This is an archived syllabus from 2020-2021

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COMP36212 Mathematical Systems and Computation syllabus 2020-2021

COMP36212 materials

COMP36212 Mathematical Systems and Computation

Level 3
Credits: 10
Enrolled students: 69

Course leader: Oliver Rhodes

Additional staff: view all staff

Requisites

Pre-Requisite (Compulsory): COMP11120

Additional requirements

COMP36212 - Enrolment restricted to students who have taken COMP11120 or are registered on the CS and Maths programme.

Assessment methods

50% Written exam
50% Coursework

Timetable

Semester	Event	Location	Day	Time	Group
Sem 2	ONLINE Lecture		Fri	12:00 - 13:00	-
Sem 2	ONLINE Lecture		Tue	12:00 - 13:00	-
Sem 2 w30-32	ONLINE Lecture	Stopford TH 3	Wed	15:00 - 16:00	-
Sem 2 w30,32	ONLINE Lecture	Stopford TH 3	Wed	14:00 - 15:00	-

Themes to which this unit belongs

Programming and Algorithms

Overview

Mathematical systems can be used to describe many aspects of the world around us, from modelling physics and chemistry, to predicting financial markets and enabling machine learning and AI. By modelling systems mathematically it is possible to analyse them, and make predictions about their performance and how it can be optimised.

Solution of these mathematical systems often relies on computational hardware and the application of algorithms which solve an approximate form of the problem. It is therefore important to understand the limitations imposed by the computational implementation of a given problem, and the effect this can have on a given solution.

The course explores these concepts from three perspectives: by introducing the notion of finite precision computation and error propagation within a computational process; through exploring techniques for the numerical solution of differential equations; and through the use of optimisation algorithms to maximise the performance of a solution to a given problem. These techniques are then applied to real-world problems, including physical and engineering systems, and machine learning operations within neural networks.

The course targets students seeking to gain experience of how numerical computation is employed in industry and research, and who want a deeper understanding of how numerical algorithms and hardware combine when solving problems. It will help develop the skills necessary to work at the hardware-software interface, and in harnessing the power of hardware accelerators and modern computer architectures to develop fast, accurate and precise analysis tools.

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact. Please see Blackboard / course unit related emails for any further updates.

Aims

This unit investigates how real-world problems can be described via mathematical systems and explores the impact of using numerical computation to analyse their performance.

Teaching methods

Assignment 25%, Assignment 25%, Mid-unit test 10%, and Exam 40%.

Feedback methods

We will maintain a continuous feedback with students through active participation in the classroom. At the end of the course, there will be general feedback on the exam results.

Study hours

Assessment written exam (1 hours)
Lectures (24 hours)

Employability skills

Analytical skills
Group/team working
Innovation/creativity
Oral communication
Problem solving
Research

Learning outcomes

On successful completion of this unit, a student will be able to:

ILO 1-Describe issues associated with finite precision computing (including floating point, integer, and mixed-precision arithmetic).

ILO 2- Explain techniques enabling improved accuracy in finite precision computing (e.g. stochastic rounding, multi-word arithmetic, extended precision).

ILO3-Describe and apply numerical algorithms for the solution of mathematical systems, including those described by ordinary differential equations, and linear algebra.

ILO 4-Describe and apply a range of optimisation and bio-inspired algorithms to find solutions to computationally hard problems (e.g. direct search, stochastic, and evolutionary algorithms).

ILO 5-Apply numerical techniques and knowledge of computational hardware to develop accurate and precise numerical solvers for a range of problems across multiple disciplines

Reading list

Title	Author	ISBN	Publisher	Year
Practical Methods of Optimization	Fletcher, R	0471494631	John Wiley & Sons, Incorporated	2000
An introduction to numerical analysis	Süli, Endre,	9780521007948; 0521007941; 9780521810265 (hbk.); 0521810264	Cambridge University Press	2003.
Accuracy and stability of numerical algorithms	Higham, Nicholas J	0898715210	Society for Industrial and Applied Mathematics	2002
Handbook of Floating-Point Arithmetic	Muller, Jean-Michel.	9783319765266	Imprint Birkhäuser; Springer International Publishing	2018.

Additional notes

Course unit materials

Links to course unit teaching materials can be found on the School of Computer Science website for current students.