# Math 386: Combinatorics

## Fall 2022

Teacher
Thomas Zaslavsky
Office: WH-216
Email: zaslav@math.binghamton.edu
Class meets M, W, F 3:00–4:30 in CW 307.

Office hours

• M, W, F 1:00–2:30. No appointment is necessary at these times.
• Other hours by arrangement; feel free to make an appointment by e-mail or catch me after class.

Syllabus
The textbook is Richard A. Brualdi, Introductory Combinatorics, fifth edition. (No other edition will fit the course.) This list of chapters is what I hope to cover in the class (skipping some sections). You will have to do a lot of reading and thinking outside class.

• Chapter 1. What is Combinatorics?
• Chapter 2. Permutations and Combinations
• Chapter 3. The Pigeonhole Principle
• Chapter 4. Generating Permutations and Combinations
• Chapter 5. The Binomial Coefficients
• Chapter 6. The Inclusion-Exclusion Principle and Applications
• Chapter 7. Recurrence Relations and Generating Functions
• Chapter 8. Special Counting Sequences
• Chapter 10. Combinatorial Designs

The minimum time you'll need to spend outside class is about 10 hours a week. Count on that.

Here is a link to the schedule of topics and assignments.

Course goals:
Develop theoretical and computational skills in basic combinatorics and several areas of more advanced combinatorics.

• There will be three tests, including the final exam. There will also be quizzes and homework collection. Your grade will be based on the tests, quizzes, homework, and class participation.

• Test 1 (10/24): 20%.
• Test 2 (11/30 or 12/2, tentative): 20%.
• Final (12/12): 30%.
• Quizzes, homework, and other classwork: 30%.

Homework

• Homework is essential in combinatorics.
• It's a problem-oriented subject where you learn by doing. It can be challenging, too; don't expect to solve every single problem.
• For harder problems, it often helps a lot if you try the problem one day and go back to it a day later. Work ahead.
• I will not cover everything in lectures; you have to learn a lot by reading for yourself.
• I expect you to read the assigned sections carefully before the class.
• The assignments will be weekly so you can spread them out, but don't delay.
• You must write your homework solutions by yourself.
• You may discuss the problems before writing up the solution, but you must write in your own words and formulas.
• Copying is a violation of academic honesty (see the policy).
• I encourage you to form study groups. Discussion with other students is a big part of learning math.
• Hand-in homework should be typed in LaTeX or neatly written, and not squeezed into a small space. (I must be able to read your solution.)
• Staple multiple sheets (paper clips and paper folds don't work).
• Also, remove all stubs if you tear out pages from a spiral binder.
• Hand-in homework is due at the beginning of class.
• If you're late to class, leave your papers on my desk when you arrive, not when you leave.
• Late homework will have a penalty or be refused.
• Homework grading system: 4 points per graded problem or part of a problem.
• 4 pts: Complete and correct.
• 3 pts: Almost complete and correct.
• 2 pts: A significant part is correct but there is a significant lack.
• 1 pt: A good start.
• 0 pts: Anything that isn't even a good start: a bad start, very confused, etc.

• PLAGIARISM WARNING.
• Do the homework. That does not include looking up solutions on line (or off line), even if you don't copy them. I do allow you to work together, but I do not allow copying and I do not allow looking up solutions except from scholarly publications. If you find a solution to one of Brualdi's exercises on line, DO NOT USE IT. If you are not sure, ask me.
• Update, 14 November 2022: From now on, solutions that appear not to be your own work will receive negative credit and possibly more serious consequences.
• If you solve a problem together with other students, list their names.
• If you do use any assistance, on line or off, including help from other people in the class or not in the class (that includes tutors), you must cite your source (or credit the person) and explain what kind of help you got from the source. If you don't do that, you are committing plagiarism, which is not only a scholarly crime but is also subject to disciplinary action from the university.

Quizzes
There will be short quizzes. There are no make-up quizzes.

Test dates

• Test 1: Mon., Oct. 24
• Test 2: Mon., Nov. 28
• Final exam: Mon., Dec. 12

Exam policy

• University PHOTO ID is required to take the final exam.
• No calculators are allowed during exams or quizzes.