BSc Computer Science and Mathematics with Industrial Experience

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.

 

COMP36212 - Enrolment restricted to students who have taken COMP11120 or are registered on the CS and Maths programme. Although programming experience is not essential, some knowledge of development is desirable, particularly in C/C++

COMP36212 - Enrolment restricted to students who have taken COMP11120 or are registered on the CS and Maths programme. Although programming experience is not essential, some knowledge of development is desirable, particularly in C/C++

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. 

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

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

ILO 3: Describe and apply numerical algorithms for the solution of mathematical systems, including those described by ordinary differential equations, and linear algebra.

ILO 4: Apply numerical techniques and knowledge of computational hardware to develop accurate and precise numerical solvers for a range of problems across multiple disciplines

ILO 5: 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).

• Lectures (24 in total, 2 per week);
   
• Independent study through online videos and worked examples;
   
• Coursework exercises implementing theories and techniques from the lectures on real-world problems

We will maintain continuous feedback with students through active participation in the classroom and via online formative assessments.  There will also be individual feedback given on all coursework reports.

Practical Methods of Optimization    Fletcher, R    John Wiley & Sons, Incorporated    2000    ISBN: 0471494631

An introduction to numerical analysis     Süli, Endre,    Cambridge University Press    2003    ISBN: 9780521007948

Accuracy and stability of numerical algorithms    Higham, Nicholas J    Society for Industrial and Applied Mathematics    2002    ISBN: 0898715210

Handbook of Floating-Point Arithmetic     Muller, Jean-Michel.    Imprint Birkhäuser    2018    ISBN: 9783319765266

Please note: AI forms part of the assessment method for this course unit. Coursework requires students to investigate training of a neural network (Category D: AI-integrated). For more information, please see: AI in Teaching and Learning Policy. 

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £39,700 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our  undergraduate student finance pages .