Instructor Name: Dustin Cartwright
Office Hours: M 11:15–12:15 (except for 8/19), W 8–9, F 1:45–2:45 or by appointment, in Ayres 210
Email: cartwright@utk.edu
Course Webpage: All further information, including updates to this syllabus, will be on the Canvas webpage for this course.
Course Communications: Reminders and routine announcements will be made in class. I will use Canvas announcements for important messages, such as changes to assignments. I will only email you for urgent messages, such as class being canceled.
The best way for you to contact me is by email. I will reply on the same day to emails received before 3pm on a work day. For emails received after 3pm or on a weekend or holiday, I will reply by 10am on the next work day.
Upon completion of this course, students should be able to manipulate elements of many examples of groups and rings as well as construct proofs involving their basic properties.
I expect you to attend every lecture, pay attention, and participate in class activities. During lectures, you should not use your laptop, cell phone, or any other electronic devices. Taking notes on a tablet is okay.
Introduction to Abstract Algebra: With Applications by Thomas Judson, Fall 2024 edition. The book is available to read online.
Scale for letter grades: A 90–100, A- 85–89, B+ 80-84, B 75-79, B- 70-74, C+ 65-69, C 60-64. These cut-offs may be adjusted to be more generous at my discretion.
Homework: Homework is due by 7:00am each Tuesday morning. You will submit your homework on Canvas in PDF format. Assignments will be posted on Canvas at least a week in advance.
All homework answers require justification.
Some homework assignments will contain designated “quiz problems,” which you must complete on your own without talking to anyone or using resources other than your own notes or the course textbook.
On the other hand, you are strongly encouraged to discuss the non-quiz problems with other people in class. However, you must write up your own solutions and you must acknowledge your collaborators or any other sources used beyond the standard course resources, as described below.
Homework will be graded based on a subset of the problems, which will always include any quiz problem.
Citation policy: You must write your own homework solutions and you must credit any person or source who helped you understand the solution. Specifically:
In all cases, you must understand your answer and write in your own words. You will find solutions on the Internet that use different notation and conventions than this class and you should not just blindly copy those.
Group work: Group work will be done in class, in collaboration with other students in class, possibly unannounced. You will be graded on effort.
Exams: The midterms and final must be taken without any books, notes, or electronic devices. The second will cover material since the first midterm. The final will be cumulative.
Late homework will generally not be graded or counted for credit. Instead, I will drop the lowest homework score and the lowest group work score.
Missed exams will be excused only in circumstances which unavoidably prevent you from taking the exam, such as a medical or family emergency. Excuses will need to be documented, usually through Student Life Division. Accommodation is at my discretion.
Missed midterms might have a make-up or might be replaced by your final exam grade.
Please let me know as soon as possible if you will miss an exam.
Every day: Come to class. Do the homework. Look at the book, either before or after class. Look over your own notes. Start the homework early. Work on the problems yourself before getting help. Look over your homework and exams after they’ve been graded. Look at the solutions.
If things go badly: If you find yourself falling behind, it is important to adjust sooner or later. You can talk to me during office hours to catch up.
Proofs: Unlike many other math problems, proofs are not necessarily written from the beginning to the end. If you’re not sure where to start, try making assumptions that make the problem easier, such as replacing abstract objects with more concrete versions. Then, see what needs to be changed to make the assumptions abstract. Look for theorems in the book or your notes that seem to apply. If the theorem doesn’t quite apply, can you find an argument to fill the gap? Or modify the proof so that it would work? In almost all cases, you will use all given hypotheses, so if you get stuck partway through a proof, look at which hypotheses you haven’t used.
We will cover modular arithmetic, rings, and groups, with an emphasis on examples such as polynomial rings and permutation groups. We will cover most of Chapters 2–12 from the textbook.
The approximate schedule of daily topics is listed on the Canvas page “Daily schedule.”
If the instructor finds it necessary to make informational changes (e.g. office hours, schedule adjustments) due to students’ needs or unforeseen circumstances, students will be notified in writing/email of any such changes.