Applied Combinatorics

Fall 2025

Combinatorics can be described as the art of counting. Polya once said that "an idea which can be used only once is a trick. If one can use it more than once it becomes a method." Our course will discuss several powerful combinatorics methods and their applications.

The course is designed to develop advanced problem-solving skills, as well as the skills needed to effectively communicate the solutions of problems. Most mathematicians use aesthetics to guide their work; we will attempt to convey the sense of what is beautiful (and, occasionally, what is not) in mathematics.

This course will use a different correspondence between the numeric grades and the letter grades than the more usual 90-80-70 scheme. The percentage score 80% is the dividing line between A and A-; 72% and above is a B; and 60% is (barely) a C. For written homeworks, this means that the score of 20 of 25 is an A; 18 of 25 is a B; and please try not to get below 15 too often. On the exams, this means that you can skip a problem and still get an A, if all the other problems are solved correctly.

This grading scheme takes into account the level of difficulty of the assignments and the exams as well as the rigorous grading style of your instructor.

Your written homework score (the one that's worth 30% of your final grade) is the average of the grades you get for each problem when you submit the work for the first time. In addition, you will lose up to 10 points on both mid-term exams, as well as on the final, unless you revise (i.e., solve correctly by the revision cut-off date) each of the homework problems that received a bad score. The revisions have to be done individually; each revision should be a self-contained solution of the problem.

The grading scheme for homework problems is explained in the Homework Guide. To get the full 10 points on the exam, you need to have a grade 4 or higher for each of the homework problems. To get 5 points, you need to have a grade of 3 or higher for each of the problems. If there is a problem with the grade 2 or lower, the homework component grade will be 0.

Revisions can be submitted any time, in person or electronically, before the start of the corresponding exam. There is one restriction (meant to discourage procrastination): you can submit only three revised solutions in any 24 hour period.

If your presentations and participation/quizzes are consistently good (feel free to ask me for feedback if you are not sure), I will add a third of a letter grade to your final grade. At worst (if you are not ready or miss the class half the time), I will subtract one full letter grade from your final grade.

Office Hours. I encourage you to come to my office hours (listed above) with questions you have in the course. If you are not able to come during these hours, I am available by appointment, just talk to me after the class or send an email.

Peer tutoring. The Math Tutoring Center does have tutors for our class (but not every tutor may be comfortable with the material). In addition, the Math Department has established peer-led sessions, called Prime Time, that will be happening daily in YR 307.

You should expect to spend a considerable amount of time working on this course outside of class. At the same time, try to be efficient. If you are spending a lot of time on homework or lab assignments without making much progress, talk to me.

You are expected to be familiar with TU's University's Academic Integrity Policy, especially the sections that define plagiarism, cheating and complicity (II.B-II.E) and describe the possible grade penalties (V.C). You are encouraged to work with other students in the course on homework assignments, but each student must submit their own version of the solutions.

Tests are to be written strictly individually, everyone caught cheating on any test will have his course grade decreased by one letter grade.

Normally, no make-up tests will be given; if for some reason you are not able to take a test, please, let me know as soon as possible.

Everyone participating in this course is expected to be respectful of each other without regard to race, class, linguistic background, religion, political beliefs, sex, gender identity or expression, sexual orientation, ethnicity, age, veteran's status, or physical ability. If you feel these expectations have not been met, please feel free to discuss it with me or with the designated diversity liaison Dr. Elizabeth Goode.

This course is in compliance with Towson University policies for students with disabilities. Students with disabilities are encouraged to register with TU ADS.

If you have questions or concerns about the course, be sure to discuss them with me during my office hours or by appointment.