The aims of this module are:

• To introduce the notion of convergence as this applies to sequences and series.
• To introduce the notion of continuous function of one real variable.
• To provide a firm basis for future modules in which the idea of convergence and continuity is used.
• To help students recognize the necessity and power of rigorous argument.

The aims of this module are:

• To learn how to programme in a standard computer programming language.
• To learn elementary numerical methods and associated theory.
• To apply numerical methods to solve mathematical problems of appropriate level of difficulty.
• To implement numerical methods on the computer and to critically interpret numerical results.

The aims of this module are:

• To introduce basic ideas of vector spaces.
• To introduce linear transformations and explain their relationship to matrices.
• To provide the basic methods of linear algebra for other modules throughout all mathematics-based programmes.

The aims of this module are:

• To develop logical skills.
• To provide students with an appropriate language for the study of mathematics.
• To introduce different types of mathematical proof.

The aims of this module are to:

• Introduce students to the basic concepts of probability and statistics.
• Illustrate the relevance of these concepts to practical problem solving.

A part aim for this module is to enable students to become aware of and develop their academic, professional and personal skills through Personal Best. Personal Best is a development programme available to all students at Loughborough University.

The aim of this module is to develop further the main concepts of linear algebra.

The aims of this module are to introduce the basic ideas of kinematics and particle dynamics, connecting the mathematics with physical applications.

A part aim for this module is to enable students to become aware of and develop their academic, professional and personal skills through Personal Best. Personal Best is a development programme available to all students at Loughborough University.

The aims of this module are:

• To give a rigorous introduction to the analytical theory underpinning calculus for functions of one real variable.
• To develop the basic ideas of real analysis in several variables.

The aim of this module is to introduce the basic ideas and methods of the classical differential geometry of curves and surfaces in three-dimensional Euclidean space.

The aims of this module are:

• To introduce basic concepts and methods of probability theory.
• To provide the requisite theoretical background for later probability and statistics modules.

The aim of this module is to introduce students to the classical results in the theory of analytic functions of a complex variable.

The aims of this module are:

• To introduce the main ideas and techniques of the qualitative theory of ODEs and the calculus of variations.
• To teach students how to apply these ideas and techniques to the study of systems of ODEs and variational problems.

The aim of this module is to give a grounding in the central ideas of topology, sufficient for the main applications in geometry, analysis and mathematical physics.

The module aims to develop students' ability to communicate mathematical content clearly and in a manner that is appropriate to the target audience.

The aims of this module are to:

• Raise students' awareness of the nature of mathematics and how this can affect learning and teaching.
• Introduce students to what it means to learn and teach mathematics.
• Encourage them to reflect critically on their own experiences.
• Consider issues that are central to effective education in mathematics.

The aims of this module are:

• To introduce fundamental statistical concepts.
• To introduce statistical methods and associated theory for design and analysis of studies and experiments.
• To develop statistical software skills.
• To reinforce skills regarding the interpretation of statistical analyses.

The aims of this module are to introduce students to modern concepts and methods of combinatorics and graph theory.

The aims of this module are to introduce the students to the basic notions and methods of classical analytical dynamics.

The aim of this module is to give a theoretical and practical knowledge of numerical methods for the approximation of ordinary and partial differential equations.

The aims of this module are:

• To introduce fundamental statistical modelling concepts.
• To introduce associated theories for statistical inference.
• To develop statistical software skills.
• To reinforce skills regarding the interpretation of statistical analyses.

The aims of this module are to develop oral and written communication skills through writing and presenting an individual report, and for students to have the opportunity to learn unfamiliar topics in mathematics largely independently.

The aims of this module are:

• To introduce the concept of small and large parameters in equations and how they can be exploited to simplify difficult mathematical problems.
• To introduce a wide range of approximation techniques to analyse differential equations and integrals.

The aims of this module are:

• To introduce Bayesian statistics.
• To study posterior distributions and their properties.
• To discuss applications of Bayesian statistics to a range of data sets.

The aim of this module is to introduce students to the notions and methods of the theory of dynamical systems with an emphasis on its applications.

This module provides an introduction to the mathematical theory of formal languages - i.e. sets of sequences of symbols. It is the primary goal of the module to develop a student's knowledge of various concepts of defining formal languages, and to raise awareness of their relation to a range of fields of application, such as data mining, programming languages and natural language processing. In addition, the module shall explain the intrinsic connection of formal language theory to the mathematical foundations of computer science, thus deepening a student's understanding of the nature of computation.

The aim of this module is to create awareness of the power and range of abstract mathematical concepts through a basic introduction to the methods of functional analysis.

The aims of this module are to:

• Introduce the basics of algebraic geometry.
• Compare the structure of affine and projective varieties.
• Analyse examples and their properties including dimension and singularities.

The aim of this module is to provide students with fundamental methods of classical number theory and some of its diverse applications.

The aims of this module are:

• To introduce students to the nature of operational research and its techniques.
• To study linear programming, its applications and associated algorithms.

The aims of this module are:

• To provide students with a rigorous mathematical introduction to the modern financial theory of security markets in discrete and continuous time models.
• To give students a solid theoretical background in the derivatives industry in discrete and continuous time models.

The aims of this module are to introduce students to more advanced complex variable methods and demonstrate how these can be applied to sum series, evaluate integrals and define special functions.

This module aims to:

• Introduce numerical methods and associated theory for modelling of financial options.
• Teach students how to implement such numerical methods on computers.
• Gain experience in interpreting numerical results.

The aims of this module are to:

• Introduce students to the geometry of elliptic curves.
• Illustrate the difference between complex geometry and Diophantine geometry over the rational numbers.

The aim of this module is to explore fundamental algebraic structures and their connection to solving equations.

The aims of this module are:

• To introduce rigorous mathematical tools which are useful in economics analysis.
• To give students a solid mathematical background in game theoretic models.

The aims of this module are:

• Gain familiarity with linear ODEs with non-constant coefficients.
• To introduce linear PDEs with constant and non-constant coefficients.

The aims of this module are:

• To introduce some mathematical models of biological systems and various techniques for analysing them.
• To enable students to appreciate how mathematics can be used to model biological systems.

The aims of this module are to reinforce students' skills in interpreting statistical tests and using statistical software, and to introduce the methods and theory for the design and analysis of medical trials.

The aims of this module are to:

• Introduce the group representations as symmetries of vector spaces.
• Examine the special characteristics of the category of representations.
• Help students appreciate and use the connections between different areas of mathematics.

The aim of this module is:

• To introduce both supervised and unsupervised methods for learning from data.
• To introduce methods of dimensionality reduction.
• To introduce the R statistical programming language for implementing methods using real data.

The aims of the module are:

• To develop a range of skills within students and provide an early introduction to teaching for those interested in pursuing it, or a related field, as a career.
• To develop confidence and competence in communicating their subject.
• To provide opportunities to devise and develop science and mathematics projects and teaching methods appropriate to the age and ability of those the student is working with.

The aim of this module is to investigate physical phenomena that involve vibrations and waves using appropriate mathematical tools.

This is a 10 credit module from the University-wide language programme.

The aims of this module are:

• To develop oral and written communication skills.
• To give students the experience of working independently on an advanced topic in mathematics or its applications.

The aims of this module are:

• To introduce the concept of small and large parameters in equations and how they can be exploited to simplify difficult mathematical problems.
• To introduce a wide range of approximation techniques to analyse differential equations and integrals.

The aim of this module is:

• To derive the fundamental equations of fluid mechanics.
• To develop students' expertise in solving simplified forms of these equations applicable to a variety of fluid flows.
• To learn about some industrial and environmental applications of fluid mechanics.

The aim of this module is to create awareness of the power and range of abstract mathematical concepts through a basic introduction to the methods of functional analysis.

The aims of this module are:

• To introduce manifolds, tensors and integration theory on manifolds.
• To study basic geometric operations and their properties.
• To discuss applications of geometric methods to submanifold geometry, differential equations and general relativity.

The aims of this module are to introduce the notions of a Lie group and Lie algebra and to study their properties and methods.

The aims of this module are:

• To develop skills in the mathematical modelling of real life situations.
• To develop the ability to work effectively in a group.

The aims of this module are to:

• Provide a mathematical understanding of the Lebesgue measure and integration.
• Generalise concepts to abstract measure spaces.
• Build a solid rigorous mathematical background for students to proceed to stochastic analysis and financial mathematics.

The aim of this module is to:

• To provide students with a rigorous mathematical introduction to the modern financial theory of security markets in discrete and continuous time models.
• To give students a solid theoretical background in the derivatives industry in discrete and continuous time models.

This module aims to:

• Introduce numerical methods and associated theory for modelling of financial options.
• Teach students how to implement such numerical methods on computers.
• Gain experience in interpreting numerical results.

The aims of this module are:

• To develop skills in the mathematical modelling of real life situations.
• To develop the ability to work effectively in a group.

The aims of this module are to:

• Introduce students to the main ideas and techniques of the modern theory of nonlinear waves.
• Demonstrate how these ideas and techniques can be used in a wide range of applications.

The aim of this module is to create awareness of the power and range of abstract mathematical concepts through a basic introduction to the methods of spectral theory.

The aim of this module is to gain familiarity with theory and techniques of static optimisation and dynamic optimisation.

The aim of this module is:

• To introduce both supervised and unsupervised methods for learning from data.
• To introduce methods of dimensionality reduction.
• To introduce the R statistical programming language for implementing methods using real data.

The aim of this module is to introduce students to:

• The basics of stochastic calculus by using Brownian motion as an integrator.
• Mathematical modelling of pricing via the Black-Scholes model.

The aims of this module are to gain familiarity with modern qualitative theory of linear PDE's with particular emphasis on second-order equations, as well as to study selected aspects of modern methods for simple nonlinear PDEs.