Numerical Mathematics and Computer Algorithms

Course summary

Course code: MATH1106
Level: 5
Credits: 30
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Erwin George

Specification

Aims

This course provides the student with fundamental knowledge in topics of numerical mathematics, in-depth understanding of foundation concepts in programming and experience in the design of computer programs implementing numerical algorithms. The main aims of this course are:
• To provide a sound introduction to the theory, methods, and real-world applications of numerical mathematics.
• To provide a broad introduction to programming methods.
• To build experience in the design of computer programs for scientific and numerical computing using a programming language.

Learning outcomes

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

1. Select suitable numerical methods for different applications.
2. Perform analysis of selected numerical algorithms.
3. Design computer programs implementing suitable numerical methods.
4. Apply numerical methods to solve selected modelling problems.

Indicative content

A selection of topics from the following list will be covered:

Computer arithmetic and error analysis.
Approximation theory.
Numerical differentiation and integration.
Numerical solutions of initial value problems: multi-step methods, predictor-corrector methods, error analysis.
Numerical solutions of boundary value problems: shooting methods, finite difference methods, error analysis.
Concepts of procedural and object oriented programming: functions and subroutines, classes, interfaces.
Testing and debugging computer programs.
Applications of numerical mathematics in a variety of fields such as mechanics and the life sciences.

Teaching and learning activity

Concepts will be introduced through lectures and supported by tutorials. The latter will include a structured programme of laboratory sessions in which most of the programming aspects of the course will be taught.

Assessment

Summative assessment:

Coursework 1 - 25%
LO - 1, 2, 3.
Coursework covering the learning outcomes, which may include selected tutorial work.

Coursework 2 - 25%
LO - 1, 2, 3, 4.

Examination - 50%
LO - 1, 2, 3, 4.
Examination of 3 hours in duration covering learning outcomes.

Formative assessment: Weekly tutorial exercises reinforcing the lecture material