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## MATH2210 Introduction to Discrete Mathematics

### 10 creditsClass Size: 130

Module manager: Dr Nicola Gambino
Email: N.Gambino@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2016/17

### Pre-requisite qualifications

MATH1010 or MATH1060, or MATH1331, or equivalent.

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), and finding algorithms to solve problems (e.g. is there an algorithm that checks if a number is prime). Correspondingly, the module will introduce key ideas from Combinatorics, Graph Theory and Computability Theory.

### Objectives

To introduce students to combinatorial thinking, and to demonstrate the wide range of applications.

On completion of this module, students should be able to:
a) solve counting problems involving permutations, combinations and the Inclusion-Exclusion principle;
b) solve linear difference equations, formulate counting problems as linear difference equations and know some applications;
c) test a graph to determine whether it is connected;
d) use Kruskal's algorithm to find minimal connectors;
e) in simple cases, determine whether or not a graph is planar;
f) prove and apply Euler's formula for planar graphs;
g) devise register machines programs for simple functions;
h) in simple cases, prove that a function is recursive;
i) prove that the Halting Problem is undecidable.

### Syllabus

1. Combinatorial Enumeration Problems: permutations and combinations; the inclusion-exclusion principle; linear difference equations; combinatiorial problems solvable by difference equations; applications.
2. Introductory Graph Theory: Basic definitions. Connected graphs. Eulerian graphs. Kruskal's algorithm for minimal connectors. Planar graphs. Euler's formula for planar graphs.
3. Introduction to Computability Theory: Register Machines; Recursive functions; Undecidable problems; the Halting Problem.

### Teaching methods

 Delivery type Number Length hours Student hours Workshop 10 1.00 10.00 Lecture 22 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 Standard exam (closed essays, MCQs etc) 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