MATH1501 Calculus This module covers key topics in calculus and will prepare students for the rest of their degree. It has a greater emphasis on proof and rigour than at A-level. It also introduces some more advanced multi-dimensional calculus. The module contains various applications from pure and applied mathematics as well as from statistics, physics and finance.
MATH1502 Reasoning and Analysis This module introduces the basic reasoning skills needed for the development and applications of modern mathematics. The utility of clear logical thinking will be explored in various important topics and current applications, including security on the internet, fractal geometry and the continuous nature of real numbers.
MATH1503 Linear Algebra and Complex Numbers This module explores the concepts and applications of vectors, matrices and complex numbers. The deep connection between algebra and geometry will be explored. The techniques that will be presented in this module are at the foundation of many areas of mathematics, statistics, physics, and several other applications.
MATH1504 Numerical and Computational Methods This module provides an introduction to the Maple and Matlab software, computational mathematics and creating simple computer programs. Students will use Maple/Matlab interactively and also write procedures in the Maple/Matlab computer languages. The elementary numerical methods which underly industrial and scientific applications will be studied.
MATH1505 Probability and Statistical Inference This module provides a mathematical treatment of basic probability and statistical techniques including random variables, estimation, hypothesis testing, as well as regression and correlation. It also covers exploratory data analysis. All methods are implemented using real data and professional computer software such as R.
MATH1506 Geometry, Graphs, and Groups This module introduces three important areas of pure mathematics. First, key theorems and constructions from classical Euclidean geometry will be introduced. Then we study elementary graph theory, and consider graphs on surfaces, and polynomial invariants of graphs. Finally, we define groups, explore a wide variety of examples, and study cosets and quotients.
MATH2501 Advanced Calculus and Transforms This module extends the differential and integral calculus of severable variables and uses them to solve a wide range of problems. The important techniques of Laplace transforms, Fourier series and transforms are introduced. The applications explored in this module include the solutions of important differential equations and the construction of functions and generalised functions in terms of a basis of orthogonal functions.
MATH2502 Vector Calculus and its Applications This module introduces the student to the methods of vector calculus and the fundamental integration theorems. The applications include a range of important scientific problems primarily from classical mechanics and cosmology. The module also introduces the idea of curvature and applies this to the geometry of bubbles and minimal surfaces.
MATH2503 Ordinary Differential Equations The module aims to provide an introduction to different types of ordinary differential equations and analytical and numerical methods to obtain their solutions. Extensive use will be made of computational mathematics packages. Applications to mechanical and chemical systems are considered as well as the chaotic behaviour seen in climate models.
MATH2504 Operational Research and Monte Carlo Methods This module gives students the opportunity to work on open-ended case studies in operational research (OR) and Monte Carlo methods, both of which are important methods in, for example, industry and finance. It allows students to work on their own and in teams to develop specific skills in OR and programming as well as refining their presentation and communication skills.
MATH2505 Real and Complex Analysis This module deepens the student’s understanding of real analysis and introduces complex analysis. The important distinction between real and complex analysis is explored and the utility of the complex framework is demonstrated. The central role of power series and their convergence properties are studied in depth. Applications include the evaluation of improper integrals and the construction of harmonic functions.
MATH2506 Advanced Probability and Statistical Inference This module extends the probability theory covered in the first year. It discusses and demonstrates the links between various distributions, with a focus on some standard continuous distributions. The module also covers topics from the theory of statistical inference and methods of maximum likelihood estimation. This will equip students with the skills required to perform a number of statistical tests, including randomisation tests, using statistical packages where appropriate.
MATH2507 Regression Modelling This module develops your understanding of advanced regression modelling by extending and generalising the linear model. The module will develop your understanding of the underlying mathematical theory by careful use of case studies in a variety of applications using professional software.