Instructor Name: Dustin Cartwright
Office Hours: M 2:45–3:45, W 12:40–1:40, or by appointment in Ayres 210
Email: cartwright@utk.edu
Course Webpage: Additional information, including updates to this syllabus, is on the Canvas webpage for this course.
Course Communications: Reminders and routine announcements will be made in class. I will use Canvas announcements only for more important messages, such as major changes to assignments. I will use email for urgent messages, such as class cancellation.
The best way for you to contact me is by email. I will reply on the same day to emails received before 3:00pm on a work day. For emails received after 3:00pm or on a weekend or holiday, I will reply no later than 10am on the next work day.
By the end of the course, students will be able to solve problems in enumerative combinatorics, using methods such as sieve methods, generating functions, inclusion-exclusion, and others.
I expect you to attend every class, pay attention, and participate in class activities. During lectures, you should not use your laptop, cell phone, or other electronic devices. Taking notes on a tablet is okay.
A Course in Enumeration by Martin Aigner
An alternative source for most of the material is Enumerative Combinatorics, Volume 1 by Stanley, which is a more comprehensive and somewhat more advanced text.
Your grade will be based on homework. Homework will be due every other Thursday at 7:00am on Canvas. Assignments will be available two weeks in advance. You are encouraged to typeset your solutions.
Citation policy: You are strongly encouraged to collaborate with others on your homework. You must write your own homework solutions and you must credit any person or source who helped you understand the solution. You must make sure you understand your answer and write it out in your own words.
Homework solutions: I will use your submitted answers to make solutions to post on Canvas. If you do not wish to have your answers shared, you may request that by email or in a note with your submission. Otherwise, your homework submission gives me permission to aggregate your answers into posted solutions.
Late homework will not be counted for credit without a valid excuse.
Consistency: Go over the material after each class, either from your own notes, or by reading the corresponding section in the textbook. Talk to other people in the class. Come to office hours to ask questions. Ask questions in class. Read the textbook. Read Wikipedia or other sources.
Homework: Doing the homework is an integral part of this course. The best way to understand the material is to work with it. I can tell you how things work out, but it is also important to see the things that don’t work out, and the only way to experience those is to try the wrong approaches. Part of being a research mathematician is distinguishing correct proofs elegant but incorrect proofs.
Always try to work problems by yourself before looking for outside help. Being comfortable with struggling with new concepts may be unfamiliar and you may have to learn to do it.
Make connections: You are strongly encouraged to work with other students in this class. You will find that your peers know different things than you do and you can learn from the ways that they approach problems. Also, the process of explaining your ideas to someone else will help you to understand the material better.
If things go badly: If you find yourself falling behind, adjust sooner rather than later. Come to office hours. Go back over old material. Look for other resources.
We will cover Chapters 1–6 from the textbook, as well as additional topics as time allows. I will list the topics and sections covered on the Daily schedule, as well as anticipated topics to the extent possible.
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.