Module Catalogue 2026/27

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

The aim of this module is to provide an understanding of statistical and other quantitative methods, appropriate to research in water resources and hydroinformatics engineering disciplines. It is designed to provide the foundations for the mathematics and statistics that students will encounter in subsequent MSc modules related to Hydrology and Water Management.
This module provides students with a range of quantitative methods they will need when interpreting and analysing data and developing models in water resources and hydroinformatics.
The above aims will be achieved by adopting a combination of lectures, tutorials and computer-based workshops.
The subsequent, essentially engineering and technically-focussed modules, will provide the student with opportunity to apply the knowledge gained.

Outline Of Syllabus

Algebraic manipulation – linear and non-linear; Functions;
Differentiation;
Differential equations;
Integration;
Matrices;
Vectors;
Solutions of simultaneous equations; Probability & statistics;
Probability distribution; Estimation and confidence limits; Significance tests;
Regression;
Time series analysis;
Spatial analysis
This module will introduce the students to programming in Python.

Intended Knowledge Outcomes

On successful completion of this module, students will have the ability to analyse and interpret data and develop simple quantitative models using appropriate numerical techniques (M1, M2, M3).
Specific knowledge will be gained on:
•       Manipulating equations;
•       Solving systems of equations;
•       Figures raised to a power;
•       Matrices;
•       Vectors;
•       Functions: polynomials, trigonometric functions (sine, cosine, tangent), exponentials and logarithms
•       Radians ;
•       Setting up a simple model;
•       Units and the relationship between them;
•       Understanding differentiation;
•       Obtaining maximum and minimum values of a function;
•       Understanding definite integration;
•       Finite difference approximation to a derivative;
•       Acceleration due to gravity, g = 9.81 m/s2;
•       Numerical integration (Trapezium and Simpson’s rule);

Intended Skill Outcomes

On successful completion of this module, students will have developed skills in problem solving, numeracy, computer literacy & data analysis (M4, M17).
Specific skills gained will include the ability to
•       manipulate equations and formulae;
•       recognise and sketch simple functions (polynomials, trigonometric functions, exponentials, logarithms);
•       differentiate and integrate a simple function;
•       find maximum and minimum values of a known function;
•       perform numerical integration and understand its meaning;
•       recognize ordinary and partial differential equations;
•       set up a simple mathematical model and solve it using an analytical or numerical technique;
•       perform statistical analysis on data sets
Python programming basics

Teaching Rationale And Relationship

The rationale for the teaching methods employed on this module is to provide ample opportunity for students to try out problems, understand how the methods introduced are applied in in water resources and hydroinformatics engineering disciplines. Formal lectures are used to teach the skills necessary for statistical and other numerical techniques. Taught sessions typically consist of an hour of interactive lecture directly followed by an hour and a half of tutorial. During tutorial sessions, students are expected to apply methods learnt to solve mathematical and statistical problems. These sessions are supervised and help is given when needed to aid skill development. Students then undertake practical-based activities in which their new skills, knowledge and understanding can be reinforced including, for example, statistical analysis. The computer-based workshop (practical) is intended both to introduce students to modelling tools/data manipulation and to consolidate learning by drawing on examples introduced in lectures and tutorials.

Assessment Rationale And Relationship

Assessed by written examination and coursework. This format allows a student's knowledge and understanding of quantitative methods to be monitored, applied and tested. Assessment is split between:-

(a)       Numbas practice questions – self-assessment tests which monitor progress and test basic skills in mathematics and statistics (formative);
(b)       Practice questions (formative);
(c)       Coursework - which monitor development and application of data analysis skills in statistics. and assessing AHEP4 M1, M2, M3, M4, and M17.
(d)       Examination covering mathematics part of module and assessing AHEP4 M1, and M3.
(e)       Formative assessment is intended to feed directly into taught sessions, giving students the opportunity to highlight areas of difficulty which can be reviewed during in person sessions.

General Notes

N/A