Faculty Guidelines: Academic departments will procure a supply of masks through Facilities Management to make available to faculty for students who do not have a mask. If a student is required to wear a mask but is not wearing one as required in academic areas, faculty will provide a mask to the student and inform the student that it is a violation of the Code of Student Conduct not to wear a mask. If the student does not use the mask, the student will be required to leave the classroom and the faculty will advise them that they will report it as a violation of the Code of Student Conduct. The faculty will complete the Community Reporting Form found on the Office of Student Rights and Responsibilities website. Any class missed due to a students failure to adhere to the requirement of wearing a mask will be recorded as an unexcused absence. The student will not be allowed into the academic setting until clearance has been provided from the Office of Student Rights and Responsibilities. Students should stay in contact via e-mail with their instructors/professors pending clearance. Health or Safety Risk: The University may request or require a student to leave campus when that students continued presence on campus poses a health or safety risk for community members. Links: A copy of these guidelines, in WORD format, is available from the Academic Affairs Division, at https://academicaffairs.louisiana.edu/sites/academicaffairs/ files/Syllabus%20Statement%20COVID-19_word.docx More information is also available at the COVID-19 webpage of the Academic Affairs Division, https://academicaffairs.louisiana.edu/covid-19-information and at the University COVID-19 update page: https://louisiana.edu/covid19 5

Course On-line Component and Contingency Plans As I indicated above, formally I am calling this a HyFlex course; the University defines this as a “course that is usually taught face-to-face that utilizes a combination of online technology and on- campus learning to deliver the course during emergencies.” Though I hope that we all feel the situation is safe and that we can mostly meet in-person for the class, I realize that this may not be the case, and that in any case some may face challenges or have concerns that will make this difficult. I will be as accommodating as I can. Some lectures or content may be delivered online (I will notify you ahead of time if this will be the case). Even for lectures delivered face-to-face, I will try to make relevant content covered in class (especially answers to the “question a day” and material not contained in the text) available online in as timely a manner as I can manage for those who miss the class due to COVID-19. Do call me on it if you notice I have not kept up on a timely manner: this is all new to me as well. The online material may take several forms, as I become more familiar and profficient with the available tools. Due to my hardware restrictions it is unlikely to include video lectures, but VoiceThread

• r screen capture is more likely.

Should the University be forced to close off campus, or if we determine that the best course forward is to go fully remote, you may expect the following:

• 1. “Lectures” will go fully remote. As of this time, I expect they would take the form of typed-up

class notes with VoiceThread and/or screen capture videos taking the place of the lectures.

• 2. Answers to the “question of the day” that I consider important for everyone to hear will also be

posted as either a short write-up/VoiceThread or a short screen capture video. Other answers will be answered individually via e-mail.

• 3. I will continue assigning homework and holding virtual office hours.
• 4. Homework will have to be delivered remotely, via an “assignment activity” in Moodle.

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