Advanced Mathematical Methods
Overview
- Credit value: 30 credits at Level 6
- Convenor: Dan Mcveagh
- Assessment: a three-hour examination (80%) and assessed coursework (20%)
Module description
This module will equip you with the methods of calculus and linear algebra which are essential to the study of statistics at graduate level.
Indicative syllabus
- Functions of more than one variable
- Linear programming
- Partial differentiation and its applications
- Multiple integrals
- Differential equations
- Matrices and systems of linear equations
- Determinants
- Real vectors
- Eigenvalues and eigenvectors
- Markov chains
Learning objectives
By the end of this module, you will be able to:
- understand and use mathematical methods and techniques
- work with functions of more than one variable
- demonstrate knowledge of partial differentiation and its applications
- calculate multiple integrals
- find an orthogonal basis of a subspace of n-dimensional real space
- evaluate the determinant, eigenvalues and eigenvectors of a square matrix
- demonstrate when a square matrix is diagonalisable, and diagonalise such matrices
- demonstrate the notation and terminology of calculus of more than one variable
- demonstrate knowledge of the properties of n-dimensional real space
- demonstrate awareness of the use of mathematics to model problems in the natural and social sciences, and formulate such problems using appropriate notation
- calculate maxima and minima of functions of more than one variable
- model a finite stochastic process using a Markov matrix, and find the solution
- model optimisation problems as a linear programme.