# 2022/23 Undergraduate Module Catalogue

## MATH2230 Discrete Mathematics

### 10 creditsClass Size: 180

**Module manager:** Dr Richard Elwes**Email:** r.h.elwes@leeds.ac.uk

**Taught:** Semester 2 (Jan to Jun) View Timetable

**Year running** 2022/23

### Pre-requisite qualifications

MATH1010 or MATH1005 or MATH1060 or MATH1331, or equivalent.### This module is mutually exclusive with

MATH2210 | Introduction to Discrete Mathematics |

MATH2231 | Discrete Mathematics with Computation |

**This module is approved as a discovery module**

### Module summary

Discrete mathematics is the area of mathematics concerned with the study of discrete (i.e. distinct, separate, unconnected) objects. The typical problems studied in discrete mathematics involve counting the elements of a finite set (e.g. how many ways are there of choosing a 4-digit PIN number?), studying graphs (e.g. can we check that two computers in a network are connected). Correspondingly, the module will introduce key ideas from Combinatorics and Graph Theory.### Objectives

Discrete mathematics is a wide and very active subject, spanning across pure and applied mathematics. It is generally concerned with objects that are finite (the ways in which we can arrange two teams of 5 players from a group of 10 people) and on finding explicit methods and algorithms to establish their properties. The module will look at two particularly important topics of discrete mathematics: combinatorics and graph theory. The first is generally concerned with counting problems, including aspects of the theory of difference equations. The second is concerned with graphs, which provides effective ways of representing finite (and sometimes even infinite) data. The module offers also good background for MATH3143 (Combinatorics) and MATH3033 (Graph Theory).**Learning outcomes**

On completion of this module, students should be able to:

1) Solve counting problems involving binomials, permutations, and the inclusion-exclusion principle;

2) Formulate counting problems as linear difference equations and know some applications;

3) Solve linear difference equations and some linearizable ones;

4) Test a graph to determine whether it is connected;

5) In simple cases, determine whether or not a graph is planar;

6) Use algorithms to find shortest paths and spanning trees in a graph;

7) Prove and apply Euler's formula for planar graphs.

### Syllabus

1. Combinatorics: counting problems and their relevance for calculating probability; number of functions between finite sets; the binomial theorem and applications to the number of surjections and derangements; combinatiorial problems solvable by difference equations; linear difference equations; some linearizable difference equations; applications.

2. Graph Theory: graphs; adjacency matrices; handshaking lemma; subgraphs; isomorphism of graphs; connected graphs; algorithms to find a shortest path; trees; Cayley's formula; spanning trees; the matrix-tree theorem; planar graphs; Euler's formula; planarity tests.

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Workshop | 10 | 1.00 | 10.00 |

Lecture | 11 | 1.00 | 22.00 |

Private study hours | 68.00 | ||

Total Contact hours | 32.00 | ||

Total hours (100hr per 10 credits) | 100.00 |

### Private study

Studying and revising of course material.Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular problem solving assignments### Methods of assessment

**Coursework**

Assessment type | Notes | % of formal assessment |

In-course Assessment | . | 15.00 |

Total percentage (Assessment Coursework) | 15.00 |

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

**Exams**

Exam type | Exam duration | % of formal assessment |

Open Book exam | 2 hr 00 mins | 85.00 |

Total percentage (Assessment Exams) | 85.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

### Reading list

The reading list is available from the Library websiteLast updated: 09/05/2022 09:13:03

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- Undergraduate module catalogue
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- Taught Postgraduate programme catalogue

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