Welcome to SF2730 - An introduction to the fascinating subject of applied combinatorics! This course will cover material from both abstract and practical perspectives, rigorously developing the theory while consistently motivating it through applications. Consequently, it should appeal to students from across the mathematics, computer science, and engineering disciplines.
While there are no specific prerequisites for this course, we shall assume familiarity with basic enumeration and linear algebra. Additionally, students should be prepared to work on, construct, and carefully write logical arguments and proofs. The focus will not be on memorizing a set of standard formulas or techniques, which may be different from other math courses. Instead the aim of this class is to develop problem-solving skills that can be applied thorughout a variety of mathematical and computational settings.
Combinatorics is the study of finite or countable structures. Many questions center around understanding the relationship between a finite set of objects and enumerating or counting such objects. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, geometry, topology, and probability theory, and have many applications in optimization, computer science, decision theory, and physics.
The course textbook is "Concrete Mathematics" by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. We will follow the book loosely, at best, so it is imperative that you attend lectures regularly. The major topics include:
An official syllabus for the course will be posted here shortly.
The project will consist of writing a short paper on a prescribed topic related to applied combinatorics. A list of preapproved topics will be posted half way through the course.
The Final Exam will be given TBA. It will be comprehensive, i.e., covering material from throughout the entire course.
There will be no make-up exams. Students should contact the instructor immediately if they have an unavoidable scheduling conflict with the exam date.