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Advanced Mathematical Methods


  • 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.