Introductory description

This module is designed to introduce students to language and methods of the area of Discrete Mathematics.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Introduction to combinatorics: counting techniques, pigeonhole principle, inclusion-exclusion.
Recurrence relations, solving recurrences using generating functions.
Master Theorem for solving recurrences.
Graphs. Basic graph algorithms. Trees. Applications of graphs.
Applications of linear algebra and matrix algebra in algorithms (e.g., in web searching).
Algorithmic applications of random processes and Markov chains, for example, cover time in graphs and card shuffling.
Partitions, enumerations with symmetries.

Learning outcomes

By the end of the module, students should be able to:

• - Understand the notion of mathematical thinking, mathematical proofs, and algorithmic thinking, and be able to apply them in problem solving.
• - Understand the basics of discrete probability and number theory, and be able to apply the methods from these subjects in problem solving.
• - Use effectively algebraic techniques to analyse basic discrete structures and algorithms.
• - Understand asymptotic notation, its significance, and be able to use it to analyse asymptotic performance for some basic algorithmic examples.
• - Understand some basic properties of graphs and related discrete structures, and be able to relate these to practical examples.

Indicative reading list

Please see Talis Aspire link for most up to date list.

View reading list on Talis Aspire

Subject specific skills

Basic knowledge of graph theory and its applications in algorithms
Basic knowledge of discrete probability and its applications in algorithms
Understanding and using asymptotic notations in design and analysis of algorithms

Transferable skills

Communication - Reading and writing mathematical proofs
Critical thinking - problem solving
Technical - Technological competence and staying current with knowledge