Combinatorics, Spring 2022

Course: Math 636, Spring 2022.
Instructor: Christopher Hanusa — Email: — Office: Kiely Tower 606
Meeting Times: Mondays and Wednesdays from 1:40–2:55 in KY 283
Course Web Site:

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! The homework assignments involve two or three questions per day that are relevant to recent class topics. You will be expected to present these homeworks at the board throughout the semester. Presentations need not be complete solutions, but you must make some effort to explain what you know. These presentations will count toward your class participation grade. 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.

It is important to learn how to express yourself in the language of mathematics. When you are working on the homework and writing it up for yourself, 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.

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 leads 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.

Grading Scheme:

Your grade will be based on content assessment, class participation, and your course project, each described in detail below. Each component of your grade is calculated independently; then all pieces are combined using the following weighted average.

Class Participation: 10%
Content Assessment: 65%
Project, including poster, presentation, and podcast: 25%

Class Participation:

Succeeding in this class will require your participation. You will earn a class participation grade based on your attendance and your participation. A great way to participate is to ask questions. A question as simple as "I don't really understand how/why you did X; can you explain it in a different way?" is a great question to ask and it shows that you are involved in the class. You will participate in the in-class activities, our group discussions, and by presenting the homework to the class.

If you miss a class, you are responsible for the material you missed—get the notes from your classmates and study group and make sure that you understand the material that you missed.

Content Assessments:

This semester your content assessment grade will be based on a grading system called "Standards Based Grading". In essence, your grade will depend on your proficiency with a set of course standards. The goal for this system is that your grade will be based on how well you know the material by the end of the semester, and not on how well you do on a small number of high-stakes midterm exams. The distribution of your scores on the standards will determine your content assessment grade.

Throughout the semester I anticipate around 16 standards. Your standards grade will be calculated as follows:

A   (95+)   Show proficiency in 13 of 14 standards.
B (85) Show proficiency in 11 of 14 standards.
C (75) Show proficiency in 10 of 14 standards.
D (65) Show proficiency in 8 of 14 standards.
F (50–)   Show proficiency in fewer than 8 standards.

Throughout the semester you will be able to show mastery of the standards by way of periodic assessments that occur at the end of certain class periods. The score you earn will be either "Pass" or "Needs Improvement" depending on whether you have conveyed complete mastery of the material. The key will be making sure you have written enough to show me that you understand the material, and not just give "the right answer".

What is different from the high-stakes "tests" that you might associate with a math class is that there is an opportunity for you to re-assess standards when you want to improve your scores. This allows you to focus your studying on the concepts that you have not fully understood. You will be able to reassess up to two standards per week, so be sure to take advantage of this opportunity throughout the semester.

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 and then record an interview with me during finals week. More information is available here.

Math Lounge:

The Math department has a lounge open to math students and faculty on the fifth floor of Kiely Tower. (The room number is 508.) This is a great place to meet with your groupmates to chat about math and have blackboard space for working through ideas. Feel free to take advantage of this comfortable studying space!

Office Hours:

I am happy to help you with your homework and other class-related questions during my office hours. Office hours will be determined by group consensus during the first week of class and will be announced in class and posted on my schedule. In addition, you are welcome to make an appointment or stop by my office in Kiely Tower Room 606 at any time. (You can call 718-997-5964 to see if I'm there.)

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 assessment, 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 at 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.