## MATH2210 Introduction to Discrete Mathematics

### 10 creditsClass Size: 250

Module manager: Professor J.K. Truss
Email: J.K.Truss@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

### Pre-requisite qualifications

MATH1015, or MATH1060, or MATH1331, or equivalent.

This module is approved as an Elective

### Module summary

Discrete mathematics deals with finite mathematical structures. The module introduces key ideas from Combinatorics (for example, how many poker hands are there of each type?), Graph Theory (an important mathematical tool used in operational research, linguistics, chemistry and more) and Computability (including Register Machines, a theoretical model of computation).

### 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) formulate counting problems as linear recurrence relations, and solve linear recurrence relations;
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 URM-programs for simple functions;
h) prove the closure properties of the class of computable functions;
i) prove that the Halting Problem is recursively unsolvable.

### Syllabus

1. Combinatorial Enumeration Problems: Permutations and combinations. The inclusion-exclusion principle. Recurrence relations.
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. Computability: algorithms and undecidable problems. Unlimited Register Machines (URMs). Closure properties of URM-computable functions. Recursive functions. The Busy Beaver function. Undecidable problems.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Example Class 11 1.00 11.00 Lecture 22 1.00 22.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 100.00 Total percentage (Assessment Exams) 100.00

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