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ST208: Mathematical Methods

Lecturer(s): Dr Paul Jenkins

Prerequisite(s): MA106 Linear Algebra, MA137 Mathematical Analysis.

Commitment: 3 lectures per week, 1 tutorial each in weeks 3, 5, 7 and 9. This module runs in Term 1.

Aims: This is a course of techniques which are in everyday use in probability and statistics, and which are essential to a proper understanding of any second or third year course in these subjects. It will provide the mathematical background for optimization, convergence, regression and best approximation, and develop mathematical thinking.

Objectives: At the end of the course students will be familiar with and be able to apply the following concepts and techniques:

a) multivariate calculus; multiple integration, calculation of volumes under surfaces; change of variable formulae and Fubini's Theorem; partial derivatives, critical points and extrema; constrained optimization;

b) eigenvalues/eigenvectors; diagonalisation; orthogonal bases and orthonormalisation; inner products; generalised Fourier coefficients; quadratic forms; projections; Spectral Decomposition Theorem;

c) metrics; open, closed and compact sets; convergence and continuity in metric spaces.

Main reference: Riley, Hobson and Bence: "Mathematical Methods for Physics and Engineering"

Additional references for particular topics: 

  • Anton & Rorres, “Elementary linear Algebra”,
  • Sutherland, “An Introduction to Metric Spaces,
  • Finney and Thomas, “Calculus”.

Assessment: 90% by examination (at the start of Term 3), 10% by coursework,.

Deadlines: Assignment 1: week 2, Assignment 2: week 4, Assignment 3: week 6 and Assignment 4: week 8.

Feedback: You will hand in answers to selected questions on the fortnightly exercise sheets. Your work will be marked and returned to you in the tutorial taking place the following week when you will have the opportunity to discuss it.

You may also wish to see:

ST208: Resources for current students (restricted access)