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Mathematics BSc(Hons)

Attendance UCAS code/apply Year of entry
3 years full time G100 2015
4 years full time including sandwich year G102 2015
4 years full time including foundation year G108 2015
6 years part time Apply direct to the University 2015

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Why choose this course?

This degree provides a broad mathematics programme that includes application and statistics modules. It covers the fundamental techniques of mathematics with appropriate computational and statistical support to give you the tools to tackle real-world problems that require quantitative investigation.

What will you study?

The flexible curriculum of this course enables you to transfer to related courses at the end of the first year, and you may choose among applied mathematical, statistical and computational modules as your interests develop.

In Year 1, you will be introduced to a variety of topics to lay the foundations for further work. Your study of mathematical methods will include calculus, linear algebra, ordinary differential equations, an introduction to numerical methods and exposure to symbolic algebra and linear algebra packages. There is broad coverage of probability and statistics, and financial mathematics is introduced as an area of application leading to a large number of lucrative careers, providing a set of skills and knowledge that is becoming essential for everyone who wishes to prosper in our increasingly financially sophisticated world.

In Year 2, the module Mathematical and Numerical Methods introduces a range of further useful mathematical techniques. You will develop more skills that are highly valued by employers (eg constructing and communicating rigorously logical arguments) as you explore some of the underlying principles of calculus in the Mathematical Analysis and Argument module to see how the mathematics of change is built on solid foundations. You will also extend your problem-solving skills by studying more-sophisticated mathematical and statistical modelling. Your investigation of real-world problems will require the application of up-to-date industry-standard software (such as SAS, Maple and Matlab) in addition to the more traditional pencil and paper.

Once you have successfully completed Year 2, you will have the opportunity to take a professional placement year to develop your skills in a real work setting.

In Year 3, you will extend your study to partial differential equations and optimisation (areas of mathematics that may be applied to a vast range of real-world problems). You will undertake a major project (independent study) or studies in mathematical education (including a short placement in a local school) – this will draw together the academic strands of the course and significantly enhance your employability skills. In addition, you may select specialist option modules from across different areas of mathematical and statistical applications, such as fluid dynamics, medical statistics and operational research.

Module listing

Please note that this is an indicative list of modules and is not intended as a definitive list. Those listed here may also be a mixture of core and optional modules.

Year 1

  • This module provides the foundations for further study of (applicable) mathematics. The basic ideas of mathematics as a discipline are introduced. Topics from different areas of mathematics which may readily be applied to solve problems in the real world are considered with emphasis on study of the Calculus, one of the most powerful tools of modern mathematics and theoretical science. As a necessary preliminary to this work we first clarify our ideas of rational, real and complex numbers. The fundamental concepts of calculus, in particular, that of a limit, are introduced and the continuity and differentiability of functions on the real line are explored. The derivative concept is generalised for functions of several variables extending the breadth of its application greatly and the study of ordinary differential equations is commenced.

    On successful completion of the module, you will be able to:

    • Discuss the idea of systems constructed on axiomatic foundations and the use of definitions, theorems and proof in mathematics.
    • Explain the evaluation of derivatives and integrals of functions as limiting processes, and perform the evaluation for simple examples.
    • Apply the techniques of calculus in a range of appropriate situations.
    • Formulate and solve mathematical models based on simple ordinary differential equations (ODEs).
    • Perform calculations with sets of vectors to determine their theoretical properties and to solve simple geometrical problems in three dimensions.
    • Communicate simple mathematical ideas and arguments in written form – where appropriate incorporating material from a variety of information sources.
     
  • This module is a core part of most mathematics courses and builds upon A-level study in three strands: it aims to develop s personal skills and understanding of degree-level study; it introduces computer programming and software as a useful problem-solving tool in mathematics; and it develops mathematical techniques in a computing context that will be used in parallel and subsequent modules.

    On successful completion of the module, you will be able to:

    • Work in groups to solve problems and present their work effectively.
    • Describe the relationship between the role of professional societies, their codes of practice and ethical (professional) behaviour.
    • Use computer packages for symbolic algebra and linear algebra.
    • Use a modern programming environment to assist in the solution of computational problems in mathematics.
    • Integrate a function numerically, showing awareness of the concepts of convergence and errors in arithmetic processes.
    • Use matrices to represent, analyse and solve simple systems of equations.
     
  • This module introduces basic probability and statistical theory, concepts and their applications to real life problem solving and learn about different types of data and how to present and summarise these. The module also covers statistical inference and the concepts of confidence intervals and hypothesis testing for the population mean and variance, for proportions, for comparing measures between two populations and for contingency tables and goodness of fit to a known distribution.

    On successful completion of the module, you will be able to:

    • Summarise the main features of a dataset by using appropriate statistical measures and diagrams.
    • Apply the concepts of probability, random variables, probability distributions and random sampling; and select probabilistic models appropriate to problems described in words.
    • Construct confidence intervals and conduct hypotheses tests for unknown parameters in well-defined circumstances and interpret the results.
    • Investigate the linear relationship between variables using correlation and regression analysis.
    • Use appropriate software for basic statistical analysis and presentation of data.
     
  • This module is designed to build on the work previously gained in order to deliver more advanced tools in calculus and numerical methods thus permitting the solution of a much wider set of problems associated with the real world. In turn, concepts developed in this module are used extensively at Level 6.

    On successful completion of the module, you will be able to:

    • evaluate multiple integrals, in different co-ordinate systems.
    • perform vector algebra and calculus, including evaluations of gradient, divergence and curl  and applications of (integral) theorems linking these quantities.
    • solve a variety of ordinary differential equations (ODEs) including linear systems of ODEs.
    • solve systems of linear and nonlinear equations numerically.
    • obtain eigenvalues numerically.
    • understand and apply methods of approximation using truncated series or splines.
     

Year 2

  • This module is designed to build on the work previously gained in order to deliver more advanced tools in calculus and numerical methods thus permitting the solution of a much wider set of problems associated with the real world. In turn, concepts developed in this module are used extensively at Level 6.

    On successful completion of the module, you will be able to:

    • Evaluate multiple integrals, in different co-ordinate systems.
    • Perform vector algebra and calculus, including evaluations of gradient, divergence and curl  and applications of (integral) theorems linking these quantities.
    • Solve a variety of ordinary differential equations (ODEs) including linear systems of ODEs.
    • Solve systems of linear and nonlinear equations numerically.
    • Obtain eigenvalues numerically.
    • Understand and apply methods of approximation using truncated series or splines.
     
  • This module builds upon the foundations in mathematics and computing with the aim to systematically develop mathematical modelling skills and computer programming as well as systems analysis skills, whilst continuing to develop mathematical techniques in a computing context.

    On successful completion of the module, you will be able to:

    • Solve simple deterministic mathematical problems using appropriate algorithms, models and software systems.
    • apply principles of program analysis, design and testing to mathematical problem solving.
    • use concrete examples within reports and presentations to illustrate the stages of the mathematical modelling cycle and their inter-relationships.
    • Assess the connection between initial assumptions and results produced from models, and discuss the limitations of applicability of these models.
    • Demonstrate improved communication and group interaction skills through investigating case studies in groups.
     
  • This module develops and builds on the concepts of probability and statistical modelling studied at the previous level. The module introduces some of the major discrete and continuous statistical distributions which underpin statistical methodology and the concepts of joint distributions. The module also deals with statistical modelling and how to take data analysis beyond basic techniques. The theory and practical application involved in investigating multivariate data using statistical modelling from initial investigation through to validation of a model is investigated. Example driven practice in using industry standard statistical software for the purpose of statistical modelling and how to communicate the results of their analyses effectively and coherently will be reviewed. This module provides a sound grounding in theoretical and practical statistical analysis and forms the basis for learning more advanced multivariate methodologies later in the program. It also covers much of the material required to satisfy the IFA CT3 criteria.

    On successful completion of the module, you will be able to:

    • Distinguish between discrete and continuous random variables, calculate probabilities and moments for discrete and continuous random variables and median and mode for continuous random variables.
    • Derive moments and generating functions for discrete and continuous variables and use generating functions to derive moments and the distribution of the sum of independent random variables.
    • Derive marginal and conditional distributions from joint distributions, and distributions of functions of random variables.
    • Derive the maximum likelihood and method of moment estimators and estimates of parameters of univariate probability distributions.
    • Use regression modelling to investigate multivariate data, obtain the model of best fit and test the validity of the model.
    • Use statistical software to construct, analyse and fit regression models, interpret the output and communicate the results.
     
  • This module builds upon previous mathematics studied, by concentrating initially on methods of proof and clear, logical exposition of mathematical arguments. These are essential skills for mathematicians to possess in order to perform their academic tasks and to communicate their findings efficiently. Armed with this approach to mathematics, the module progresses to develop more rigorously, various techniques involving real variables to include more detailed justification of some calculus techniques which have previously been encountered. The remaining content builds on the complex number work studied by moving into the realm of complex valued functions.

    On successful completion of the module, you will be able to:

    • Evaluate the quality of mathematical arguments and prove simple results whilst utilising consistent and rigorous mathematical notation in their arguments.
    • Apply to sequences and series appropriate tests for convergence.
    • Identify intervals of continuity and differentiability of a real valued function.
    • Approximate definite integrals using Riemann sums.
    • Ascertain the differentiability of complex valued functions.
    • Perform complex integration and apply this to evaluate appropriate real integrals.
     

Optional sandwich year

Year 3/4

  • This module consolidates and further develops the concepts previously acquired; consisting of two distinct but interrelated parts. The PDE part builds on analytical and numerical methods for solving ODEs whilst in the optimisation section the ideas of using calculus to find stationary points of functions (of one or two variables), introduced in earlier modules are generalised and extended to cases where the functions are constrained (by both equations and inequalities). An holistic approach covering both analytical and (approximate) numerical techniques is adopted throughout. This means that a wide range of PDEs covering many areas of application may be solved – and similarly a variety of calculus-based methods for finding optima is considered and their appropriateness for different situations discussed in the context of recent research in the area.

    On successful completion of the module, you will be able to:

    • Find the characteristics and classify a partial differential equation.
    • Use Fourier method of separation of variables to solve a partial differential equation.
    • Use finite difference methods for solving PDEs and understand limitations of numerical methods.
    • Find analytically the extrema of functions of two or more variables, with and without constraints.
    • Apply appropriate numerical methods to solve unconstrained and constrained optimisation problems.
    • Apply the above theory to deduce optimal strategies in a range of application areas.
     
  • Mathematics Education: Theory and Practice
    This module gives an insight into the theoretical and practical aspects of mathematics education in schools, particularly for the 11–16 age range. It is intended to foster skills of independent learning, critical analysis, information retrieval and enhanced communication. The first half of the module covers important issues in mathematics education such as the role and content of the National Curriculum. Armed with theoretical knowledge the student is placed in a local secondary school or college for the second semester. The process is based on the nationally recognised model of the undergraduate ambassador scheme which is designed to give students interested in becoming mathematics teachers a chance to gain relevant experience in the field. In the placement they act initially as observers, but gradually they progress to become classroom assistants and, if they can demonstrate appropriate aptitude, ultimately deliver a session to a group or to the whole class, under the guidance of the mentoring teacher.

    On successful completion of the module, you will be able to:

    • Appraise some contrasting views of the nature of mathematics and approaches to its acquisition.
    • Display knowledge of current documentation for curriculum and assessment in primary and secondary schools in England.
    • Distinguish between concepts, skills and process in learning a mathematical topic from the 11–16 curriculum.
    • Show awareness and understanding of current research on the affective dimension of learning mathematics – particularly issues of equality of opportunity and inclusion with respect to gender, class and culture.
    • Reflect upon and critically analyse personal presentation skills whilst appraising their experience of working in a challenging and unpredictable working environment.
    • Prepare lesson plans and teaching materials.

    Individual Project
    This module offers the opportunity to demonstrate skills and understanding gained to date on the course through application to a project of their choice. Typically it involves drawing upon work from several different areas of the course thus reinforcing the coherence of the programme, highlighting connections (and often interdependence) between the different areas studied to be able to give an overview. It also represents an opportunity to further develop vital skills in areas of research, time and project management, and presentation as well as in technical areas. 

    On successful completion of the module, you will be able to:

    • Carry out a literature search to summarise and evaluate background work relevant to the project.
    • Plan tasks within time and other commitment constraints.
    • Undertake an investigation of the planned topic and critically evaluate the outcomes.
    • Produce a well-structured written report demonstrating a sound understanding of the theory of the chosen project area, including correct use of relevant references, language, data, diagrams, tables and graphs as appropriate to your project.
    • Give a presentation and answer questions clearly and concisely in a structured interview about your work.
    • Design, implement and test an application, as appropriate to your project.
     
  • Choose from the following:

    • This module aims to introduce database systems and the study of artificial intelligence with applications in research-informed topics such as language modelling, speech recognition or data mining. It introduces both 'traditional' (logic-based) and 'modern' (eg neural networks and probabilistic 'machine learning' systems) approaches to artificial intelligence, and includes some case studies of modern practical applications. It deals with the ability to design and manipulate relational databases using entity-relationship modelling and the structured query language (SQL). The module also develops an understanding of the wider context in which relational databases exist.

      On successful completion of the module, students will be able to:

      • Describe the mathematical and philosophical basis behind A.I. and the computational modelling of cognitive processes and "knowledge representation"
      • Identify classes of problems for which A.I.-based approaches to solutions are appropriate and discuss the limitations of such approaches
      • Evaluate the variety of computational and cognitive approaches to problem-solving in humans and machines, and strategies for implementing such techniques
      • Discuss both the theoretical basis and practical applications of modern A.I techniques, such as Neural Networks and Bayesian systems
      • Formulate data structures using normalisation rules and design a logical data model from a problem specification
      • Implement a database, evaluate the solution and investigate its performance.
       
    • This module consolidates previous experience using the equations of fluid motion as a basis. The module consists of two distinct but interrelated parts: the analytical part builds on understanding of partial differential equations and further develops the understanding of applications in the area of fluid dynamics, where the module introduces commonly occurring flows, both theoretically and through a series of practical examples. The numerical part takes the fluid equations and explores approaches to solving them numerically, using a software package and students' own models where appropriate.

      On successful completion of the module, you will be able to:

      • State the basic assumptions made about the physical properties of a fluid and the derivation of the equations of fluid dynamics, discuss their limitations and define appropriate boundary conditions.
      • Solve the equations for some simple flows.
      • Use numerical methods for solving PDEs and understand the limitations of numerical methods.
      • Describe some commonly occurring phenomena such as tidal bores and surface waves.
      • Construct appropriate solid models for CFD analysis, setup the solution domain and generate suitable surface and volume grids with a meshing tool.
      • Use CFD software to model flow problems, analyse and evaluate the CFD results.
       
    • This module introduces the applications of statistical methodologies in clinical, medical and health scenarios. The module considers how the health resources in populations are assessed, monitored and used to produce routinely published health statistics. How to determine and apply appropriate statistical methodologies for the analysis of epidemiological studies and how to interpret, present and contextualise the findings of such analyses will be considered. The processes involved in the implementation of clinical trials will be introduced to further statistical methods which are routinely used in the development of new therapies and medical interventions. An introduction to the methodology of survival analysis and to some advanced multivariate methodologies which are being increasingly used in the medical and health fields.

      On successful completion of the module, you will be able to:

      • Explore sources of medical data and compute and discuss appropriate statistics for a particular investigation.
      • Identify and analyse data obtained from epidemiological studies, and interpret and report the results of such analyses.
      • Demonstrate a comprehensive understanding of the issues, ethical considerations and statistical analysis methods involved in planning, conducting and reporting the results of clinical trials.
      • Identify and analyse survival data using statistical techniques for the analysis of such data and interpret and report results.
      • Demonstrate knowledge and understanding of issues and considerations in the analysis of medical data, choose and apply appropriate techniques for the analysis of such data and interpret and report the results.
      • Use appropriate modern computational software for the implementation of the statistical techniques learned.
       
    • This module serves as an introduction to the mathematics and statistics of modern portfolio theory, the mathematical, stochastic and statistical models of risky assets and the theory of pricing contracts based on these assets. It is intended to cover the requirements of CT8 from the Institute and Faculty of Actuaries.

      On successful completion of the module, you will be able to:

      • Analyse the return on an asset or portfolio – as well as the mean and variance of return – and compare investment opportunities using a variety of measures of risk.
      • Identify a portfolio of assets which is optimal given a set of selection criteria.
      • Describe various models of asset returns, including the capital asset pricing model (CAPM) and perform calculations using these models.
      • Discuss the various forms of the efficient market hypothesis and their limitations.
      • Formulate models of the securities markets using discrete and continuous-time stochastic processes and partial differential equations.
      • Use and extend these models to obtain the value of options and other contingent claims on assets.
       
    • This module builds upon the foundations in computing previously studied and aims to further develop mathematical modelling, computer programming, problem-solving and systems analysis skills with applications in a mathematical context. Further topics in computing are presented and analysed as solutions to common problems in mathematical and computational modelling.

      On successful completion of the module, you will be able to:

      • Formulate and solve both new and established models involving systems of ordinary differential equations or partial differential equations.
      • Use phase-plane analysis to extract qualitative information from systems and mathematical software to obtain quantitative results.
      • Implement finite difference methods for solving PDEs.
      • Analyse algorithms, including recursion and search techniques, estimate complexity and design optimised solutions.
      • Apply 'divide and conquer' and dynamic programming approaches to certain problems.
      • Demonstrate further development of their communication and group interaction skills through investigating case studies individually and in groups.
       
    • This module has two aspects: firstly, the application of time series modelling techniques in forecasting is introduced with background gained in earlier modules. This part includes both non-probabilistic algorithmic methods as well as the Box-Jenkins ARIMA probabilistic modelling techniques. The methods are applied to real and up-to-date time series data sets using MS-Excel and SAS software packages. Emphasis is placed on practicability of methods and their applications, although the theoretical foundation also plays a significant role in introducing the methodologies involved. You will have the opportunity to acquire, develop and consolidate both modelling and software skills through a series of exercises during practicals and tutorial sessions.

      The second part of the course uses and builds upon the distribution theory with an introduction to the important properties of estimators, Neyman-Pearson's lemma and the generalised likelihood ratio test with numerical applications; followed by the Bayesian methodology and its relevance to the statistical decision making problems. Here emphasis is placed on introducing theoretical concepts but numerical techniques such as statistical simulation is also used in demonstrating applications. Bayesian and frequentist's approaches to decision-making problems are also compared with the advantages involved are identified and discussed.

      On successful completion of the module, you will be able to:

      • Analyse time series and select appropriate forecasting techniques for them.
      • Evaluate and critically assess the validity of the modelling results for time series data from the computer output.
      • Suggest tentative models and use appropriate criteria to identify the optimal model for forecasting using Box-Jenkins methodology.
      • Identify and use the properties of estimators.
      • Construct likelihood ratio test for both simple and composite hypotheses.
      • Understand the application of the basic concepts of the Bayesian procedure to decision theory and make comparison with the classical non-Bayesian approach.
       
    • The module introduces a variety of operational research techniques and the basic concepts and ideas of mathematical programming. The module goes on to explain how to apply operational techniques such as network models, inventory models, quality control and heuristics to real life problem solving issues. The module shows how  industrial problems of optimization may be written in  mathematical form. The module also introduces the simplex algorithm and its variants and demonstrates how such problems may be solved via these methods. Problems of a nonlinear nature are also discussed and solved. Other topics covered within the module include the methods of Lagrange multipliers, the Kuhn-tucker procedure and an introduction to game theory. The module provides an essential introduction to operational research and mathematical programming techniques and provides a depth of detail that sufficiently prepares for further study and research into advanced techniques within the applied mathematics and statistics fields.

      On successful completion of the module, you will be able to:

      • Use several types of operational research methodology such as critical path analysis, network models, inventory models, quality control, heuristics.
      • Identify problems where the various techniques are relevant.
      • Formulate models, solve them, interpret and define the limitations of solutions found by the above methodology.
      • Identify the basic principles of mathematical programming methods.
      • Display a deep understanding of several mathematical programming algorithms for linear programming.
      • Develop models for the solution of real-life problems by the use of mathematical programming, interpret solutions and define sensitivities to parameter specifications.
       
     

You will have the opportunity to study a foreign language, free of charge, during your time at the University on a not-for-credit basis as part of the Kingston Language Scheme. Options currently include: Arabic, French, German, Italian, Japanese, Mandarin, Portuguese, Russian and Spanish.

Most of our undergraduate courses support studying or working abroad through the University's study abroad programme or Erasmus programme.

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