2021 Spring Course Syllabus - Mathematics 8012.001
Course: Mathematics 8012.001.
Course Title: Abstract Algebra II.
How this course will be taught: The course will be taught in a synchronous online format using Zoom; the Zoom link for all lectures is https://temple.zoom.us/j/91294070819.
Time: TR 11:00-12:20.
Place: Zoom.
Instructor: Martin Lorenz.
Instructor Office: Wachman 528.
Instructor Email: martin.lorenz@temple.edu
Instructor Phone: Use email.
Office Hours: TR 2-3:30pm.
Prerequisites: Math 8011 or equivalent or permission of instructor.
Textbook: Dummit & Foote: Abstract Algebra, 3rd ed., John Wiley & Sons, 2004.
Technology specifications for this course: A working computer with a reliable internet connection, a Webcam, and audio capability. Recommended Internet Speed: 8mbps download & 5mbps upload. You can test your connection at https://www.speedtest.net. Please note: Hard-wired connections are more consistent than Wi-Fi for Zoom sessions. A scanning app such as AdobeScan or CamScanner is required as is access to Zoom and Canvas (the Canvas app is also recommended).
Limited resources are available for students who do not have the technology they need for class. Students with educational technology needs, including no computer or camera or insufficient Wifi-access, should submit a request outlining their needs using the Student Emergency Aid Fund form. The University will endeavor to meet needs, such as with a long-term loan of a laptop or Mifi device, a refurbished computer, or subsidized internet access.
Course Goals: This course, the second part of a two-semester sequence, will give a thorough introduction to the methods and terminology of modern abstract algebra. The abstract algebra sequence Math 8011/8012 is a prerequisite for many of the higher-level graduate courses in pure mathematics, and it provides the background needed for the PhD qualifying exam in Algebra.
Topics Covered: We will start where the previous fall semester finished: wrapping up finite Galois theory. This will be followed by a discussion of Galois extensions that are not necessarily finite. The next part of the course will be devoted to rings and modules. Topics to be covered in this part include noetherian rings and modules and the structure of modules over principal ideal domains. An introduction to tensor products and other constructions of modern multilinear algebra will be given at the end of the semester.
Course Grading: The course grade will be based on homework and two exams, a midterm exam and a comprehensive final exam. The final exam will count for 40% of your grade; the midterm and the total score from all homework assignments will each count for 30%.
Exam Dates: The Midterm Exam will be given on Tuesday, March 9, 11-1pm; the Final Exam on Tuesday, May 4, 10:30-12:30 (as per the TU Examination Schedule). Both exams will be online.
Remote proctoring statement: Zoom, Proctorio or a similar proctoring tool may be used to proctor exams and quizzes in this course. These tools verify your identity and record online actions and surroundings. It is your responsibility to have the necessary government or school issued ID, a laptop or desktop computer with a reliable internet connection, the Google Chrome and Proctorio extension, a webcam/built-in camera and microphone, and system requirements for using Proctorio, Zoom, or a similar proctoring tool. Before the exam begins, the proctor may require a scan of the room in which you are taking the exam.
Attendance Policy: I will track the attendance for each class. If you cannot make a class, then please let me know beforehand so that I don't wait for you to join the Zoom class. Missed classes will not adversely affect your grade, but it is in your own best interest to attend class regularly because the material to be covered is not easily absorbed by selfstudy.
The University's attendance policy (opens in new tab/window) has been standardized to accommodate students who are ill or are required to self-quarantine for a period of time due to the COVID-19 pandemic.
To achieve course learning goals, students must attend in-person classes, and/or participate in classes or portions of classes that are taught remotely, to the extent that they are able. Though increased flexibility will be granted, in all cases, course assessments such as assignments, tests and exams must be completed for learning goals to be reached.
In order to facilitate contact tracing, instructors are required to ensure that attendance is recorded for each in-person meeting using an online attendance system designated by the university. Students who are exhibiting symptoms such as cough, fever, shortness of breath, muscle or body aches, headache, chills, sore throat, congestion, or new loss of taste or smell, or who have been in close contact with others who have symptoms, or who are engaging in self-quarantine at the direction of the Philadelphia Health Department, Student Health Services, or any healthcare professional, should not attend in-person classes. Students will not be required to provide formal documentation from a healthcare provider for COVID-related absences. For more information, see the Student Health Services COVID-19 site (opens in new tab/window).
It is also important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Treat your classmates and instructor with respect in all communication, class activities, and meetings. All opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse. You are encouraged to comment, question, or critique an idea but you are not to attack an individual. Our differences, some of which are outlined in the University's nondiscrimination statement (opens in a new tab/window), will add richness to this learning experience.
Please consider that sarcasm, humor and slang can be misconstrued in online interactions and generate unintended disruptions. Profanity should be avoided as should the use of all capital letters when composing responses in discussion threads, which can be construed as "shouting" online. Remember to be careful with your own and others' privacy. In general, have your behavior mirror how you would like to be treated by others.
Online Classroom Etiquette: It is expected that each student attends every class on time for the full duration of each class and behaves, in the same professional manner, as if you are in a regular classroom. This refers in particular to your location and attire. It is not appropriate to eat a large meal, drink alcohol, smoke, or get up often during an online class.
Statement on recording and distribution of recordings of class sessions: Any recordings permitted in this class can only be used for the student's personal educational use. Students are not permitted to copy, publish, or redistribute audio or video recordings of any portion of the class session to individuals who are not students in the course or academic program without the express permission of the faculty member and of any students who are recorded. Distribution without permission may be a violation of educational privacy law known as FERPA as well as certain copyright laws. Any recordings made by the instructor or university of this course are the property of Temple University.
Homework: Homework will be assigned and collected regularly. It is important that you give the assigned problems your best effort--this is by far the best way to learn the material. I do encourage you to discuss the assignments with each other, but I expect everybody to write up their own solutions. Obvious copies from classmates or the internet will not be accepted. While the internet is of course a source for solutions to all kinds of problems, you will not learn abstract algebra by relying on internet searches. Ideally, you should write your homework solutions in LaTeX, but this is not a strict requirement.
Canvas: I will continue posting complete classnotes for my lectures shortly after each lecture on Canvas. It is important that you work through these classnotes afterward. (You should also consult the textbook for additional information and alternative points of view.) Besides my notes for each class, homework assignments and their solutions, various announcements, and other materials will also be posted on Canvas. Furthermore, recordings of all lectures will be available on Canvas.
Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in 100 Ritter Annex (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).
Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.
During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).
The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).