matthias beck

MATH 420/720 Combinatorics Spring 2025

Course objectives. Math 420/720 gives an introduction to fundamental combinatorial objects, their uses in other fields of mathematics and its applications, and their analysis. We will learn how to use combinatorial structures to represent mathematical and applied questions and will become comfortable with the combinatorial tools commonly used to analyze such structures. Given a hypothetical combinatorial object that must satisfy certain properties, we will learn how to prove the existence or non-existence of the object, compute the number of such objects, and understand their underlying structure.

Textbook. Bruce Sagan, Combinatorics: The Art of Counting, American Mathematical Society (2020).

The math. The way to learn math is through doing math. It is vital and expected that you attend every lecture. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended.

Homework. I will assign homework problems as we go through the material. You may (and should) work together with your class mates. We can discuss the homework problems at any time during class, and you can hand any of your solutions for feedback. We will have a homework quiz every TBD at the beginning of class, in which you will be asked one definition and one problem given in the previous week.

Grading system.

I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.

Fine print.
SFSU academic calender
BS rule
Academic integrity and plagiarism
Tutoring
CR/NCR grading
Incomplete grades
Late and retroactive withdrawals
Student disclosures of sexual violence
Students with disabilities
Religious holidays

This syllabus is subject to change. All assignments, as well as other announcements on tests, policies, etc., are given in class. If you miss a class, it is your responsibility to find out what's going on. I will try to keep this course web page as updated as possible, however, the most recent information will always be given in class. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.