Combinatorics, Fall 2014
This page is for a past course. Find your current course here.

Course: Math 636, Fall 2014.
Instructor: Christopher Hanusa — Email: — Office: Kissena Hall 355
Meeting Times: Tuesdays and Thursdays from 5:00–6:15 in KY 273
Course Web Site:
Link to Blackboard: Blackboard

Textbook: Combinatorics: A Guided Tour, by David R. Mazur (ISBN 9780883857625)
This class covers: Chapters 1-4, plus additional topics. [See course notes for more specifics.]

Course goals:

By the end of this course, students should:

  1. Recall key combinatorial techniques and be able to know when certain techniques apply and when they do not apply.
  2. Internalize and be able to apply important combinatorial proof techniques and problem solving skills to unfamiliar problems.
  3. See greater mathematics as a group effort instead of as a solitary pursuit. Develop the ability to work productively on mathematics with others.
  4. Become inquisitive about mathematics in the real world. Formulate one's own interesting counting questions and apply course techniques to solve them.
  5. Get a taste of and gain an appreciation for current research in combinatorics.

Homework Policy:

DO IT! There will be two types of homework in this class, due daily. There will be written homework assignments that you turn in for grading, and discussion homeworks that will be presented at the board. Each homework will be posted on the course web page the week beforehand. You are expected to complete the homework assignments only by consulting your classmates or your professor, and not through internet searches nor students that previously took this class.

Written Homeworks:

The written homeworks contribute towards your homework grade. They will normally consist of 4 five-point questions or 5 four-point questions. You are expected to complete homework questions requiring proof only by consulting your classmates, the course materials, or your professor, and NOT through internet searches nor by contacting students who previously took this class. I expect all solutions to be fully justified, unless otherwise noted. Each of the problems will be graded on the following scale.

4  or  + A well-written homework solution that hits on all the main points.
In other words, Perfect!
3  or  A well-written homework solution that contains most of the main ideas needed to solve the problem completely.
2  or  - A homework solution that contains some of the main ideas but is not complete.
1  or  A very partial solution or a good start.
0  or  0 No work, a weak start, or an unsupported answer

I require you to follow some relatively strict guidelines for homework submission. It is especially important that your homework be legible and clearly presented, or I may not grade it.

It is important to learn how to express yourself in the language of mathematics. In the homework, you should show your work and explain how you did the problem. This is the difference between an Answer and a Solution. It should be obvious to the person reading the homework how you went about doing the problem. This will often involve writing out explanations for your work in words. Imagine that you need an example to help refresh your memory for another class in six months!

A guiding principle that I suggest you follow is "Be precise and concise." That is, you should take great care to write your solutions so that you leave no ambiguity to what you mean and that you write no more than is necessary.

Late Written Homework:

I understand that outside factors may affect your ability to turn in your homework on time. During the semester you will be allowed five total grace days. If a homework is due on Wednesday and you turn it in on Friday, this counts as two of your five grace days. Once you have zero grace days, I will not accept late homework. If you are not planning to be in class, let me know and get it to me beforehand. This is your responsibility. I can accept clearly scanned homework by email, but I will likely expect a physical copy at the next class session.

Discussion Homeworks:

Once every four or five class sessions, you will have a discussion homework assignment consisting of approximately six homework questions. Discussion homeworks may optionally be turned in for grading (see below); in any case, they should be approached with as much detail as their written counterparts since they will be part of in-class presentations and discussions.

You will be expected to present at least one of these homework questions on the board throughout the semester. Presentations need not be complete solutions, but you must make some effort to explain what you know.

I will take volunteers for the presentation problems, but if there are no volunteers, I will call on students randomly. If you are not prepared when called upon, it will be counted against you.

You may turn in well-written solutions to discussion homework problems for grading. This is not required; you will receive no penalty if you decide to not submit solutions. If you submit a discussion homework for grading, I will (casually) grade your solutions and average the scores from the best four solutions you submit. The corresponding homework grade will count as one homework assignment to be averaged into your written homework assignments. Realize that this is not "extra credit" in that a bad grade will negatively impact your homework grade; however, if you take it seriously, it will likely improve your grade in the long run.

Study Groups:

An important component of your learning in this class is through study groups. Study groups allow you to learn the intricacies of the material; discussion of problems often lead to better understanding and new and more efficient ways to solve the problems. One of the best ways to learn something is to explain it to someone else; misunderstandings that you never knew you had will appear under someone else's questioning! In addition, seeing that others also struggle with the material helps to put your own level of understanding in a better perspective and will hopefully reduce some of your anxiety. If you can not find a study group, e-mail me so that I can help you get involved.

Most importantly, I assume that you will be working in groups when I make up the homework assignments. At the beginning of the semester, the problems will seem easy enough to plug and chug on your own, but as the term progresses the questions become quite complex indeed. When a group works on a problem, everyone can participate. But when you write up the answers to the problems, write it up in your own way. I will take off points from all parties if multiple solutions are the same. Be sure to include an acknowledgment to your groupmates on your homework.


There will two exams during the semester. They will be a class period in length and no calculators, cell phones, or study aides are allowed (or are necessary). There will be no make-up exam except in the case of a documented emergency. In the event of an unavoidable conflict with the midterm (an athletic meet, wedding, funeral, etc...), you must notify me at least one week before the date of the exam so that we can arrange for you to take the exam BEFORE the actual exam date.

Final Project:

Working alone or in a group of two, you will research a combinatorial question and present your findings through a poster in a class poster session the last week of class. More information is available here.

Grading Scheme:

Your grade will be based on written homework, class participation including homework presentations, your course project, and the two exams. Each component of your grade is calculated independently; then all pieces are combined using the following weighted average.

Class Participation: 15%
Written Homework: 20%
Exam 1: 20%
Exam 2: 20%
Project, including poster, presentation, and podcast: 25%

Office Hours:

I am happy to help you with your homework and other class-related questions during my office hours. I have official office hours as posted on my schedule. In addition, you are welcome to make an appointment or stop by my office in Kissena 355 at any time. (You can call my office phone 718-997-5964 to see if I'm there.)


DON'T DO IT! It makes me very mad and very frustrated when students cheat. Cheating is the quickest way to lose the respect that I have for each student at the beginning of the semester. Both receiving and supplying the answers on an exam is cheating. Copying homework solutions is considered cheating. Copying text from sources for your project is cheating. I take cheating very seriously. If you cheat, you will receive a zero for the homework/exam and I will report you to the academic integrity committee in the Office of Student Affairs to be placed on your permanent file. If you cheat twice, you will receive a zero for the class.

**Please do realize that working together on homework as described above is not cheating.**

Accommodations for Students with Disabilities:

Students with disabilities needing academic accommodation should register with and provide documentation to the Office of Special Services, Frese Hall, room 111. The Office of Special Services will provide a letter for you to bring to your instructor indicating the need for accommodation and the nature of it. This should be done during the first week of class. For more information about services available to Queens College students, contact the Office of Special Services (718-997-5870) or visit their website ( If you need special accommodation for an exam, you MUST contact me at least one week beforehand.

Course Evaluations

During the final four weeks of the semester, you will be asked to complete an evaluation for this course by filling out an online questionnaire. Please remember to participate in these course evaluations. Your comments are highly valued, and these evaluations are an important service to fellow students and to the institution, since your responses will be pooled with those of other students and made available online, in the Queens College Course Information System ( Please also note that all responses are completely anonymous; no identifying information is retained once the evaluation has been submitted.

Technical Support

The Queens College Helpdesk (, (718) 997-4444, is located in the I-Building, Room 151 and provides technical support for students who need help with Queens College email, CUNY portal, Blackboard, and CUNYfirst.