Mathematics with a Year in Industry MMath

This module consists of a self-directed investigation of a project selected from a list of projects or, subject to prior approval of the School, from elsewhere.

The project will be supervised by a member of staff and will be based on a substantial mathematical problem, an application of mathematics or investigation of an area of mathematics not previously studied by the student. The course includes training in the use of IT resources, the word-processing of mathematics and report writing.

40 compulsory credits throughout the year

You will develop your knowledge and skills relevant to the mathematical modelling of investment and finance. Also, research experience will be broadened by undertaking some independent reading, computer simulations, group work and summarising the material in a project report.

The development of techniques for the study of nonlinear differential equations is a major worldwide research activity to which members of the School have made important contributions. This course will cover a number of state-of-the-art methods, namely:

• use of green function methods in the solution of linear partial differential equations
• characteristic methods, classification and regularization of nonlinear partial differentiation equations
• bifurcation theory

These will be illustrated by applications in the biological and physical sciences.

This module presents the fundamental features of algebraic number theory, the theory in which numbers are viewed from an algebraic point of view. Numbers are often treated as elements of rings, fields and modules, and properties of numbers are reformulated in terms of the relevant algebraic structures.

This approach leads to understanding of certain arithmetical properties of numbers (in particular, integers) from a new point of view.

You’ll systematically study black holes and their properties, including astrophysical processes, horizons and singularities. You’ll have an introduction to black hole radiation to give you an insight into problems of research interest. You’ll gain knowledge to help you begin research into general relativity.

Since the chromosome of H. influenzae was sequenced in 1995 hundreds of thousands of genomes have been analysed, revealing surprises that include how abundant, non-coding RNAs can control cellular processes, and how failure of these processes can trigger disease. As a result, there is a now growing understanding of the fundamental importance of non-coding RNAs in all regulatory networks and cellular mechanisms.

The first part of this module will describe the role of non-coding RNAs in the regulation of biological processes, focusing on new and exciting discoveries in micro-RNAs, piwi-RNAs and long non-coding RNAs. Information will be presented and linked to experimental models of neuron development and function, currently being investigated at the University of Nottingham.

Throughout, this module will describe these RNA molecules and their associated proteins, and how their discovery revolutionised how we understand biological systems, causes of disease, and the development of novel approaches such as RNA silencing and CRISPR for use in medical research and biotechnology. Similar to the first part of the module, students will be taught about these RNA technologies by those using them directly in state-of-the-art research projects.

There is a need for students to learn about this emerging and cutting-edge knowledge, because it is important to fully appreciate biochemistry and molecular biology across all organisms. Moreover, it will provide a detailed background on one of the fastest evolving areas of cellular and molecular biology, with incredible promise in the development of future therapeutic options across multiple disease backgrounds.

This course provides an opportunity for third-year students to gain first-hand experience of being involved with providing mathematical education. Students will work at local schools alongside practising mathematics teachers in a classroom environment and will improve their skills at communicating mathematics. Typically, each student will work with a class (or classes) for half a day a week for about sixteen weeks.

Students will be given a range of responsibilities from classroom assistant to leading a self-originated mathematical activity or project. The assessment is carried out by a variety of means: on-going reflective log, contribution to reflective seminar, oral presentation and a final written report.

This module introduces computational methods for solving problems in applied mathematics. You will develop knowledge and understanding to design, justify and implement relevant computational techniques and methodologies.

By studying this module, you’ll be equipped with the tools and knowledge to extend your understanding of general relativity. You’ll explore more abstract and powerful concepts using examples of curved space-times such as Lie groups and manifolds among others.

The first part of the module introduces no-arbitrage pricing principle and financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part of the module considers the pricing and hedging of options and discrete-time discrete-space stochastic processes. The final part of the module focuses on the Black-Scholes formula for pricing European options and also introduces the Wiener process. Ito integrals and stochastic differential equations.

This module gives a mathematical introduction to quantum information theory. The aim is to provide you with a background in quantum information science. This will help with your further independent learning and allow you to understand the scope and nature of current research topics.

In this year-long module you’ll be introduced to the study of the quantum dynamics of relativistic particles. You’ll learn about the quantum description of electrons, photons and other elementary particles, leading to an understanding of the standard model of particle physics.

The purpose of this course is to introduce concepts of scientific programming using the object oriented language C++ for applications arising in the mathematical modelling of physical processes. Students taking this module will develop knowledge and understanding of a variety or relevant numerical techniques and how to efficiently implement them in C++.

20 credits in the Autumn Semester

Machine Learning is a topic at the interface between statistics and computer science that concerns models that can adapt to and make predictions based on data. This module builds on principles of statistical inference and linear regression. It introduces a variety of methods of regression and classification, trade-off, and on methods to measure and compensate for overfitting.

You will benefit with hands-on learning using computational methods to tackle challenging real world machine learning problems.

This module will provide you with a general introduction to the analysis of data that arise sequentially in time. You will discuss several commonly-occurring models, including methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values.

This module illustrates the applications of advanced techniques of mathematical modelling using ordinary and partial differential equations. A variety of medical and biological topics are covered bringing you closer to active fields of mathematical research.