• For Entry: September
  • Duration: 12 months
  • School: Science & Engineering
  • Study Mode: Full Time

This masters course is designed to provide students with the necessary mathematical and financial knowledge and skills to meet the demands of employers in the financial sector.

TEF Gold - Teaching Excellence Framework

The financial sector is increasingly using sophisticated mathematical models to predict the development of markets and risks related to the services and products it provides. Banks, building societies, accountancy, insurance, investment and pension companies demand graduates with strong quantitative skills. This programme aims to prepare you for a successful career in these fields.

Taught by Mathematics at the School of Science and Engineering and Business at the School of Social Sciences, we ensure you can experience both the mathematical and economic perspective of the subject.

This courses offers a challenging range of modules across disciplines at the University of Dundee, one of the highest ranked universities in in UK for student experience and satisfaction.

Mathematics is central to many disciplines across a wide variety of fields particularly in the financial sector. You will enhance your analytical and critical abilities and competence in the application of mathematics to solve real world problems.

Demand for people with mathematical qualifications in the financial sector is particularly high and graduates of this programme will gain a significant advantage to further their career within the financial industry.

Mathematics at the University of Dundee consistently enjoys high rankings in student satisfaction and experience. It was ranked second in Scotland, and sixth in the UK by The Times & Sunday Times Good University Guide 2016.

The University has an international reputation for world class teaching and research. Mathematics at the University of Dundee was ranked top in Scotland and eighth in the UK for the quality and impact of its research.

You will be taught by staff who have experience applying mathematical models to financial problems or who have gained insight into the financial sector through practical experience or research.

The MSc Mathematics for the Financial Sector is a highly marketable qualification which will prepare you for a successful and rewarding career.

Teaching Excellence Framework (TEF)

The University of Dundee has been given a Gold award – the highest possible rating – in the 2017 Teaching Excellence Framework (TEF).

Read more about the Teaching Excellence Framework

TEF Gold - Teaching Excellence Framework

How you will be taught

You'll learn by traditional methods such as lectures, tutorials, and workshops as well as via computer assisted learning. We also teach the use of professional mathematical/statistical/financial software packages in order to allow students to explore more complex problems and as a preparation for their future employment.

Individual reading and study takes a particularly important role in the summer project. For the project, we will guide you with preparation of your research project plan and to develop skills and competence in research including project management, critical thinking and problem solving, project reporting and presentation.

How you will be assessed

About 50% of the assessments are written (formal) examinations, 35% are coursework/continuous assessment and the remaining 15% is the project report.

What you will study

The course comprises the following modules in Semester 1 and 2:

Compulsory modules

The course comprises the following modules in Semester 1 and 2:

This module will develop your understanding of the behaviour of financial agents and the workings of global financial markets within the framework of modern finance theory. Topics include the time value of money and discounted cash flow analysis; theories of the yield curve and bond valuation; risk-return trade-off and mean-variance portfolio theory; Capital Asset Pricing Model and the Efficient Market Hypothesis; alternative approaches to stock valuation and financial ratio analysis; influence of corporate dividend policy and capital structure on stock pricing; functions of futures exchanges and the valuation of financial and commodity futures and the properties and valuation of option contracts.

The module will broaden your knowledge and understanding of the quantitative theory of financial risk, and how that risk can be managed by financial derivatives; develop critical reasoning skills in the context of financial derivatives and financial risk management; equip you with the practical skills to apply most appropriate financial derivatives to managing and hedging the financial markets volatility. When you finish the module you will be able to explain (i) the sources of financial markets risk, (ii) the key characteristics of various derivative products; (iii) the use of these products as risk management tools and understand the implications of hedging via risk-neutral replication and construct hedge portfolios, and understand pricing and hedging principles of a range of derivatives.

About the module

In this module the Level 5 student will learn to write their own code and to apply built-in "black box" solvers in MATLAB and COMSOL to mathematical modelling problems. This module is mandatory for Level 5 students taking the MMath in Mathematics or the MSci in Mathematical Biology. This module may be taken in combination with another at Level 5 by students taking the MSci in Mathematics and Physics. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must usually have achieved a pass mark in each of the modules MA32005 and MA42003, or equivalent.

Indicative Content

  • MATLAB fundamentals

    Students will learn basic operations in MATLAB, and implement various finite difference schemes to solve ODEs (primarily initial value problems) originating in celestial mechanics, population dynamics, and cell biomechanics.

  • MATLAB ODE solvers for initial value problems

    Students will learn to use standard built-in solvers with MATLAB, particularly ode45 and ode23s, and possibly dde23. We will apply these solvers to initial value problems (and possibly delay differential equations) stemming from celestial mechanics, cell biomechanics, and population dynamics.

  • MATLAB random variables, stochastic processes, and SDEs

    After a brief introduction to stochastic differential equations (SDEs), students will learn MATLAB solution techniques, with applications to Brownian motion and related physical processes. We will also learn to simulate discrete and continuous stochastic processes, and generate samples from random variables with arbitrary distributions.

  • MATLAB ODE solvers for boundary value problems

    Students will implement a standard "shooting" method to solve a BVP from heat transfer. We will learn to use the standard built-in solvers, particularly bvp4c. We explore alternate solution techniques, such as by formulating the discretised equation as a linear algebraic system, and as the steady state solution to a PDE; these approaches help drive us towards PDE solution methods. The class will apply these solvers to boundary value problems stemming from heat transfer and fluid mechanics.

  • MATLAB for PDEs

    Students will implement explicit finite difference methods in MATLAB, with a focus on reaction-diffusion problems. The overall goal will be to solve coupled reaction-diffusion problems (with heterogeneous coefficients) and cell growth.

  • Weak formulations for partial differential equations; introduction to FEMs

    We repose PDEs using a weak formulation, using the context of function spaces. Using this framework, we develop an understanding of finite element methods (FEMs).

  • FEMs and COMSOL fundamentals

    Students will learn to solve reaction-diffusion equations using the built-in FEMs in COMSOL.

Delivery and Assessment

Delivery of this module will take a hands-on, interactive approach, where lectures are integrated with guided computer lab time. Assessment will be based on computational coursework (100%).

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.

About the module

This module, aimed at Level 5 students, gives a non-measure theoretic introduction to stochastic processes, considering the theory and some applications and going on to introduce stochastic differential equations and their solutions. This module may optionally be taken in combination with others by Level 5 students taking the MMath in Mathematics or the MSci in Mathematical Biology or Mathematics and Physics. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module would find it beneficial to have taken each of the modules MA32001 and MA51007, or equivalent.

Indicative Content

  • Probability fundamentals

    Elementary probability concepts such as random variables, expected value, moment generating and characteristic functions, conditional expections, probability inequalities and limit theorems, etc.

  • The Poisson process

    (Homogeneous) Poisson process and related examples such as interarrival and waiting time distributions and conditional distribution of the arrival times. Some practical examples such as the busy period of the M/G/1 queueing system. Introduction to the nonhomogeneous Poisson process.

  • Markov chains

    (Discrete-time) Markov chains and some related examples. Chapman-Kolmogorov equations and classification of states.

  • Continuous-time Markov chains

    Continuous-time Markov chains, birth and death processes, and the Kolmogorov differential equations.

  • Brownian motion and stochastic differential equations

    Basics of Brownian motion, Ito^ integral and Ito^ formula, and then stochastic differential equations (SDEs). A number of commonly used SDEs and their solutions will be discussed.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/presentation classes and assessed via coursework (100%) consisting of homeworks and a presentation.

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.

About the module

Optimisation problems arise from modelling a wide variety of systems in science, technology, industry, business, economics as well as in many other fields. This module, aimed at Level 5 students, covers practical methods of optimisation that are supported by a growing body of mathematical theory. Students are expected to implement the methods and solve problems numerically. This module may optionally be taken in combination with other modules at this level by Level 5 students on the MMath in Mathematics or MSci in Mathematics and Physics degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must usually have achieved a pass mark in the module MA32005, or equivalent.

Indicative Content

  • Introduction

    Examples of optimization problems. Mathematical background.

  • Unconstrained Optimization

    Line search and Descent methods. Newton′s method. Conjugate gradient method.

  • Linear Programming

    Simplex method. Slack and artificial variables. Simplex tableau.

  • Constrained Optimization

    Lagrange multipliers. Theory of constrained optimization.

  • Application in Finance and Energy

    Application problems such as factory location problem, oil pipeline problem.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/presentation classes and assessed via coursework (100%) consisting of homeworks, tests, presentations and project work.

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.

About the module

This module is a personal research project for students on the MSc in Mathematics for the Financial Sector, which runs over the summer. If you have questions about this module please contact your Advisor of Studies.

Prerequisites

Students taking this module must have achieved an average mark of at least 50% (C3) over the Mathematics MSc modules taken in Semesters 1 and 2 and have obtained at least 75 credits in these modules.

Indicative Content

  • Project

    Carry out a substantial project in an area of mathematics and document the work in a project report.

Delivery and Assessment

The project will require substantial independent work as well as regular meetings with the project supervisor(s). Assessment will be based on coursework (100%) consisting of the project report.

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 60 SCOTCAT credits or 30 ECTS credits.

Advised modules

This module enables you to evaluate and manage the risks involved in international business in order to make sound financing and investment decisions. You will develop a knowledge and understanding of foreign exchange and eurocurrency markets; models of foreign exchange rate determination and financial products that manage currency risk; models of interest rate determination and financial products that manage interest rate risk; the practical uses of international capital markets for managing risk; the international economic and political environment in which multinational companies operate; the risks of foreign direct and foreign portfolio investment; practical perspectives of risk, and techniques for assessing the risk of capital and financial investments.

The module provides you with an intuitive grasp of the theoretical concepts and basic skills required to estimate and interpret economic models. In particular, it will allow you to apply statistical techniques to problems in finance by (i) translating theoretical models into an empirically implementable form; (ii) analysing statistical data; and (iii) interpreting econometric results. The module also provides you with an overview of the empirical methods used by financial academics and professionals in the analysis of financial asset prices.


* Requires prior knowledge of econometrics.

About the module

This module, aimed at the Level 5 student, takes an advanced look at dynamical systems. The time evolution of many biological, chemical, or physical processes, as well as systems considered in engineering or economics, can be described by difference or differential equations. Dynamical systems theory allows us to study these systems of equations and inver information about the behaviour of the corresponding biological, chemical or physical systems. It addresses questions like the existence and stability of solutions, how the behaviour of solutions changes depending on the system parameters, or determines the existence of strange attractors or chaos in the system.

This module may optionally be taken by students on the MMath in Mathematics, or the MSci in Mathematical Biology or Mathematics and Physics degrees. If you have questions about this module, please contact your Advisor of Studies.

Prerequisites

Students taking this module must usually have achieved a pass mark in each of the modules MA31002 and MA32001, or equivalent.

Indicative Content

  • One-Dimensional Maps

    Definition, Cobweb Plot: Graphical Representation of an Orbit, Stability of Fixed Points, Periodic Points, Chaos: Lyapunov Exponents.

  • Ordinary Differential Equations

    Background, Examples of main Physical and Biological Processes described by Ordinary Differential Equations (ODEs), Existence and uniqueness of solutions of ODEs, Linearised Stability Analysis, Two-dimensional Systems: Hamiltonian and Gradient systems, Periodic solutions: Floquet theory, Poincare Map and Stability of Periodic Orbits, Bifurcation and Chaos.

  • Partial Differential Equations

    Definitions, Background, Well-posedness, Maximum Principles, Spectral Theorem for Laplace Equation, Semigroups for Evolution Equations in Banach Spaces, Nonlinear Evolution Equations: Linearised Stability Analysis for Reaction-Diffusion Equations.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/presentation classes and assessed via an exam (60%) and coursework (40%).

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.

About the module

This is a Level 5 course that offers a robust understanding of the inverse problems theoretical framework and methods suitable for medical and financial applications. The aim is to achieve comprehensive knowledge in the theoretical fundaments and general methodology for inverse problems in various heterogeneous media, including medical applications and finance. This module may optionally be taken in combination with other modules at this level by Level 5 students on the MMath in Mathematics or MSci in Mathematics and Physics degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must usually have achieved a pass mark in the module MA32001, or equivalent.

Indicative Content

  • Examples of Inverse Problems

    Examples from medical applications and finance.

  • Inverse Methodology Preliminary Foundation

    Necessary Basic Definitions and Theorems in Measure Theory and Function Spaces

  • General Regularisation Theory

    Tikhonov′s regularization method. Landweber Iteration. The Discrepancy Principle of Morozov. Conjugate gradient method.

  • Galerkin Methods

    Galerkin General formulation. The Least Squares Method. The Dual Least Squares Method.

  • The Truncated Singular Value Decomposition Method

  • Stable inversion via the Mollification Method

  • Inverse Problems in General Heterogeneous Media and Medical Applications

    Backward heat conduction problem. Inverse problems in reaction-diffusion equations.

  • Inverse problems in finance

    Formulation of forward model: Black-Scholes and Dupire's Formula. Inverse Problem formulation of market volatility. Reconstruction of time- and price-dependent volatilities.

Delivery and Assessment

The module is delivered in the form of lectures and assessed via coursework (100%) consisting of tests and homeworks.

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.

About the module

This module, aimed at the Level 5 student, covers the fundamentals of Measure Theory including Lebesgue Measure and Integration and Lebesgue Spaces as well as their pivotal implications in the modern analysis of partial differential equation and probability theory. This module may optionally be taken in combination with other modules at this level by Level 5 Students on the MMath in Mathematics or MSci in Mathematics and Physics degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must usually have achieved a pass mark in the module MA32001 or equivalent.

Indicative Content

  • Construction of a general measure space

    Definition and properties of a σ-algebra. The concept of measures as a non-negative σ-additive real valued set functions defined on a σ-algebra. Measurable sets, σ-finite measurable sets, the notion of algebra of generators of a σ- algebra of parts. Construction of the Lebesgue Measure. Charatheodory Extension Theorem: characterising the unique extension of a finitely additive non-negative real valued function on an algebra of generators to a measure on the generated σ-algebra.

  • Measurable functions

    Definition. Approximation by measurable simple/step functions as well as by continuous functions.

  • Construction of the Lebesgue Integral

    Construction of the integral for measurable indicators (characteristic) functions as well as for measurable simple/step functions. Construction of the integral for a general measurable function. Properties of Lebesgue Integrable functions (additivity, multiplication by scalars, positivity, monotonicity). Definition and basic vectorial properties of the space of Lebesgue Integrable Functions L1.

  • Limit theorems (concerning point-wise convergence, almost everywhere convergence, and convergence in measure)

    Fatou Lemma. Monotone Convergence Theorem. Dominated Convergence Theorem.

  • Product Measures and the Fubini Theorem

  • Absolutely continuous measures and the Lebesgue-Radon-Nikodym Theorem

  • Definition and properties of general Lebesgue Spaces Lp and their embedding relations

If time permits then the following will also be covered:

  • The Sobolev Spaces H1 and their implications for the analysis of elliptic equations partial differential equations

  • Connection with probability theory, including random variables, cumulative distribution functions and martingales

Delivery and Assessment

The module is delivered in the form of lectures and seminars and assessed via an exam (60%) and coursework (40%).

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.

About the module

This module, aimed at the Level 5 student, specifically aims to develop students' knowledge, skills and understanding of the fundamentals of function spaces (infinite dimensional spaces) and linear operators and functionals defined on function spaces.

Functional analysis plays an important role in many areas of applied mathematics and is essential for the theory of Partial Differential Equations, Numerical Analysis, Probability theory and Theoretical Physics. Functional analysis originated from classical analysis and is formed by the study of infinite dimensional vector spaces and linear functions defined on these spaces. The theory of functional analysis was developed by some of the most famous mathematicians of the 20th century such as Hilbert, Schmidt, Riesz, Banach and von Neumann. Functional analysis can be characterised as a combination of infinite-dimensional linear algebra and classical analysis. Methods of functional analysis will allow us to analyse the properties of function spaces and to characterise solutions of integral and differential equations, arising in modelling of many biological and physical systems.

This module may optionally be taken by students on the MMath in Mathematics, or the MSci in Mathematical Biology or Mathematics and Physics degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must usually have achieved a pass mark in MA32001, or equivalent.

Indicative Content

  • Function Spaces

    • Normed spaces and inner product spaces (Banach and Hilbert spaces)
    • Lebesgue integral and Lebesgue spaces
    • Orthogonality in Hilbert spaces
    • Weak derivatives and Sobolev spaces
    • Notion of weak convergence in Function Spaces
  • Linear Operators and Linear Functionals

    • Definition of linear operators and linear functionals
    • Definition of a norm of a bounded linear operator
    • Riesz and Lax-Milgram theorems
    • Definition, main properties and examples of compact operators
    • Spectral theory for compact operators
  • Well-posedness results for Integral and Partial Differential Equations

    • Application of Lax-Milgram theorem and theory of compact operators to prove the well-posedness results

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (60%) and coursework (40%) consisting of homeworks and tests.

Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.

This is complemented with a project (25 credits) over the summer, which may take the form of either a review-based analysis of applications of mathematics to the financial sector or a report based on work experience gained in the financial sector.

Non-compulsory modules of up to 30 credits can be replaced with a selection of comparable modules from School of Science and Engineering or the School of Business.

Employers value the precision and reasoning of mathematics graduate which makes them some of the most high-sought and highly paid graduate in the UK. This programme will equip you with analytical and decision tools required for careers in fields such as finance, banking and business.

This programme is designed distinguish our graduates from an increasingly large graduate population within these sectors.

You should have at least a 2.2 Honours BSc (or equivalent) in Mathematics or another relevant mathematical discipline.

 EU and International qualifications


English Language Requirement

IELTS Overall 6.0
Listening 5.5
Reading 5.5
Writing 6.0
Speaking 5.5

 Equivalent grades from other test providers

 

English Language Programmes

We offer Pre-Sessional and Foundation Programme(s) throughout the year. These are designed to prepare you for university study in the UK when you have not yet met the language requirements for direct entry onto a degree programme.

 Discover our English Language Programmes

The fees you pay will depend on your fee status. Your fee status is determined by us using the information you provide on your application.

 Find out more about fee status

Fee statusFees for students starting 2017/18
Scottish and EU students £5,950 per year of study
Rest of UK students £5,950 per year of study
See our scholarships for UK/EU applicants
Overseas students (non-EU) £14,950 per year of study
See our scholarships for international applicants

You apply for this course via the UCAS Postgraduate (UKPASS) website which is free of charge. You can check the progress of your application online and you can also make multiple applications.

You'll need to upload relevant documents as part of your application. Please read the How to Apply page before you apply to find out about what you'll need.

  Degree Course Code
Apply NowMathematics for the Financial Sector MScP052301

Course Contact

Dr Dumitru Trucu
Science and Engineering
pgt-maths@dundee.ac.uk
+44 (0)1382 384462

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