Title of the course: Generating Functions and Their Applications
Instructor: Mr. Arif Mardin
Institution: Retired
Dates: 7-13 September 2026
Prerequisites: Since generating functions are formal power series, their convergence properties will not be discussed. Consequently, ability to carry out basic algebraic operations, partial fraction decompositions will be sufficient to follow the course.
Level: Motivated highschool students, beginning or advanced undergraduates.
Abstract: Generating functions provide one of the most useful techniques in enumerative combinatorics. Over the years they have been used in a very efficient manner in many areas of pure and applied sciences, including algorithmics, probability theory, statistical physics. Our course will be concerned with some of the most basic properties of ordinary and exponential generating functions: their addition, multiplication and composition: Time permitting, we hope to be able to discuss the Lagrange Inversion Formula in this context.
Language: EN
Textbook:
i) H.Wilf: “Generatingfunctionology”, 2nd edn. Academic Press, 1994.
ii)  D.Knuth: “The Art of Computer Programming: Vol.1: Fundamental Algorithms”, 2nd edn. Addison-Wesley, 1973.
iii) Ö.Eğecioğlu, A.M.Garsia: “Lessons in Enumerative Combinatorics”, Springer Verlag, 2021.