Project III 2022-23

Combinatorial Methods

Mustazee Rahman

Description

Combinatorics is a broad subject with applications to many areas of mathematics and computer science. Fundamentally, combinatorics is about counting and how we can count mathematical objects in its many guises. For instance, how many ways are there to tile a chess board with dominoes? How many trees are there with n vertices? How many ways can a polygon be triangulated? All of these questions can be answered with combinatorial methods such as recurrences, generating functions and bijections.

This project will be an introduction to some advanced topics in combinatorics, building on what it is covered in the module Discrete Mathematics. Students will choose a topic depending on their interest and following discussions with the supervisor. The board aim is to learn some powerful combinatorial method and see the utility and unity of combinatorics. Topics of interest may include:
  • Permutations and their properties
  • Generating functions and their applications
  • Algebraic combinatorics
  • Graph theory and graph algorithms
  • Fibonacci numbers, Catalan numbers, etc.

Prerequisites

Algebra II and Analysis in Many Variables II are essential.

Resources

Students will be guided to lecture notes or textbooks for certain topics. The following textbooks will be helpful.

  • R. Diestel, Graph Theory.
  • R. Stanley, Algebraic Combinatorics.
  • H. Wilf, Generatingfunctionology.
  • J.H. Van Lint and R.M. Wilson, A course in combinatorics.

Get in touch by email if you have questions.

email: Mustazee Rahman