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You can study this Mathematical Sciences MSc programme full-time or part-time. It offers students the opportunity to specialise in a broad range of areas across pure and applied mathematics, statistics and probability, and theoretical physics. Read more
You can study this Mathematical Sciences MSc programme full-time or part-time. It offers students the opportunity to specialise in a broad range of areas across pure and applied mathematics, statistics and probability, and theoretical physics.

The topics we cover include:

- advanced probability theory
- algebra
- asymptotic methods
- geometry
- mathematical biology
- partial differential equations
- quantum field theory
- singularity theory
- stochastic analysis
- standard model/string theory.

By completing the first semester you qualify for the PG certificate. By completing the second, you qualify for the PG Diploma. Then, by completing your dissertation, you qualify for the MSc.

Key Facts

REF 2014
92% of our research impact judged at outstanding and very considerable, 28% improvement in overall research at 4* and 3*.

Facilities
A dedicated student resource suite is available in the Department, with computer and reading rooms and a social area.

Why Department of Mathematical Sciences?

Range and depth of study options

We offer a very wide range of modules, from advanced algebra and geometry, to partial differential equations, probability theory, stochastic analysis, and mathematical physics. With these you can tailor your programme to specialise in one of these areas, or gain a broad understanding of several. This allows you to build up the required background for the project and dissertation modules, which offer the opportunity to undertake an in-depth study of a topic of your choice, supervised by a leading expert in the field.

Exceptional employability

At Liverpool, we listen to employers’ needs. Alongside key problem solving skills, employers require strong communication skills. These are integral to this programme. Graduates go on to research degrees, or become business and finance professionals, or to work in management training, information technology, further education or training (including teacher training) and scientific research and development.

Teaching quality

We are proud of our record on teaching quality, with five members of the Department having received the prestigious Sir Alastair Pilkington Award for Teaching. We care about each student and you will find the staff friendly and approachable.

Accessibility

We take students from a wide variety of educational backgrounds and we work hard to give everyone the opportunity to shine.

Supportive atmosphere

We provide high quality supervision and teaching, computer labs, and and you will benefit from the friendly and supportive atmosphere in the Department, as evidenced by student feedback available on our university website. A common room and kitchen for the exclusive use of the Department’s students, and a lively maths society help to foster a friendly and supportive environment.

Career prospects

The excellent University Careers Service is open to all postgraduates. Graduates of the MSc and PhD programmes move on to many different careers. Recent graduates have moved into fast track teacher programmes, jobs in finance (actuarial, banking, insurance), software development, drugs testing and defence work, as well as University postdoctoral or lecturing posts. The MSc programme is of course a natural route into doctoral study in Mathematics and related fields, both at Liverpool and elsewhere. Some of our PhD students move on to postdoctoral positions and to academic teaching jobs and jobs in research institutes, both in the UK and elsewhere.

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Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes. Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Read more
Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes: Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Postgraduate loans are also available to English and Welsh domiciled students. For more information on fees and funding please visit our website.

The MRes in Stochastic Processes: Theory and Application is delivered through optional modules for the taught element followed by a large research project that contributes to the field in an explicit way, rather than merely applying existing knowledge.

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

The Department’s research groups include:

Algebra and Topology Group
Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.

Analysis and Nonlinear Partial Differential Equations Group
Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.

Stochastic Analysis Group
Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multi-fractal and multi-scale systems, Infinite dimensional stochastic analysis and others.

Mathematical Methods in Biology and Life Sciences Group
Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing.

Key Features

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

Course Content

As a student on the MRes Stochastic Processes programme you will study a range of topics for the taught element including:

Stochastic Calculus based on Brownian Motion
Levy processes and more general jump processes
The advanced Black-Scholes theory
Theory and numerics of parabolic differential equations
Java programming

The Stochastic Processes: Theory and Application course consists of a taught part (60 credits) and a research project (120 credits). Students will have a personal supervisor for their research project from the start of their studies.

Research projects could be of a theoretical mathematical nature, or they could be more applied, for example in financial mathematics or actuarial studies. Some of the research projects will be of an interdisciplinary character in collaboration with some of Swansea's world class engineers. For such projects it is likely that EPSRC funding would be available.

Facilities

The Aubrey Truman Reading Room, located in the centre of the Department of Mathematics, houses the departmental library and computers for student use. It is a popular venue for students to work independently on the regular example sheets set by their lecturers, and to discuss Mathematics together.

Our main university library, Information Services and Systems (ISS), contains a notably extensive collection of Mathematics books.

Careers

The ability to think rationally and to process data clearly and accurately are highly valued by employers. Mathematics graduates earn on average 50% more than most other graduates. The most popular areas are the actuarial profession, the financial sector, IT, computer programming and systems administration, and opportunities within business and industry where employers need mathematicians for research and development, statistical analysis, marketing and sales.

Some of our students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where maths graduates will find plenty of career opportunities.

Research

The results of the Research Excellence Framework (REF) 2014 show that our research environment (how the Department supports research staff and students) and the impact of our research (its value to society) were both judged to be 100% world leading or internationally excellent.

All academic staff in Mathematics are active researchers and the department has a thriving research culture.

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This cutting edge MSc programme will equip you with the mathematical, financial and computational skills needed to quantify and manage risk effectively in today’s finance, investment and insurance industries. Read more
This cutting edge MSc programme will equip you with the mathematical, financial and computational skills needed to quantify and manage risk effectively in today’s finance, investment and insurance industries. Such companies use advanced probabilistic models at the core of their business. They recruit people with the right mathematical, statistical and programming skills and financial knowledge who can understand, develop and implement such models.

The course is also an excellent preparation for students wishing to embark upon research degree (PhD) in financial or actuarial mathematics. Working professionals who would like to move from their current field into finance or for finance professionals who would like to take their careers to the next level will also benefit greatly from this course.

You will gain a strong understanding of:

- applied probability theory, stochastic analysis and mathematical modelling
- computational methods
- financial derivatives
- risk management methodologies
- financial econometrics

The 12-month programme consists of seven taught compulsory modules plus one taught elective module, followed by a research project carried out over the summer period upon completion of Semester Two. The course is taught mainly by members of the Institute for Financial and Actuarial Mathematics which is part of the Department of Mathematical Sciences . Some relevant modules are taught by the Management School.

Why Department of Mathematical Sciences?

Range and depth of study options

We offer a very wide range of modules, from advanced algebra and geometry, to partial differential equations, probability theory, stochastic analysis, and mathematical physics. With these you can tailor your programme to specialise in one of these areas, or gain a broad understanding of several. This allows you to build up the required background for the project and dissertation modules, which offer the opportunity to undertake an in-depth study of a topic of your choice, supervised by a leading expert in the field.

Exceptional employability

At Liverpool, we listen to employers’ needs. Alongside key problem solving skills, employers require strong communication skills. These are integral to this programme. Graduates go on to research degrees, or become business and finance professionals, or to work in management training, information technology, further education or training (including teacher training) and scientific research and development.

Teaching quality

We are proud of our record on teaching quality, with five members of the Department having received the prestigious Sir Alastair Pilkington Award for Teaching. We care about each student and you will find the staff friendly and approachable.

Accessibility

We take students from a wide variety of educational backgrounds and we work hard to give everyone the opportunity to shine.

Supportive atmosphere

We provide high quality supervision and teaching, computer labs, and and you will benefit from the friendly and supportive atmosphere in the Department, as evidenced by student feedback available on our university website. A common room and kitchen for the exclusive use of the Department’s students, and a lively maths society help to foster a friendly and supportive environment.

Career prospects

The excellent University Careers Service is open to all postgraduates. Graduates of the MSc and PhD programmes move on to many different careers. Recent graduates have moved into fast track teacher programmes, jobs in finance (actuarial, banking, insurance), software development, drugs testing and defence work, as well as University postdoctoral or lecturing posts. The MSc programme is of course a natural route into doctoral study in Mathematics and related fields, both at Liverpool and elsewhere. Some of our PhD students move on to postdoctoral positions and to academic teaching jobs and jobs in research institutes, both in the UK and elsewhere.

Upon successful completion of the degree you will be ideally equipped to work in investment banks, pension or investment funds, hedge funds, consultancy and auditing firms or government regulators.

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Joining the Department as a postgraduate is certainly a good move. The Department maintains strong research in both pure and applied mathematics, as well as the traditional core of a mathematics department. Read more
Joining the Department as a postgraduate is certainly a good move. The Department maintains strong research in both pure and applied mathematics, as well as the traditional core of a mathematics department. What makes our Department different is the equally strong research in fluid mechanics, scientific computation and statistics.

The quality of research at the postgraduate level is reflected in the scholarly achievements of faculty members, many of whom are recognized as leading authorities in their fields. Research programs often involve collaboration with scholars at an international level, especially in the European, North American and Chinese universities. Renowned academics also take part in the Department's regular colloquia and seminars. The faculty comprises several groups: Pure Mathematics, Applied Mathematics, Probability and Statistics.

Mathematics permeates almost every discipline of science and technology. We believe our comprehensive approach enables inspiring interaction among different faculty members and helps generate new mathematical tools to meet the scientific and technological challenges facing our fast-changing world.

The MPhil program seeks to strengthen students' general background in mathematics and mathematical sciences, and to expose students to the environment and scope of mathematical research. Submission and successful defense of a thesis based on original research are required.

Research Foci

Algebra and Number Theory
The theory of Lie groups, Lie algebras and their representations play an important role in many of the recent development in mathematics and in the interaction of mathematics with physics. Our research includes representation theory of reductive groups, Kac-Moody algebras, quantum groups, and conformal field theory. Number theory has a long and distinguished history, and the concepts and problems relating to the theory have been instrumental in the foundation of a large part of mathematics. Number theory has flourished in recent years, as made evident by the proof of Fermat's Last Theorem. Our research specializes in automorphic forms.

Analysis and Differential Equations
The analysis of real and complex functions plays a fundamental role in mathematics. This is a classical yet still vibrant subject that has a wide range of applications. Differential equations are used to describe many scientific, engineering and economic problems. The theoretical and numerical study of such equations is crucial in understanding and solving problems. Our research areas include complex analysis, exponential asymptotics, functional analysis, nonlinear equations and dynamical systems, and integrable systems.

Geometry and Topology
Geometry and topology provide an essential language describing all kinds of structures in Nature. The subject has been vastly enriched by close interaction with other mathematical fields and with fields of science such as physics, astronomy and mechanics. The result has led to great advances in the subject, as highlighted by the proof of the Poincaré conjecture. Active research areas in the Department include algebraic geometry, differential geometry, low-dimensional topology, equivariant topology, combinatorial topology, and geometrical structures in mathematical physics.

Numerical Analysis
The focus is on the development of advance algorithms and efficient computational schemes. Current research areas include: parallel algorithms, heterogeneous network computing, graph theory, image processing, computational fluid dynamics, singular problems, adaptive grid method, rarefied flow simulations.

Applied Sciences
The applications of mathematics to interdisciplinary science areas include: material science, multiscale modeling, mutliphase flows, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, astrophysics and space science.

Probability and Statistics
Statistics, the science of collecting, analyzing, interpreting, and presenting data, is an essential tool in a wide variety of academic disciplines as well as for business, government, medicine and industry. Our research is conducted in four categories. Time Series and Dependent Data: inference from nonstationarity, nonlinearity, long-memory behavior, and continuous time models. Resampling Methodology: block bootstrap, bootstrap for censored data, and Edgeworth and saddle point approximations. Stochastic Processes and Stochastic Analysis: filtering, diffusion and Markov processes, and stochastic approximation and control. Survival Analysis: survival function and errors in variables for general linear models. Probability current research includes limit theory.

Financial Mathematics
This is one of the fastest growing research fields in applied mathematics. International banking and financial firms around the globe are hiring science PhDs who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. The trend has been accelerating in recent years on numerous fronts, driven both by substantial theoretical advances as well as by a practical need in the industry to develop effective methods to price and hedge increasingly complex financial instruments. Current research areas include pricing models for exotic options, the development of pricing algorithms for complex financial derivatives, credit derivatives, risk management, stochastic analysis of interest rates and related models.

Facilities

The Department enjoys a range of up-to-date facilities and equipment for teaching and research purposes. It has two computer laboratories and a Math Support Center equipped with 100 desktop computers for undergraduate and postgraduate students. The Department also provides an electronic homework system and a storage cloud system to enhance teaching and learning.

To assist computations that require a large amount of processing power in the research area of scientific computation, a High Performance Computing (HPC) laboratory equipped with more than 200 high-speed workstations and servers has been set up. With advanced parallel computing technologies, these powerful computers are capable of delivering 17.2 TFLOPS processing power to solve computationally intensive problems in our innovative research projects. Such equipment helps our faculty and postgraduate students to stay at the forefront of their fields. Research projects in areas such as astrophysics, computational fluid dynamics, financial mathematics, mathematical modeling and simulation in materials science, molecular simulation, numerical ocean modeling, numerical weather prediction and numerical methods for micromagnetics simulations all benefit from our powerful computing facilities.

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The MSc Financial Mathematics draws on tools from applied mathematics, computer science, statistics and economic theory to prepare you for roles in which you will combine in-depth knowledge of financial products and risk with sophisticated technical and programming skills. Read more
The MSc Financial Mathematics draws on tools from applied mathematics, computer science, statistics and economic theory to prepare you for roles in which you will combine in-depth knowledge of financial products and risk with sophisticated technical and programming skills.

You will acquire solid knowledge of probability theory and stochastic processes, numerical analysis and programming languages, asset pricing theory and risk analysis, with special emphasis on valuation and risk management.

Typical career paths of graduates from our MSc Financial Mathematics include research positions (in both financial and academic institutions), or roles involving the development, management and improvement of derivatives models using advanced programming languages, and model validation such as Equity/Equity Derivatives Quant, Quantitative Financial Engineer, or Quantitative Risk Analyst.

This programme is rigorous with respect to the mathematics but also places great emphasis on linking theory with real world developments. You will often be exposed to the teaching of real world practitioners from the City of London.

Cass's proximity to the City of London, and our close links to many of its institutions, will help you to access outstanding networking and career opportunities.

Visit the website: http://www.cass.city.ac.uk/courses/masters/courses/financial-mathematics

Course detail

There are two Induction Weeks The Financial Mathematics course starts with two compulsory induction weeks, focused on:

• an introduction to careers in finance and the opportunity to speak to representatives from over 75 companies during a number of different industry specific fairs.

• a reminder course of advanced financial mathematics, statistics and basic computing which forms a prerequisite of the core modules in term 1.

Attendance is mandatory.

Format

To satisfy the requirements of the degree course students must complete:

• eight core courses (15 credits each)
and
• two additional core modules plus three electives (10 credits each)
or
• three electives (10 credits each) and an Applied Research Project (20 credits)
or
• one elective (10 credits) and a Business Research Project (40 credits)

Assessment

Assessment of modules on the MSc in Financial Mathematics, in most cases, is by means of coursework and unseen examination. Coursework may consist of standard essays, individual and group presentations, group reports, classwork, unseen tests and problem sets. Please note that any group work may include an element of peer assessment.

Career opportunities

Many graduates from the MSc in Financial Mathematics progress to one of two fields:

• derivatives valuation and portfolio management within investment houses
• research departments within banks and consultancy firms

Some examples of where graduates from the MSc in Financial Mathematics class of 2014 are working are:

• Bank of China - Management Trainee
• Santander - Credit Fraud Analyst
• Renaissance Re - Analyst
• Deutsche Bank - Bookrunner

How to apply

Apply here: http://www.city.ac.uk/study/postgraduate/applying-to-city

Funding

For information on funding, please follow this link: http://www.city.ac.uk/study/postgraduate/funding-and-financial-support

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This programme provides intensive training in statistics applicable to the social sciences, econometrics and finance. The aim of the programme is to foster an interest in theoretical and applied statistics and equip you for work as a professional statistician. Read more

About the MSc programme

This programme provides intensive training in statistics applicable to the social sciences, econometrics and finance. The aim of the programme is to foster an interest in theoretical and applied statistics and equip you for work as a professional statistician. You will learn how to analyse and critically interpret data, build statistical models of real situations, and use programming tools and statistical software packages.

The compulsory course in Statistical Inference: Principles, Methods and Computation will provide you with comprehensive coverage of fundamental aspects of probability and statistics methods and principles. This course provides the foundations for the optional courses on more advanced statistical modelling, computational methods, statistical computing and advanced probability theory. Options also include specialist courses from the Departments of Methodology, Management, Mathematics, Economics and Social Policy. Students on the taught master’s programme will take optional courses to the value of three units, while those on the research track will substitute one unit with a dissertation, making the research track a 12 month programme.

Graduates of the programme are awarded Graduate Statistician (GradStat) status by the Royal Statistical Society.

Graduate destinations

Students on this programme have excellent career prospects. Former students have taken up positions in consulting firms, banks and in the public sector. Many go on to take higher degrees. Graduates of the MSc are awarded Graduate Statistician (GradStat) status by the Royal Statistical Society.

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The School of Mathematics and The Manchester Business School at The University of Manchester have combined their academic strength and practical expertise to deliver this MSc in Mathematical Finance (UK 1 year), ensuring that students can experience both the Mathematical and Economic perspective of the subject. Read more
The School of Mathematics and The Manchester Business School at The University of Manchester have combined their academic strength and practical expertise to deliver this MSc in Mathematical Finance (UK 1 year), ensuring that students can experience both the Mathematical and Economic perspective of the subject.

This is also supported by invited lectures from senior staff members of leading financial institutions and outstanding mathematicians who are internationally recognised for contributions to Mathematical Finance. Past lectures include:
•Professor M. Schweizer (ETH Zurich and Swiss Finance Institute) An overview of quadratic hedging and related topics
•Professor H. Follmer (Humboldt University of Berlin) Monetary valuation of cash flows under Knightian uncertainty
•Professor M. H. A. Davis (Imperial College London) Contagion models in credit risk

The course provides students with advanced knowledge and understanding of the main theoretical and applied concepts in Mathematical Finance delivered from a genuinely international and multi-cultural perspective with a current issues approach to teaching. The focus is on mathematical theory and modelling, drawing from the disciplines of probability theory, scientific computing and partial differential equations to derive relations between asset prices and interest rates, and to develop models for pricing, risk management and financial product development.

The finance industry demands recruits with strong quantitative skills and the course is intended to prepare students for careers in this area. The course provides training for those who seek a career in the finance industry specialising in derivative securities, investment, risk management and hedge funds. It also provides research skills for those who subsequently wish to pursue research and/or an academic career (e.g. university lecturer) or continue the study at doctoral level, particularly those wishing to pursue further/advanced studies in Mathematical Finance.

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The MSc Financial Mathematics programme enables graduates and professionals with a strong mathematics background to research, develop and apply quantitative and computational techniques to finance. Read more
The MSc Financial Mathematics programme enables graduates and professionals with a strong mathematics background to research, develop and apply quantitative and computational techniques to finance. It covers topics from classical options pricing to post-crisis investment and risk management. The Department of Mathematics has a superb reputation for research-led teaching and strong links to industry and our graduates are highly sought after.

Key benefits

- A rigorous approach to quantitative finance taught entirely by the Department of Mathematics.

- End-to-end coverage of the skills needed for working in the financial, actuarial or related industry: probability theory, optimisation, statistics and computer implementation.

- Unrivalled facilities, including access to live market data in our Bloomberg Data laboratory.

- A stone’s throw from the City of London's financial centre

- Full or part time study (most lectures given late afternoons)

Visit the website: http://www.kcl.ac.uk/study/postgraduate/taught-courses/financial-mathematics-msc.aspx

Course detail

- Description -

Financial mathematics plays a crucial role in all sectors of financial markets including fixed income, credit derivatives, pensions, insurances, energy and even bets on the weather. The application of mathematics has had a profound effect upon finance and has allowed the creation of entirely new markets for financial products.

The financial mathematics programme at King’s is unique in its emphasis upon mathematical rigour. It encompasses all the skills required for successful risk management, trading and research in quantitative finance: probability, statistics, optimisation, computing and financial markets. Our outstanding teaching is matched by outstanding facilities for the study and research of financial markets.

- Course purpose -

This programme is suitable for students or professionals with a strong mathematical background. It covers the principles and techniques of quantitative finance to prepare students for advanced work in the financial sector or research in mathematical finance.

- Course format and assessment -

At least eight taught modules assessed by written examinations and one individual project. Two prizes are normally awarded each year for best overall performance in the MSc in Financial Mathematics.

Career prospects

Our graduates are highly sought after by investment banks, corporate risk management units, insurance companies, fund management institutions, financial regulatory bodies, brokerage firms, and trading companies. Recent employers of our graduates include, Capital Investment, Credit Suisse, European Bank for Reconstruction & Development, Fitch Ratings, HSBC and Morgan & Stanley. Some graduates have pursued research degrees in financial mathematics.

How to apply: http://www.kcl.ac.uk/study/postgraduate/apply/taught-courses.aspx

About Postgraduate Study at King’s College London:

To study for a postgraduate degree at King’s College London is to study at the city’s most central university and at one of the top 20 universities worldwide (2015/16 QS World Rankings). Graduates will benefit from close connections with the UK’s professional, political, legal, commercial, scientific and cultural life, while the excellent reputation of our MA and MRes programmes ensures our postgraduate alumni are highly sought after by some of the world’s most prestigious employers. We provide graduates with skills that are highly valued in business, government, academia and the professions.

Scholarships & Funding:

All current PGT offer-holders and new PGT applicants are welcome to apply for the scholarships. For more information and to learn how to apply visit: http://www.kcl.ac.uk/study/pg/funding/sources

Free language tuition with the Modern Language Centre:

If you are studying for any postgraduate taught degree at King’s you can take a module from a choice of over 25 languages without any additional cost. Visit: http://www.kcl.ac.uk/mlc

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A degree highly respected by quantitative analysts and their employers. About the course. -A highly technical programme for those with strong mathematical skills. Read more
A degree highly respected by quantitative analysts and their employers.

About the course:
-A highly technical programme for those with strong mathematical skills
-Gain knowledge of derivatives pricing tools and methods, as well as the use of programming languages like C++ and VBA
-Designed with the support of industry practitioners to equip students with the skills and knowledge needed to succeed
-Graduates are able to make an early contribution through the unique combination of hands-on, practical skills and the necessary underlying finance theory
-Benefit from the combined expertise of both the ICMA Centre and the Department of Mathematics

COURSE OVERVIEW

The ICMA Centre’s financial engineering degree is highly respected by quantitative analysts and their employers. The credit crunch and subsequent events have emphasised the need to develop better pricing and better hedging models for all complex products. The practical and quantitative skills that you will develop on the programme will equip you to meet this challenge.

Our compulsory modules provide a firm grounding in probability theory, stochastic calculus, derivatives pricing, quantitative and numerical methods, structuring products, volatility analysis, and the modelling of credit, equity, foreign exchange and interest rate derivatives. We also provide a thorough training in C++ and other programming tools.

Optional modules will allow you to focus on risk analysis, portfolio management, designing trading strategies or econometric analysis. This newly structured degree aims to further enhance the strong reputation of its precursor – the MSc in Financial Engineering and Quantitative Analysis, which was established back in 1999. A good background in mathematics is required for acceptance to this programme.

EMPLOYABILITY

Many of our financial engineering graduates are now working as Quants in large London banks and other financial institutions. Others have pursued PhDs and have successful academic careers. Financial instruments are becoming ever more sophisticated, so graduates that understand complex modelling techniques are always in great demand. The high quantitative content of this programme opens many doors to a wide range of careers. You could structure and develop new debt or equity solutions to meet clients funding and hedging needs, or you could become a proprietary trader in exotic derivatives, or a software specialist or a quantitative analyst supporting the traders.

There are excellent opportunities on the buy-side, with hedge funds and investment institutions, as well as in investment banking and in software analytics. Opportunities in quantitative research, or with a rating agency, are among the many other attractive alternatives. Outside of mainstream banking and investment, you might also consider firms involved in commodity and energy trading, or the treasury divisions of leading multinationals and management consultancies.

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Programme structure. The programme offers four "core" modules, taken by all students, along with a variety of elective modules from which students can pick and choose. Read more
Programme structure
The programme offers four "core" modules, taken by all students, along with a variety of elective modules from which students can pick and choose. There are examinations and coursework in eight modules altogether, including the four core modules. Additionally, all students complete a dissertation.

Core modules
0.Probability and stochastics. This course provides the basics of the probabilistic ideas and mathematical language needed to fully appreciate the modern mathematical theory of finance and its applications. Topics include: measurable spaces, sigma-algebras, filtrations, probability spaces, martingales, continuous-time stochastic processes, Poisson processes, Brownian motion, stochastic integration, Ito calculus, log-normal processes, stochastic differential equations, the Ornstein-Uhlenbeck process.


0.Financial markets. This course is designed to cover basic ideas about financial markets, including market terminology and conventions. Topics include: theory of interest, present value, future value, fixed-income securities, term structure of interest rates, elements of probability theory, mean-variance portfolio theory, the Markowitz model, capital asset pricing model (CAPM), portfolio performance, risk and utility, portfolio choice theorem, risk-neutral pricing, derivatives pricing theory, Cox-Ross-Rubinstein formula for option pricing.


0.Option pricing theory. The key ideas leading to the valuation of options and other important derivatives will be introduced. Topics include: risk-free asset, risky assets, single-period binomial model, option pricing on binomial trees, dynamical equations for price processes in continuous time, Radon-Nikodym process, equivalent martingale measures, Girsanov's theorem, change of measure, martingale representation theorem, self-financing strategy, market completeness, hedge portfolios, replication strategy, option pricing, Black-Scholes formula.


0.Financial computing I. The idea of this course is to enable students to learn how the theory of pricing and hedging can be implemented numerically. Topics include: (i) The Unix/Linux environment, C/C++ programming: types, decisions, loops, functions, arrays, pointers, strings, files, dynamic memory, preprocessor; (ii) data structures: lists and trees; (iii) introduction to parallel (multi-core, shared memory) computing: open MP constructs; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.


0.Interest rate theory. An in-depth analysis of interest-rate modelling and derivative pricing will be presented. Topics include: interest rate markets, discount bonds, the short rate, forward rates, swap rates, yields, the Vasicek model, the Hull-White model, the Heath-Jarrow-Merton formalism, the market model, bond option pricing in the Vasicek model, the positive interest framework, option and swaption pricing in the Flesaker-Hughston model.

Elective modules

0.Portfolio theory. The general theory of financial portfolio based on utility theory will be introduced in this module. Topics include: utility functions, risk aversion, the St Petersburg paradox, convex dual functions, dynamic asset pricing, expectation, forecast and valuation, portfolio optimisation under budget constraints, wealth consumption, growth versus income.


0.Information in finance with application to credit risk management. An innovative and intuitive approach to asset pricing, based on the modelling of the flow of information in financial markets, will be introduced in this module. Topics include: information-based asset pricing – a new paradigm for financial risk management; modelling frameworks for cash flows and market information; applications to credit risk modelling, defaultable discount bond dynamics, the pricing and hedging of credit-risky derivatives such as credit default swaps (CDS), asset dependencies and correlation modelling, and the origin of stochastic volatility.

0.Mathematical theory of dynamic asset pricing. Financial modelling and risk management involve not only the valuation and hedging of various assets and their positions, but also the problem of asset allocation. The traditional approach of risk-neutral valuation treats the problem of valuation and hedging, but is limited when it comes to understanding asset returns and the behaviour of asset prices in the real-world 'physical' probability measure. The pricing kernel approach, however, treats these different aspects of financial modelling in a unified and coherent manner. This module introduces in detail the techniques of pricing kernel methodologies, and its applications to interest-rete modelling, foreign exchange market, and inflation-linked products. Another application concerns the modelling of financial markets where prices admit jumps. In this case, the relation between risk, risk aversion, and return is obscured in traditional approaches, but is made clear in the pricing kernel method. The module also covers the introduction to the theory of Lévy processes for jumps and its applications to dynamic asset pricing in the modern setting.

0.Financial computing II: High performance computing. In this parallel-computing module students will learn how to harness the power of a multi-core computer and Open MP to speed up a task by running it in parallel. Topics include: shared and distributed memory concepts; Message Passing and introduction to MPI constructs; communications models, applications and pitfalls; open MP within MPI; introduction to Graphics Processors; GPU computing and the CUDA programming model; CUDA within MPI; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.


0.Risk measures, preference and portfolio choice. The idea of this module is to enable students to learn a variety of statistical techniques that will be useful in various practical applications in investment banks and hedge funds. Topics include: probability and statistical models, models for return distributions, financial time series, stationary processes, estimation of AR processes, portfolio regression, least square estimation, value-at-risk, coherent risk measures, GARCH models, non-parametric regression and splines.

Research project

Towards the end of the Spring Term, students will choose a topic to work on, which will lead to the preparation of an MSc dissertation. This can be thought of as a mini research project. The project supervisor will usually be a member of the financial mathematics group. In some cases the project may be overseen by an external supervisor based at a financial institution or another academic institution.

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The programme provides graduates with strong mathematical skills, the necessary computational techniques and finance background relevant to subsequent employment in a sector of finance such as investment banks, hedge funds, insurance companies and the finance departments of large corporations where mathematics plays a key role. Read more
The programme provides graduates with strong mathematical skills, the necessary computational techniques and finance background relevant to subsequent employment in a sector of finance such as investment banks, hedge funds, insurance companies and the finance departments of large corporations where mathematics plays a key role.

The depth of the mathematics taught should enable graduates to pursue research careers in stochastic analysis, financial mathematics or other relevant areas.

The period October to June is devoted to lectures, tutorials and practical sessions comprising the core and optional modules. This is followed by a period of about 14 weeks devoted to an individual project.

Core study areas include measure theory and martingales, stochastic models in finance, stochastic calculus and theory of stochastic pricing and a research project.

Optional study areas include programming and numerical methods, regular and chaotic dynamics, financial economics, functional analysis, elements of PDEs, static and dynamic optimisation, asset management and derivatives, and corporate finance

See the website http://www.lboro.ac.uk/study/postgraduate/programmes/departments/mathematics/mathematical-finance/

Programme modules

Semester 1:
Compulsory Modules
- Introduction to Measure Theory and Martingales
- Stochastic Models in Finance

Optional Modules (choose two)
- Programming and Numerical Methods
- Regular and Chaotic Dynamics
- Financial Economics

Semester 2:
Compulsory Modules
- Stochastic Calculus and Theory of Stochastic Pricing
- Research Project

Optional Modules (choose three)
- Functional Analysis
- Elements of PDEs
- Static and Dynamic Optimisation
- Either Asset Management and Derivatives or Corporate Finance

Assessment

A combination of written examinations, reports, individual and group projects, and verbal presentations.

Careers and further study

This programme may lead to a wide range of employment within industry, the financial sectors, and research establishments. It may also provide an ideal background for postgraduate research in Stochastic Analysis, Probability Theory, Mathematical Finance and other relevant areas.

Scholarships and sponsorships

A number of part-fee studentships may be available to appropriately qualified international students.

Why choose mathematics at Loughborough?

Mathematics at Loughborough has a long history of innovation in teaching, and we have a firm research base with strengths in both pure and applied mathematics as well as mathematics education.

The Department comprises more than 34 academic staff, whose work is complemented and underpinned by senior visiting academics, research associates and a large support team.

The programmes on offer reflect our acknowledged strengths in pure and applied research in mathematics, and in some cases represent established collaborative training ventures with industrial partners.

- Mathematics Education Centre (MEC)
The Mathematics Education Centre (MEC) at Loughborough University is an internationally renowned centre of research, teaching, learning and support. It is a key player in many high-profile national initiatives.
With a growing number of academic staff and research students, the MEC provides a vibrant, supportive community with a wealth of experience upon which to draw.
We encourage inquiries from students who are interested in engaging in research into aspects of learning and teaching mathematics at Masters, PhD and Post Doc levels. Career prospects With 100% of our graduates in employment and/or further study six months after graduating, career prospects are excellent. Graduates go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

- Career prospects
With 100% of our graduates in employment and/or further study six months after graduating, career prospects are excellent. Graduates
go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

Find out how to apply here http://www.lboro.ac.uk/study/postgraduate/programmes/departments/mathematics/mathematical-finance/

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This programme gives you a flexible syllabus to suit the demands of employers that use modern financial tools and optimization techniques in areas such as the financial sector and energy markets. Read more

Programme description

This programme gives you a flexible syllabus to suit the demands of employers that use modern financial tools and optimization techniques in areas such as the financial sector and energy markets.

We will give you sound knowledge in financial derivative pricing, portfolio optimization and financial risk management.

We will also provide you with the skills to solve some of today’s financial problems, which have themselves been caused by modern financial instruments. This expertise includes modern probability theory, applied statistics, stochastic analysis and optimization.

Adding depth to your learning, our work placement programme puts you at the heart of financial organisations such as Aberdeen Asset Management, Barrie & Hibbert and Lloyds Banking Group.

Programme structure

This programme involves two taught semesters of compulsory and option courses, followed by a dissertation project.

Compulsory courses:

Discrete-Time Finance
Finance, Risk and Uncertainty
Fundamentals of Optimization
Optimization Methods in Finance
Research-Linked Topics
Risk-Neutral Asset Pricing
Simulation
Stochastic Analysis in Finance I
Stochastic Analysis in Finance II

Option courses:

Advanced Time Series Econometrics
Combinatorial Optimization
Credit Scoring
Fundamentals of Operational Research
Financial Risk Management
Computing for Operational Research and Finance
Large Scale Optimization for Data Science
Microeconomics 2
Nonlinear Optimization
Numerical Partial Differential Equations
Parallel Numerical Algorithms
Programming Skills
Risk Analysis
Stochastic Modelling
Stochastic Optimization

Career opportunities

Graduates have gone on to work in major financial institutions or to continue their studies by joining PhD programmes.

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The Epidemiology and Statistics module will help you become familiar with various study designs that are used in epidemiology. The module will cover the rationale for using each study design as well as the types of results produced. Read more
The Epidemiology and Statistics module will help you become familiar with various study designs that are used in epidemiology. The module will cover the rationale for using each study design as well as the types of results produced.

You will explore key statistical principles and techniques such as hypothesis testing and estimation including how to use these techniques to analyse and interpret epidemiological studies.

Module content

The module consists of two complementary parts:
Epidemiology
-Populations and considering illness in populations.
-Use of routinely available data in epidemiology.
-Measures of disease.
-Direct and indirect standardisation, years of life lost, life expectancy and DALYS.
-Absolute and relative measures of risk.
-Causality, bias and confounding.
-Study design including cross-sectional, case control, cohort, clinical trials, ecological studies.

Statistics
-The different types of data.
-Measures of central tendency and dispersion.
-Probability theory and statistical distributions.
-Point estimation and confidence intervals.
-Principles of hypothesis testing and sample size calculation.
-Linear models.
-Non-parametric tests.

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High-level training in statistics and the modelling of random processes for applications in science, business or health care. Read more
High-level training in statistics and the modelling of random processes for applications in science, business or health care.

For many complex systems in nature and society, stochastics can be used to efficiently describe the randomness present in all these systems, thereby giving the data greater explanatory and predictive power. Examples include statistical mechanics, financial markets, mobile phone networks, and operations research problems. The Master’s specialisation in Applied Stochastics will train you to become a mathematician that can help both scientists and businessmen make better decisions, conclusions and predictions. You’ll be able to bring clarity to the accumulating information overload they receive.

The members of the Applied Stochastics group have ample experience with the pure mathematical side of stochastics. This area provides powerful techniques in functional analysis, partial differential equations, geometry of metric spaces and number theory, for example. The group also often gives advice to both their academic colleagues, and organisations outside of academia. They will therefore not only be able to teach you the theoretical basis you need to solve real world stochastics problems, but also to help you develop the communications skills and professional expertise to cooperate with people from outside of mathematics.

See the website http://www.ru.nl/masters/mathematics/stochastics

Why study Applied Stochastics at Radboud University?

- This specialisation focuses both on theoretical and applied topics. It’s your choice whether you want to specialise in pure theoretical research or perform an internship in a company setting.
- Mathematicians at Radboud University are expanding their knowledge of random graphs and networks, which can be applied in the ever-growing fields of distribution systems, mobile phone networks and social networks.
- In a unique and interesting collaboration with Radboudumc, stochastics students can help researchers at the hospital with very challenging statistical questions.
- Because the Netherlands is known for its expertise in the field of stochastics, it offers a great atmosphere to study this field. And with the existence of the Mastermath programme, you can follow the best mathematics courses in the country, regardless of the university that offers them.
- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that you’ll get plenty of one-on-one time with your thesis supervisor at Radboud University .
- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating.

Career prospects

Master's programme in Mathematics

Mathematicians are needed in all industries, including the banking, technology and service industries, to name a few. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of analytical and problem-solving skills.

Job positions

The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad and is the reason why many graduates of a Master’s in Mathematics find work very quickly.
Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- Consultant
- ICT developer / software developer
- Policy maker
- Analyst

PhD positions

Radboud University annually has a few PhD positions for graduates of a Master’s in Mathematics. A substantial part of our students attain PhD positions, not just at Radboud University, but at universities all over the world.

Our research in this field

The research of members of the Applied Stochastics Department, focuses on combinatorics, (quantum) probability and mathematical statistics. Below, a small sample of the research our members pursue.

Eric Cator’s research has two main themes, probability and statistics.
1. In probability, he works on interacting particles systems, random polymers and last passage percolation. He has also recently begun working on epidemic models on finite graphs.
2. In statistics, he works on problems arising in mathematical statistics, for example in deconvolution problems, the CAR assumption and more recently on the local minimax property of least squares estimators.

Cator also works on more applied problems, usually in collaboration with people from outside statistics, for example on case reserving for insurance companies or airplane maintenance. He has a history of changing subjects: “I like to work on any problem that takes my fancy, so this description might be outdated very quickly!”

Hans Maassen researches quantum probability or non-commutative probability, which concerns a generalisation of probability theory that is broad enough to contain quantum mechanics. He takes part in the Geometry and Quantum Theory (GQT) research cluster of connected universities in the Netherlands. In collaboration with Burkhard Kümmerer he is also developing the theory of quantum Markov chains, their asymptotic completeness and ergodic theory, with applications to quantum optics. Their focal point is shifting towards quantum information and control theory, an area which is rapidly becoming relevant to experimental physicists.

Ross Kang conducts research in probabilistic and extremal combinatorics, with emphasis on graphs (which abstractly represent networks). He works in random graph theory (the study of stochastic models of networks) and often uses the probabilistic method. This involves applying probabilistic tools to shed light on extremes of large-scale behaviour in graphs and other combinatorial structures. He has focused a lot on graph colouring, an old and popular subject made famous by the Four Colour Theorem (erstwhile Conjecture).

See the website http://www.ru.nl/masters/mathematics/stochastics

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Programme structure. The programme offers five "core" modules, taken by all candidates, along with a variety of elective modules from which students can pick and choose. Read more
Programme structure

The programme offers five "core" modules, taken by all candidates, along with a variety of elective modules from which students can pick and choose. There are lectures, examinations and coursework in eight modules altogether, including the five core modules. Additionally, all students complete an individual research project on a selected topic in financial mathematics, leading to the submission of a dissertation.

Core modules

Probability and stochastics. This course provides the basics of the probabilistic ideas and mathematical language needed to fully appreciate the modern mathematical theory of finance and its applications. Topics include: measurable spaces, sigma-algebras, filtrations, probability spaces, martingales, continuous-time stochastic processes, Poisson processes, Brownian motion, stochastic integration, Ito calculus, log-normal processes, stochastic differential equations, the Ornstein-Uhlenbeck process.

Financial markets. This course is designed to cover basic ideas about financial markets, including market terminology and conventions. Topics include: theory of interest, present value, future value, fixed-income securities, term structure of interest rates, elements of probability theory, mean-variance portfolio theory, the Markowitz model, capital asset pricing model (CAPM), portfolio performance, risk and utility, portfolio choice theorem, risk-neutral pricing, derivatives pricing theory, Cox-Ross-Rubinstein formula for option pricing.

Option pricing theory. The key ideas leading to the valuation of options and other important derivatives will be introduced. Topics include: risk-free asset, risky assets, single-period binomial model, option pricing on binomial trees, dynamical equations for price processes in continuous time, Radon-Nikodym process, equivalent martingale measures, Girsanov's theorem, change of measure, martingale representation theorem, self-financing strategy, market completeness, hedge portfolios, replication strategy, option pricing, Black-Scholes formula.


Interest rate theory. An in-depth analysis of interest-rate modelling and derivative pricing will be presented. Topics include: interest rate markets, discount bonds, the short rate, forward rates, swap rates, yields, the Vasicek model, the Hull-White model, the Heath-Jarrow-Merton formalism, the market model, bond option pricing in the Vasicek model, the positive interest framework, option and swaption pricing in the Flesaker-Hughston model.

Financial computing I. The idea of this course is to enable students to learn how the theory of pricing and hedging can be implemented numerically. Topics include: (i) The Unix/Linux environment, C/C++ programming: types, decisions, loops, functions, arrays, pointers, strings, files, dynamic memory, preprocessor; (ii) data structures: lists and trees; (iii) introduction to parallel (multi-core, shared memory) computing: open MP constructs; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.

Elective modules

Portfolio theory. The general theory of financial portfolio based on utility theory will be introduced in this module. Topics include: utility functions, risk aversion, the St Petersburg paradox, convex dual functions, dynamic asset pricing, expectation, forecast and valuation, portfolio optimisation under budget constraints, wealth consumption, growth versus income.

Information in finance with application to credit risk management. An innovative and intuitive approach to asset pricing, based on the modelling of the flow of information in financial markets, will be introduced in this module. Topics include: information-based asset pricing – a new paradigm for financial risk management; modelling frameworks for cash flows and market information; applications to credit risk modelling, defaultable discount bond dynamics, the pricing and hedging of credit-risky derivatives such as credit default swaps (CDS), asset dependencies and correlation modelling, and the origin of stochastic volatility.


Mathematical theory of dynamic asset pricing. Financial modelling and risk management involve not only the valuation and hedging of various assets and their positions, but also the problem of asset allocation. The traditional approach of risk-neutral valuation treats the problem of valuation and hedging, but is limited when it comes to understanding asset returns and the behaviour of asset prices in the real-world 'physical' probability measure. The pricing kernel approach, however, treats these different aspects of financial modelling in a unified and coherent manner. This module introduces in detail the techniques of pricing kernel methodologies, and its applications to interest-rete modelling, foreign exchange market, and inflation-linked products. Another application concerns the modelling of financial markets where prices admit jumps. In this case, the relation between risk, risk aversion, and return is obscured in traditional approaches, but is made clear in the pricing kernel method. The module also covers the introduction to the theory of Lévy processes for jumps and its applications to dynamic asset pricing in the modern setting.


Financial computing II: High performance computing. In this parallel-computing module students will learn how to harness the power of a multi-core computer and Open MP to speed up a task by running it in parallel. Topics include: shared and distributed memory concepts; Message Passing and introduction to MPI constructs; communications models, applications and pitfalls; open MP within MPI; introduction to Graphics Processors; GPU computing and the CUDA programming model; CUDA within MPI; applications to matrix arithmetic, finite difference methods, Monte Carlo option pricing.

Risk measures, preference and portfolio choice. The idea of this module is to enable students to learn a variety of statistical techniques that will be useful in various practical applications in investment banks and hedge funds. Topics include: probability and statistical models, models for return distributions, financial time series, stationary processes, estimation of AR processes, portfolio regression, least square estimation, value-at-risk, coherent risk measures, GARCH models, non-parametric regression and splines.

Research project

Towards the end of the Spring Term, students will choose a topic for an individual research project, which will lead to the preparation and submission of an MSc dissertation. The project supervisor will usually be a member of the Brunel financial mathematics group. In some cases the project may be overseen by an external supervisor based at a financial institution or another academic institution.

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