## 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.