Units

Mathematical modelling of physical and biological systems and processes is a growing field that uses multiple mathematical techniques, many of which rely on nonlinear systems approaches. This unit will cover a range of these techniques, usi…

This unit takes a mathematical approach to equip students with the skills they need to perform complex analysis of datasets, be they scientific, industrial, financial or personal. This unit introduces students to the key mathematical method…

This unit of study aims to develop analytical skills using mathematical methods of vector calculus, probability and statistics. The unit introduces students to fundamental mathematical ideas and techniques and illustrates their application…

Functions of several variables, partial derivatives, extreme values, Lagrange multipliers. Multiple integrals, line integrals, surface integrals. Vector differential calculus; grad, div and curl. Integral theorems of Gauss and Stokes.

This unit is an alternative to MTH2010 for students with a strong mathematical foundation. Students enrolled in MTH2015 will follow the same curriculum as students in MTH2010 and will cover additional more advanced material. Functions of se…

This unit introduces and develops a range of basic concepts and techniques related to two main subjects: multivariate calculus and linear algebra. The programme is targeted for students following a degree in data science and the material wi…

Vector spaces, linear transformations. Determinants, eigenvalue problems, matrix decompositions. Inner products, least squares approximation. Applications to areas such as coding, economics, graph theory, Markov chains, differential equatio…

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. Linear functionals and dual spaces. Matrix decompositions, least squares approximation, power method. Application…

This unit introduces mathematical techniques for differential equations. These equations appear in a number of physical models, such as oscillations, heat conduction and transport equations. Methods to study ordinary differential equations…

When mathematics is used in real-world applications, it almost always involves the use of computers. This unit provides an introduction to numerical methods for solving maths-related problems on computers. Topics covered include error analy…

This unit is intended for students with little or no mathematical background. Through the discussion of historical, practical and conceptual questions, it will emphasise the beauty and the power of mathematics. The number of topics covered…

Prime numbers; Euclidean algorithm; congruences; the Euler totient function; the theorems of Fermat, Euler and Wilson; RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; primitive roots; factorisation and primali…

An introduction to real analysis with a special focus on sequences of real numbers and functions. Topics covered include properties of real numbers (infima/suprema and the axiom of completeness), sequences and series of real numbers (order…

Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups and quotient groups; homomorphisms, isomorphisms and isomorphism theorem; group actions; Sylow theo…

Introduction to probability - a mathematical treatment. Topics include: probability axioms, conditional probabilities and the law of total probability, discrete and continuous random variables, univariate and multivariate distributions, ind…

This unit provides an introduction to probability - mathematical treatment. Topics include: probability axioms, conditional probabilities and the law of total probability, discrete and continuous random variables, univariate and multivariat…

This unit is a rigorous introduction to the theory of mathematical statistics and more specifically of statistical inference. It provides the mathematical theory underlying the methods and concepts used in statistics, such as estimation and…

This unit provides you with an opportunity to work with a supervisor and complete a mathematical research project chosen from a range of areas of mathematics and statistics, including astrophysics, dynamics, chaos, computing algorithm desig…

This unit of study aims to convey the fundamental probability concepts necessary for an understanding of stochastic processes, introduce stochastic processes and some important related concepts, illustrate the usefulness of stochastic model…

To provide students with knowledge of ordinary differential equations required for practising scientist and engineer.

This unit will introduce students to the importance and relevance of numerical mathematics and the use of computational methods to solve real-world problems in science and engineering. Students will learn how to set up and solve complex mat…

This unit aims to develop the ability to cast real life situations as mathematical problems and apply efficient analytical and computational methods to solve them.

This unit covers exact and numerical solutions for partial differential equations of various types. Explicit solution methods include methods of characteristics, separation of variables, Fourier series and transform, fundamental solutions,…

Complex numbers and functions; domains and curves in the complex plane; differentiation; integration; Cauchy's integral theorem and its consequences; Taylor and Laurent series; Laplace and Fourier transforms; complex inversion formula; bran…

This unit provides an introduction to complex analysis and integral transform. Topics include: complex numbers and functions; domains and curves in the complex plane; complex differentiation; complex integration; Cauchy's integral theorem a…

This unit examines two particular classes of ordinary differential equations: dynamical systems and boundary-value problems. The investigation of boundary-value problems considers Sturm-Liouville eigenvalues problems and orthogonal polynomi…

This unit will explore the metric structure of curves and surfaces, primarily in 3-dimensional Euclidean space. The major focus is on the various concepts of curvature and related notions, and the relationships between them. Curvature and t…

This unit will explore the metric structure of curves and surfaces, primarily in 3-dimensional Euclidean space. The major focus is on the various concepts of curvature and related notions, and the relationships between them. Curvature and t…

From point-set topology to manifolds: sets, topological spaces, basis of topology, and properties of spaces such as compact, connected, and Hausdorff. Maps between spaces and their properties, including continuity, homeomorphism, and homoto…

Prime numbers; Euclidean algorithm; congruences; the Euler totient function; the theorems of Fermat, Euler and Wilson; RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; primitive roots; factorisation and primali…