Science, Maths & Technology

### Postgraduate Diploma in Mathematics

This diploma comprises four 30-credit modules from a wide choice. Topics include analytic number theory, calculus of variations and nonlinear ordinary differential equations. Extend your understanding of areas of mathematics applicable to science, engineering and technology. It's also the first two stages of our postgraduate mathematics programme. You can achieve the MSc in Mathematics by taking a further two 30-credit modules.

Science, Maths & Technology

### Pure mathematics

Pure mathematics is one of the oldest creative human activities and this module introduces its main topics. explores sets of mathematical objects that can be combined ? such as numbers, which can be added or multiplied, or rotations and reflections of a shape, which can be performed in succession. explores 2- and 3-dimensional space and systems of linear equations, and develops themes arising from the links between these topics. , the foundation of calculus, covers operations such as differentiation and integration, arising from infinite limiting processes. To study this module you should have a sound knowledge of relevant mathematics as provided by the appropriate OU level 1 study.

Science, Maths & Technology

### Mathematical methods and fluid mechanics

Half of this module is about modelling simple fluid flows; the other half is about mathematical methods. You'll learn how to solve ordinary and partial differential equations such as: Laplace's equation, the wave equation and the diffusion equation; some vector field theory; and Fourier analysis. The fluid mechanical aspects of the module will give you a good understanding of modelling in the context of fluids. To study this module you should have a sound knowledge of ordinary differential equations, vector calculus, multiple integrals, basic particle mechanics and some knowledge of partial differential equations and Fourier series as provided by the appropriate OU level 2 study.

Science, Maths & Technology

### Mathematical methods

This module is designed to teach you about a variety of mathematical methods which are used in modelling through their application to solving real world problems. These methods include differential equations, linear algebra and vector calculus. You will become familiar with new mathematical skills mainly by using pencil and paper and by thinking. This module will give you a good foundation for higher-level study and is essential preparation for most OU level 3 mathematics, statistics or physics modules. To study this module you should have a sound knowledge of algebra, calculus, and geometry as provided by the appropriate OU level 1 study.

Science, Maths & Technology

### Nonlinear ordinary differential equations

Relevant to scientists and engineers as well as mathematicians, this introduction to basic theory and simpler approximation schemes covers systems with two degrees of freedom. It introduces the geometric aspects of the two-dimensional phase space, the importance of fixed points and how they can be classified, and the notion of a limit cycle. You'll develop schemes to approximate the solutions of autonomous and non-autonomous equations to understand how these solutions behave. Periodically forced nonlinear oscillators and nonlinear oscillators with periodically time-varying parameters leading to parametric resonances are discussed, along with the stability of these solutions and tests for obtaining stability.

Science, Maths & Technology

### Mathematical methods, models and modelling

Solve real problems by finding out how they are transformed into mathematical models and learning the methods of solution. This module covers classical mechanical models as well as some non-mechanical models such as population dynamics; and methods including vector algebra, differential equations, calculus (including several variables and vector calculus), matrices, methods for three-dimensional problems, and numerical methods. Teaching is supported and enhanced by use of a computer algebra package. This module is essential for higher level study of applied mathematics. To study this module you'll need a sound knowledge of mathematics as developed in Essential mathematics 1 (MST124) and Essential mathematics 2 (MST125) or equivalent.

Science, Maths & Technology

### Deterministic and stochastic dynamics

is designed to be studied as your first applied mathematics module at OU level 3. It introduces core topics in applied mathematics at this level and is structured around three books: ; ; and . The module will use the Maxima computer algebra system to illustrate how computers are used to explore properties of dynamical systems. To study this module, you should have a good prior knowledge of the subject area, including differential equations, and some knowledge of mechanics, as provided by the appropriate OU level 2 study.

Science, Maths & Technology

### Optimization

This module will interest you if you need to create mathematical models or if you use numerical software in industry, science, commerce or research. It's concerned with the skills needed to represent real optimization problems as mathematical models, and with techniques used in numerical analysis and operational research for solving these models by computer. Explaining how and when modelling and numerical techniques can be applied, the module covers solutions of non-linear equations; systems of linear and non-linear equations and mathematical modelling; linear and integer programming; and non-linear optimization for unconstrained and constrained minimization problems. Knowledge from OU level 2 study of calculus and matrices is assumed.

Science, Maths & Technology

### Essential mathematics 2

(MST125) builds on the concepts and techniques in (MST124) to provide a complete foundation for higher-level mathematics studies. You'll be introduced to a broad range of enjoyable and essential topics, such as proof, differential equations, mechanics and discrete mathematics, as well as extending your knowledge of calculus and its applications. You'll use mathematical software, and learn how to typeset mathematics. To study this module you should have a sound knowledge of relevant mathematics as provided by (MST124), in particular basic calculus.

Science, Maths & Technology

### Dissertation in mathematics

This module enables you to carry out a sustained, guided, independent study of a topic in mathematics. Currently there are six topics to choose from: algebraic graph theory; aperiodic tilings and symbolic dynamics; dynamical functional equations and applications; history of modern geometry; interfacial flows and microfluidics; and Riemann surfaces. This list is subject to change. You will be guided by study notes, books, research articles and original sources (or English translations where necessary), which are provided. You'll need to master the appropriate mathematics and ultimately present your work in the form of a final dissertation.

Science, Maths & Technology

### Electromagnetism

This module is concerned with the electromagnetic fields and electromagnetic radiation that pervade the world around you. It shows how the main ideas of electromagnetism can be encapsulated in the famous Maxwell's equations. These can be used to explain the properties of light and radio waves; the magnetic fields produced by brain activity; the way a television tube works; the transparency of the cornea in your eye; and many other phenomena. If you're interested in the ways that physics and mathematics are used to understand the world around you, then this would be an appropriate module to study.

Science, Maths & Technology

### Describing motion along a line

Motion is vital to life, and to science. This free course, Describing motion along a line, will help you to understand why classical motion is probably the most fundamental part of physics. You will examine motion along a line and the ways in which such motion can be represented, through the use of graphs, equations and differential calculus.