School of Mathematics and Statistics (SoMaS)

MAS5050 Mathematical Methods for Statistics

The module is a distance-learning instrument aimed at graduates who wish to undertake a postgraduate Masters course in Statistics but lack the appropriate mathematical and statistical background. It introduces the mathematical concepts and methods needed for such a masters course and gives training in their use. It covers ideas and techniques from real analysis and linear algebra, including multiple integration and differentiation and matrix algebra and the theory of quadratic forms.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

Teaching methods

Directed reading from the textbooks listed below; discussion boards; coursework assignments.

Assessment

Formal Examination, Coursework

Full syllabus

• Sets
• Functions
• Inequalities
• Permutations and combinations
• Sum and product notation
• Introduction to series
• Limits
• Introduction to differentiation
• Product and quotient rules for differentiation
• The chain rule
• Derivatives of trigonometric functions
• Taylor series
• Exponential functions and logarithms
• Derivatives of exponential functions and logarithms
• Definite integrals
• Fundamental theorem of calculus
• Indefinite integrals
• Calculating integrals
• Improper integrals
• Integration by substitution
• Integration by parts
• Gamma and beta functions
• Maximising and minimising functions
• Vectors
• Vector arithmetic
• Partial derivatives
• Chain rule for partial derivatives
• Maxima and minima in higher dimensions
• Lagrangian multipliers
• Multiple integrals
• Linear equations
• Gaussian elimination
• Matrices, matrix multiplication
• Inverse matrices
• Determinants
• Change of variables in multiple integration
• Vector spaces, subspaces, linear combinations
• Linear dependence and independence, bases
• Eigenvalues and eigenvectors
• Diagonalisation of matrices
• Quadratic forms

Reading list