Module manager: Dr Nicola Gambino
Email: n.gambino@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2013/14
MATH1010 or MATH1060, or MATH1331, or equivalent.
This module is approved as an Elective
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).
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 and linearizable difference equations, formulate counting problems as linear difference equations and know some applications to biology, physics and economy;
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) prove that the Halting Problem is recursively insoluble.
1. Combinatorial Enumeration Problems: Permutations and combinations. The inclusion-exclusion principle.
2. Linear difference equations: Combinatiorial problems solvable by difference equations. Linearizable difference equations, e.g. Pielou equation.
3. Introductory Graph Theory: Basic definitions. Connected graphs. Eulerian graphs. Kruskal's algorithm for minimal connectors. Planar graphs. Euler's formula for planar graphs.
4. Computability: Algorithms. Register Machines (URMs). Undecidable problems.
| 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 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| 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: 2/14/2014
Errors, omissions, failed links etc should be notified to the Catalogue Team