Module overview
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Differential equations, partial differentiation and some more advanced techniques of calculus
- Continuous probability and basic statistics
- Basic differential and integral calculus
- Basic linear algebra
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Show logical thinking in problem solving
- Apply operations on vectors and matrices and solve systems of linear equations
- Recognise continuous probability distributions
- Perform calculations in simple situations and work through some longer examples
- Use statistical analysis, including sampling, hypothesis testing and regression
- Critically analyse and solve some mathematical problems
Syllabus
Algebra
- Vectors: basic properties, operations, scalar product, vector product.
- Basis: linear independence, dimensions, coordinate transformations, orthogonal bases and projections
- Linear transformations: basic properties, matrices, inverses, determinants.
- Eigenspaces: Eigenvalues, Eigenvectors, Diagonalization.
- Solving systems of linear equations.
Calculus
- Differentiation - standard rules
- Newton's method for finding roots
- Partial differentiation
- Integration - standard integrals
- Integration by parts
- Numerical integration
Probability and statistics
- Further probability: continuous probability distributions
- Introduction to statistics: sampling, confidence intervals, hypothesis testing, regression
Learning and Teaching
Teaching and learning methods
The content of this module is delivered through lectures, the module website, directed reading, pre-recorded materials and tutorials.
Students work on their understanding through a combination of independent study, preparation for timetabled activities, tutorials, and problem classes, along with formative assessments in the form of problem sheets.
| Type | Hours |
|---|---|
| Preparation for scheduled sessions | 6 |
| Lecture | 36 |
| Completion of assessment task | 10 |
| Follow-up work | 18 |
| Revision | 18 |
| Wider reading or practice | 50 |
| Tutorial | 12 |
| Total study time | 150 |
Assessment
Assessment strategy
This module is assessed by a combination of problem sheets and a final assessment in the form of a written examination.
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Problem Sheets | 10% |
| Written exam | 90% |