MMath (Hons) Mathematics with a Year in Industry Integrated Master's degree at the University of Nottingham

Pure mathematics at university is typically very different to the pure mathematics you've learnt at school or college. In this module, you'll use the language of sets, functions and relations to study abstract mathematical ideas. You will also learn how to construct mathematical proofs. Topics that you will learn about include set theory, prime numbers, symmetry and groups, and integer and polynomial arithmetic.

You'll learn how to construct and analyse differential and difference equations that model real-world systems. Applications that you'll learn about include systems governed by Newton's laws of motion, such as sets of interacting particles and the orbits of planets, as well as models of population dynamics. You will also be introduced to the mathematical basis of concepts such as work and energy, including an introduction to the basic ideas of quantum mechanics.

In this Autumn semester module, you'll be introduced to the basic mathematical concepts that underpin all degree programmes offered by the School of Mathematical Sciences. The major components are: mathematical fundamentals: logic; complex numbers; functions; set theory; introduction to cardinality; ordinary differential equations. linear algebra: systems of linear equations; introduction to matrices and matrix algebra. analysis: the real numbers; sequences; infinite series; limits and continuit

In this Spring semester module, you'll build upon the basic mathematical concepts covered in 'Core Mathematics 1' and provides practice in logical reasoning and rigorous mathematical thinking, particularly in relation to linear algebra and real analysis. The major components are: linear algebra: vector spaces; linear maps; eigenvalues and eigenvectors. analysis: single-variable and multi-variable calculus (differential and integral).

Probability theory allows us to assess risk when calculating insurance premiums. It can help when making investment decisions. It can be used to estimate the impact that government policy will have on climate change or the spread of disease. In this module, you will study the theory and practice of discrete and continuous probability, including topics such as Bayes' theorem, multivariate random variables, probability distributions and the central limit theorem. Statistics is concerned with metho

This course introduces the theory and applications of functions of a complex variable, using an approach oriented towards methods and applications. You will also learn about functions of complex variables and study topics including, analyticity, Laurent series, contour integrals and residue calculus and its applications.

In this module you will further develop your understanding of the tools of real analysis. This provides you with a solid foundation for subsequent modules in metric spaces, numerical analysis and PDE modelling. You will study topics such as convergence, norms and topology of multidimensional space, convergence of sequences of functions and applications of differentiation and integration.

In this module, you'll explore the abstract mathematical structures of different types of groups, including rings. Topics that you'll study include permutations, Abelian groups, quotient groups, ring homomorphisms and polynomial rings. Number theory is a branch of pure mathematics that primarily studies the integers, and has applications, for example, in cryptography. Topics that you will study include Diophantine equations, congruence equations and Fermat's little theorem.

In this module you will learn how Newtonian mechanics can be developed into the more powerful formulations due to Lagrange and Hamilton and be introduced to the basic structure of quantum mechanics. The module provides the foundation for a wide range of more advanced modules in mathematical physics.

This module explores how computers understand and generate human language, from the core mathematics behind Natural Language Processing (NLP) to the power of today's Large Language Models (LLMs). You will learn how neural networks are trained, how words are represented mathematically and how tools from statistics, algebra and calculus drive modern artificial intelligence (AI). Key topics include tokenisation, supervised learning, encoder–decoder systems, generative models and landmark breakthrou

This module is an introduction to methods of solving some of the most important ordinary and partial differential equations that occur in applied mathematics and mathematical physics.