Module manager: Dr Nicola Gambino
Email: N.Gambino@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2016/17
MATH1010 or MATH1060, or MATH1331, or equivalent.
This module is approved as a discovery module
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.
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.
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.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Workshop | 10 | 1 | 10 |
| Lecture | 22 | 1 | 22 |
| Private study hours | 68 | ||
| Total Contact hours | 32 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Studying and revising of course material.
Completing of assignments and assessments.
Regular problem solving assignments
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
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.
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 0 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 4/8/2016
Errors, omissions, failed links etc should be notified to the Catalogue Team