Aims and Fit of Module

To introduce the world of discrete mathematics – an active branch of contemporary mathematics, grounded in real-life problems, that serves as a mathematical foundation of computer science, and is widely applied to the other fields of mathematics as well as to operational research and data science. The aim of the module is to acquaint students with the most commonly used combinatorial techniques and the most important aspects of graph theory. In addition, the course also aims to show multiple connections with other branches of mathematics (probability, linear algebra) and real-life applications (web-search algorithm, designing clash-free timetable, etc.). A major focus of the module is in equipping the students with a robust approach for solving mathematical problems, gaining confidence in tackling various types of problems that students have not encountered before.

Learning outcomes

A. Count combinatorial objects and determine the cardinality of finite sets.

B. Solve mathematical problems using combinatorial techniques.

C. Compute various parameters of a graph, such as the clique number, the chromatic number or the spectral radius.

D. Construct proofs of statements in graph theory from the first principles and by applying the more advanced methods and theorems of graph theory.

E. State the definitions and the theorems presented in the lectures and provide proofs of the main results.

Method of teaching and learning

This module will be delivered by a combination of formal lectures and tutorials.