MMath (Hons) Mathematics Integrated Master's degree at the University of Leeds

You'll learn the foundational concepts of function, number and proof, equipping you with the language and skills to tackle your mathematical studies. The module also consolidates basic calculus, extending it to more advanced topics, such as functions of several variables. This leads to methods for solving simple ordinary differential equations. Linear algebra provides a basis for wide areas of mathematics and this module provides the essential foundation.

Calculus is arguably the most significant and useful mathematical idea ever invented, with applications throughout the natural sciences and beyond. This module develops the theory of differential and integral calculus of real-valued functions in a precise and mathematically rigorous way.

You'll be introduced to computational techniques, algorithms and numerical solutions, as well as the mathematics of discrete systems. You'll learn basic programming using the language Python and apply computational techniques to the solution of mathematical problems.

Group theory is a fundamental branch of mathematics, central also in theoretical physics. The concept of a group may be regarded as an abstract way to describe symmetry and structure. In this module, we will introduce group theory, with motivation from, and application to, specific examples of familiar mathematical structures such as permutations of lists and symmetries of shapes.

In its broadest sense, dynamics refers to the mathematical modelling of things which change with time. The main focus of this module is that of Newtonian mechanics, where forces cause accelerations which govern the motion of objects (their dynamics), but the module will also explore other examples and applications. You'll build on the methods of calculus (especially solution of ordinary differential equations) from the 'Core Mathematics' module. You'll also be introduced to a simple numerical me

'Probability is basically common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct.' So said Laplace. In the modern scientific and technological world, it is even more important to understand probabilistic and statistical arguments. This module will introduce you to key ideas in both areas, with probability forming the theoretical basis for statistical tests and inference.

You'll be introduced to ideas and methods of mathematical research. Examples and applications will be drawn from across the spectrum of pure mathematics, applied mathematics and statistics. You'll investigate a mathematical theory or concept and produce a report.

Explore the more abstract ideas of vector spaces and linear transformations, together with introducing the area of discrete mathematics.

Vector calculus is the extension of ordinary one-dimensional differential and integral calculus to higher dimensions, and it provides the mathematical framework for the study of a wide variety of physical systems, such as fluid mechanics and electromagnetism. These systems give rise to partial differential equations (PDEs), which can be solved and analysed. Students will learn to apply, among others, techniques introduced in earlier modules to PDEs, and they will also be introduced to Fourier me

The ideas of differential geometry and complex analysis are powerful products of nineteenth- and twentieth-century pure mathematics: interesting and beautiful in their own right, and with application to theoretical physics. Differential geometry is concerned with describing, understanding and quantifying properties of curved objects, while complex analysis extends and, in some ways, simplifies the differential calculus by considering functions of a complex variable. This module offers an introdu

Learn analytical and computational techniques for the solution of ordinary and partial differential equations, which describe particle motion in fields, fluids, waves, diffusion and many other phenomena.

This module is an introduction to mathematical logic introducing formal languages that can be used to express mathematical ideas and arguments. It throws light on mathematics itself, because it can be applied to problems in philosophy, linguistics, computer science and other areas.

Optimisation, "the quest for the best", plays a major role in financial and economic theory, such as maximising a company's profits or minimising its production costs. This module develops the theory and practice of maximising or minimising a function of many variables and thus lays a solid foundation for progression onto more advanced topics, such as dynamic optimisation, which are central to the understanding of realistic economic and financial scenarios.

Rings are one of the fundamental concepts of mathematics, and they play a key role in many areas, including algebraic geometry, number theory, Galois theory and representation theory. The aim of this module is to give an introduction to rings. The emphasis will be on interesting examples of rings and their properties.

The calculus of variations concerns problems in which one wishes to find the extrema of some quantity over a system that has functional degrees of freedom. Many important problems arise in this way across pure and applied mathematics. In this module, you'll meet the system of differential equations arising from such variational problems: the Euler-Lagrange equations. These equations and the techniques for their solution, will be studied in detail.

Statistical models are important in many applications. They contain two main elements: a set of parameters with information of scientific interest and an "error distribution" representing random variation. This module lays the foundations for the analysis of such models. We'll use practical examples from a variety of statistical applications to illustrate the ideas.

A stochastic process refers to any quantity which changes randomly in time. The capacity of a reservoir, an individual's level of no claims discount and the size of a population are all examples from the real world. The linking model for all these examples is the Markov process. With appropriate modifications, the Markov process can be extended to model stochastic processes which change over continuous time, not just at regularly spaced time points. You'll explore the key features of stochastic

In time series, measurements are made at a succession of times, and it is the dependence between measurements taken at different times which is important. This module will concentrate on techniques for model identification, parameter estimation, diagnostic checking and forecasting within the autoregressive moving average family of models and their extensions.