Masters Degrees in Computational Mathematics

Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Mathematics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).

The MSc Mathematics course has been designed for students who wish to build on their BSc, extending their range of mathematics expertise across a broader spread of topics, and demonstrating their literature research skills through an extended dissertation.

Such a qualification will mark graduates out as having a broader and deeper understanding of mathematics, and the skills required to pursue a significant project with a high level of independence, presenting their results in a written report. This will give MSc Mathematics graduates an edge in the ever more competitive jobs market.

On the Mathematics course you will study different elements of mathematics in a broad sense - including mathematical elements of computing if desired - in addition to developing your research, project management, and written communication skills through a project you will undertake. As a student of MSc in Mathematics, you will be fully supported to ensure that your project further develops an excellent foundation for your future career plans.

Modules

Modules on the MSc Mathematics include:

• Algebraic coding theory

• Biomathematics

• Black-Scholes theory

• Data science

• Differential geometry

• Fourier analysis

• Ito calculus

• Lie theory

• Numerical analysis

• Partial differential equations

• Stochastic processes

• Statistical mechanics

• Topology

Please visit our website for a full description of modules for the MSc Mathematics.

On top of the Mathematics modules you study, you will also complete a dissertation as part of your studies.

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.

Mathematics students will benefit from the £31m Computational Foundry for computer and mathematical sciences which will provide the most up-to-date and high quality teaching facilities featuring world-leading experimental set-ups, devices and prototypes to accelerate innovation and ensure students will be ready for exciting and successful careers. (From September 2018)

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, statistically analysis, marketing and sales.

Some of our Mathematics students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where Mathematics 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.

http://www.swansea.ac.uk/postgraduate/taught/science/mscmathematics/

Student Profile

"Further to my studies at Swansea University as a Master of Science graduate in Financial Mathematics, I am currently working at Deutsche Bank in London as part of the Structured Financial Services team providing client services for corporate lending and debt portfolios. The complex nature of the Mathematics course has helped me become a logical decision maker and a highly skilled problem solver. These transferable skills are very useful in the world of Finance since the role is highly challenging working towards deadlines and structured transaction targets. My studies at Swansea University have also enriched me with leadership, motivational skills and have enhanced my communication skills. I work in a close team of 10 people within a large department which encourages a culture that strives towards learning and effective teamwork. I thoroughly enjoyed my time at Swansea University and cherish the many fond memories. I am so pleased to be expanding my horizon within a major financial centre."

Rhian Ivey, BSc Mathematics, MSc Mathematics and Computing for Finance

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Overview

Financial Mathematics is a branch of Mathematics where advanced mathematical and statistical methods are developed for and applied to financial markets and financial management. Its main aims are to quantify and hedge risks in the financial marketplace.

Effective computational methods are crucial for the successful use of mathematical modelling in finance. The MSc in Financial and Computational Mathematics is designed to reflect this combination of knowledge and skills so that its graduates are well equipped to enter the competitive job markets of quantitative finance and related fields.

The course is focused on computational techniques and mathematical modelling used in the financial industry and on the required background in finance. The course is provided by the School of Mathematical Sciences with valuable input from the School of Economics. To ensure that the degree keeps pace with changes in employer expectations and employment opportunities, the course has its own advisory board which consists of leading experts from the financial industry and academia.

Key facts:

- The School of Mathematical Sciences is one of the largest and strongest mathematics departments in the UK, with over 60 full-time academic staff.
- In the latest independent Research Assessment Exercise, the school ranked 8th in the UK in terms of research power across the three subject areas within the School of Mathematical Sciences (pure mathematics, applied mathematics, statistics and operational research).
- In the last independent Teaching Quality Assessment, the School scored 23 out of 24.
- The course has its own advisory board (see below) consisting of leading experts from the financial industry and academia.
- The course is offered in collaboration with the School of Economics.

Module details

Core modules include: financial mathematics, advanced financial mathematics, scientific computing and c++, advanced scientific computing, financial mathematics dissertation.

Optional Stream 1 (Maths/Stats and Computing): Optimisation, Time Series and Forecasting, Statistical Foundations.

Optional Stream 2A: Econometic Theory, Financial and Macro Econometrics, Time Series Econometrics, Mathematics for Engineering Management, Game Theory.

Optional Stream 2B: Microeconomic Analysis, Financial Economics, Options and Futures Markets, Mathematics for Engineering Management, Game Theory.

English language requirements for international students

IELTS: 6.5 (with no less than 6.0 in any element)

Further information

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The M.S. in Applied and Computational Mathematics program is designed to prepare students to join the workforce as a consulting mathematician or to pursue doctoral study in computational and industrial mathematics or other computationally-intensive field of study. 

Distinctive features include:

• Project-oriented approach in all courses - real-world industrial problems motivate coursework
• Team problem-solving practica emulate an industrial microcosm in which undergrads, grads, faculty, and industrial partners work together to study real-world problems
• Dual emphasis is placed on computational mathematics in the study of all real-world projects in each course of the curriculum

Students who complete the proposed program will:

• Acquire advanced knowledge of a wide variety of topics that span the realm of applied mathematics, including differential equations, discrete mathematics, probabilistic modelling, optimisation and statistical analysis. 
• Become adept at employing all steps of the mathematical modelling process in the analysis of real-world phenomena.
• Acquire expertise in using various forms of technology and in using, modifying, and creating numerical algorithms used in the analysis of real-world phenomena,
• Develop the valuable intuition of using the right tool for the right job.

Curriculum

Required modules:

MAT 500 Fundamentals of Applied Mathematics
MAT 548 Industrial Mathematics - Continuous Models
MAT 549 Industrial Mathematics - Discrete Models
MAT 552 Operations Research
MAT 553 Stochastic Modelling
MAT 554 Scientific Computing
MAT 555 Industrial Practicum - Continuous Models
STA 505 Mathematical Statistics I
MAT 556 Industrial Practicum - Discrete Models
STA 511 Intro Stat Computing & Data Management

Electives:

One three-credit elective must be chosen from one of the following

MAT 514 Theory Of Numbers
MAT 515 Algebra I
MAT 516 Algebra II
MAT 532 Geometry I
MAT 533 Geometry II
MAT 535 Topology
MAT 545 Real Analysis I
MAT 546 Real Analysis II
MAT 575 Complex Analysis I

An additional three credit elective must be chosen from any 500-level mathematics or statistics course not completed from the above list.

Collaborators and Local Industry

Representatives from the private sector consisting of mathematicians and scientists from large companies such as Vanguard, and PrimePay; employees of up-and-coming software companies such as iPipeline; and representatives of small privately-owned consulting firms and hedge fund companies, such as Wagner Associates and TFS Capital were consulted in the creation of this program.  We are continually expanding our network of collaborators within the private sector, with our newest collaborator being Stroud Preserve in West Chester.

Vastly different types of mathematical problems are studied by the members of this group.  Many have agreed to contribute to this M.S. program by way of delivering colloquium talks about their experiences in industry, and by creating and investigating real-world problems in our practicum courses.

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Programme description

Computational Mathematics, in particular the physical applied areas and the theory and implementation of numerical methods and algorithms, have wide-ranging applications in both the public and private sectors. More recently, in this era of ubiquitous and cheap computing power, there has been an explosion in the number of problems that require us to understand processes by modelling them, and to use data sets that are large. Thus the subject of Computational Mathematics has become increasingly prominent. Consequently there is high demand also for computational modellers and data scientists. This programme concentrates on the overlap and synergy between these fields.

Programme structure

The programme consists of 120 credits of courses in total during Semesters 1 and 2, followed by a 60 credit dissertation which is completed during the Summer. The courses taken will be dependent on the availability of courses each year which may be subject to change as curriculum develops to reflect a modern degree programme.

The first semester is composed of a combination of compulsory and optional courses. The compulsory courses will build strong applied mathematical and computational foundations. The curriculum is completed with optional courses in related subjects such as statistics and optimization.

The second semester is again composed of a combination of compulsory and optional courses, building on the skills gained in Semester 1. The compulsory courses include Research Skills, which will prepare you for the Summer Dissertation Project. The optional courses cover a wide range of areas including, for example, data science, high performance computing, and related disciplines such as Informatics and Physics.

The 60 credit individual dissertation will take the form of a supervised research-style project on a topic proposed by a staff member of the Applied and Computational Mathematics group. The aim of the project is to provide practical experience and skills for tackling scientific problems which require both computational approaches and mathematical insight. This will include identifying and applying appropriate mathematical and numerical techniques, interpreting the results, and presenting the conclusions.

Career opportunities

This programme will provide training in the tools and techniques of mathematical modelling and scientific computing, and will provide students with skills for problem solving using modern techniques of applied mathematics.

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Computational mathematics is relevant to almost every science, engineering, business and finance discipline, as well as many industrial sectors. This means it’s an excellent choice if you’re considering broadening your career options whilst studying a discipline that is in high demand in an ever technological era. Studying this MSc is also excellent preparation for academic research in any area where computational techniques play a significant role, offering you a clear route to further study at PhD level.

The course delivers an outstanding combination of advanced applicationoriented mathematical concepts and computational methodologies. Broad in scope and genuinely multidisciplinary in nature, it’s based on solid and well-founded mathematical theory.

Subject modules are carefully designed to be accessible to anyone with a good first degree in mathematics or in science and engineering subjects which have a strong mathematical component.

Here at the University of Derby, our teaching team has wide-ranging expertise in contemporary areas of mathematics and their applications to modern society. You’ll be inspired by academics and practitioners who have experience of harnessing mathematics and computing to address real-world problems.

You’ll benefit from flexible study options to fit in with your lifestyle. If you’re already in employment, you can gain this MSc through part time study while developing your knowledge and technical competence in ways that are directly relevant to your job.

You’ll study modules such as:

Optimisation
Scientific Computing
Stochastic Processes
Networks and Algorithms
Nonlinear System Dynamics
Studying at Masters Level and Research Methods
Independent Scholarship

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This programme is designed to train aspiring research scientists and budding IT professionals who wish to rely on numerical proficiency to further their career goals. The programme consists of a training aspect of taught components (3 modules approximately during the first 3 months) and a significant interdisciplinary research project centered towards computational mathematics (9 months)

Research topics are chosen by students from a list of topics mirroring the computational expertise of the Mathematics group and the newly founded Systems Analytics Research Institute at Aston, with Computationally oriented projects in for example, biology, optimization, pattern analysis and physics as well as finance. The projects are supervised by academics from the Mathematics group and the Systems Analytics Research Institute at Aston.

The MSc integrates a taught component of three modules over approximately three months (30 credits) with a substantial individual research project lasting nine months (150 credits)

Core modules:
-Computational Mathematics (10 Credits)
-Research skills and Professional Development (10 Credits)
-Specialist/Technical Research Skills (10 Credits)

Exemption from these modules may be arranged through APL or APEL, provided this is done prior to enrolment.

Personal Development

Students will have the opportunity to carry out a research project in collaboration with industry and through this learn about the application context of technology and the interaction between research and business.

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Program overview

The ideas of applied mathematics pervade several applications in a variety of businesses and industries as well as government. Sophisticated mathematical tools are increasingly used to develop new models, modify existing ones, and analyze system performance. This includes applications of mathematics to problems in management science, biology, portfolio planning, facilities planning, control of dynamic systems, and design of composite materials. The goal is to find computable solutions to real-world problems arising from these types of situations.

The master of science degree in applied and computational mathematics provides students with the capability to apply mathematical models and methods to study various problems that arise in industry and business, with an emphasis on developing computable solutions that can be implemented. The program offers options in discrete mathematics, dynamical systems, and scientific computing. Students complete a thesis, which includes the presentation of original ideas and solutions to a specific mathematical problem. The proposal for the thesis work and the results must be presented and defended before the advisory committee.

Curriculum

Several options available for course sequence:
-Discrete mathematics option
-Dynamical systems option
-Scientific computing option

See website for individual module details.

Other entry requirements

-Submit official transcripts (in English) of all previously completed undergraduate and graduate course work.
-Submit a personal statement of educational objectives.
-Have an undergraduate cumulative GPA of 3.0 or higher.
-Submit two letters of recommendation, and complete a graduate application.
-International applicants whose primary language is not English must submit scores from the Test of English as a Foreign Language (TOEFL). A minimum score of 550 (paper-based) or 79-80 (Internet-based) is required. International English Language Testing System (IELTS) scores are accepted in place of the TOEFL exam. Minimum scores vary; however, the absolute minimum score required for unconditional acceptance is 6.5. For additional information about the IELTS, please visit http://www.ielts.org. Those who cannot take the TOEFL will be required to take the Michigan Test of English Proficiency at RIT and obtain a score of 80 or higher.
-Although Graduate Record Examination (GRE) scores are not required, submitting them may enhance a candidate's acceptance into the program.
-A student may also be granted conditional admission and be required to complete bridge courses selected from among RIT’s existing undergraduate courses, as prescribed by the student’s adviser. Until these requirements are met, the candidate is considered a nonmatriculated student. The graduate program director evaluates the student’s qualifications to determine eligibility for conditional and provisional admission.

Additional information

Student’s advisory committee:
Upon admission to the program, the student chooses an adviser and forms an advisory committee. This committee oversees the academic aspects of the student’s program, including the selection of a concentration and appropriate courses to fulfill the program’s requirements.

Cooperative education:
Cooperative education enables students to alternate periods of study on campus with periods of full-time, paid professional employment. Students may pursue a co-op position after their first semester. Co-op is optional for this program.

Part-time study:
The program is ideal for practicing professionals who are interested in applying mathematical methods in their work and enhancing their career options. Most courses are scheduled in the late afternoon or early evening. The program may normally be completed in two years of part-time study.

Nonmatriculated students:
A student with a bachelor’s degree from an approved undergraduate institution, and with the background necessary for specific courses, may take graduate courses as a nonmatriculated student with the permission of the graduate program director and the course instructor. Courses taken for credit may be applied toward the master’s degree if the student is formally admitted to the program at a later date. However, the number of credit hours that may be transferred into the program from courses taken at RIT is limited for nonmatriculated students.

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Accurate and efficient scientific computations lie at the heart of most cross-discipline collaborations. It is key that such computations are performed in a stable, efficient manner and that the numerics converge to the true solutions, dynamics of the physics, chemistry or biology in the problem.

The programme closely follows the structure of our Applied Mathematical Sciences MSc and will equip you with the skill to perform efficient accurate computer simulations in a wide variety of applied mathematics, physics, chemical and industrial problems.

Students will take a total of 8 courses, 4 in each of the 1st and 2nd Semesters followed by a 3-month Project in the summer. A typical distribution for this programme is as follows:

Core courses

Modelling and Tools;
Stochastic Simulation;
Applied Linear Algebra;
Numerical Analysis;

Optional Courses

Dynamical Systems;
Optimization;
Partial Differential Equations;
Numerical Analysis of ODEs;
Applied Mathematics;
Statistical Methods;
Functional Analysis;
Software Engineering Foundations;
Mathematical Biology and Medicine;
Biologically Inspired Computation;
Advanced Software Engineering;
Geometry;
Bayesian Inference;

Typical project subjects

Simulation of Granular Flow and Growing Sandpiles;
Finite Element Discretisation of ODEs and PDEs;
Domain Decomposition;
Computational Spectral Theory;
Mathematical Modelling of Crime;
Mathematical Modelling of Micro-electron Mechanical Systems.
Can we Trust Eigenvalues on a Computer?

The final part of the MSc is an extended project in computational mathematics, giving the opportunity to investigate a topic in some depth guided by leading research academics from our 5-rated mathematics and statistics groups.

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The basis of natural sciences is the modelling of phenomena and solving these models. The Master’s programme in theoretical and computational methods will give you a strong basis in the theoretical methods, modelling, and mathematical and numerical analysis within physics, mathematics, chemistry and/or computer science. The special feature of this programme is that you can combine the above disciplines into a comprehensive programme. It is well suited for the needs of basic research and for many fields of application. This programme requires a strong commitment from you to develop your own skills and plan your degree. You can tailor your programme according to your existing knowledge and interests, in cooperation with the programme professors.

The programme’s strong scientific emphasis makes it a natural gateway to further studies in physics, mathematics, chemistry, and computer science. This will usually take place within one of the research groups working on the Kumpula campus.

Upon completing the Master’s programme, you will:
-Have a solid basis of skills in your chosen scientific field.
-Have good skills in analytical and computational thinking and deduction.
-Be able to apply theoretical and computational methods to the analysis and understanding of problems in various fields.
-Be able to generalise information on scientific phenomena, and identify the inner relationships.
-Be able to create mathematical models of natural phenomena.
-Be able to solve the models, both analytically and numerically.

As a graduate of this Master’s programme you can work as an expert in many kinds of scientific jobs in the private and the public sectors. The employment rate in this field is good.

The University of Helsinki will introduce annual tuition fees to foreign-language Master’s programmes starting on August 1, 2017 or later. The fee ranges from 13 000-18 000 euros. Citizens of non-EU/EEA countries, who do not have a permanent residence status in the area, are liable to these fees. You can check this FAQ at the Studyinfo website whether or not you are required to pay tuition fees: https://studyinfo.fi/wp2/en/higher-education/higher-education-institutions-will-introduce-tuition-fees-in-autumn-2017/am-i-required-to-pay-tuition-fees/

Programme Contents

The special feature of this programme is its great scope: it consists of several modules in physics, mathematics, chemistry, and/or computer science. Out of these, you may select a suitable group of subjects according to your interests and the courses you took for your Bachelor's degree. The programme incorporates modules from e.g. the following areas:
-Theoretical physics
-Mathematics
-Cosmology and particle physics
-Computational physics
-Physical chemistry
-Laser spectroscopy
-Mathematical physics and stochastics
-Applied analysis
-Software engineering
-Theoretical computer science

The courses include group and lecture instruction, exercises, literature, and workshops. Most courses also include exams or project assignments. In addition, you can complete some courses independently, by taking exams.

Selection of the Major

This Master’s programme does not have any sub-programmes; instead, can can tailor a suitable combination according to your plans and existing knowledge from the modules in physics, mathematics, chemistry, and computer science. Your personal study plan will ensure that your courses will form a functional combination.

Programme Structure

The Master’s programme comprises 120 credits (ECTS) and it is possible to complete the degree in two academic years. The degree includes:
-90 credits of courses in the Master’s programme, including the Master’s thesis (Pro gradu) of 30 credits.
-30 credits of other courses from your Master’s programme or other programmes.

Your studies will include a personal study plan, working-life orientation, and career planning. The other studies could also include a traineeship, complementary courses in your major or minor subject, or a completely new minor subject.

Career Prospects

The Master’s degree in sciences applying theoretical and computational methods gives you an excellent basis for postgraduate studies or for work in many careers in Finland or internationally. Masters of Science employed within research and R&D in industry are very well paid. On the other hand, a career at the university or a research institute lets you carry out academic research on a topic of your own choosing.

As a graduate with an MSc degree you could embark on a career in:
-Industry, especially advanced technology corporations (applied research and R&D, leadership).
-Universities and research institutes abroad and in Finland (basic scientific research).
-Teaching in universities and universities of applied sciences.
-Software engineering, e.g. gaming industry.
-Various design and consultation jobs in the public and private sectors.

Graduates of similar programmes in the earlier degree system have found employment as researchers and teachers in universities and research institutes in Finland and abroad (e.g. CERN, ESA, NASA), for example, in administration (e.g. the Finnish Academy), and in private corporations. The strong analytical skills provided by the education are sought after in areas such as data analysis (industries, media companies, gaming industry, finance), and corporate research, product development, and consultation (e.g. Nokia, Ericsson, Apple, Sanoma, Spinverse, Supercell, Nielsen, Valo Research and Trading, Planmeca, Reaktor, Comptel, Vaisala, KaVo Kerr Group, IndoorAtlas and Goldman Sachs).

Internationalization

The Master’s programme works in a very international atmosphere, with many top researchers from Finland and abroad teaching in it. If you write your MSc thesis in one of the research groups, you will get first-hand experience of work in an international research project. In addition, the University of Helsinki and the Faculty of Science offer you many opportunities for international activities:
-Student exchange in one of the exchange locations of the faculty or university.
-Traineeships abroad.
-Courses given in English within the faculty.
-Cooperation with students in the international programme.
-International tasks within the students’ organisations or union.
-Language courses at the Language Centre of the University of Helsinki.

The Faculty of Science aims to be at the cutting edge of European research within its disciplines.

The collaboration partners include several top international research centres, such as CERN, ESA, ESRF, and ITER.R.

As a graduate student at the Faculty of Science, you will be able to apply for research training at places such as CERN in Geneva, Switzerland, or the ESRF centre in Grenoble, France. A traineeship in one of the internationally active research groups on campus will enable you to acquaint yourself and form contacts with the international research community during your studies. In addition, the international exchange programmes offer many opportunities for you to complete part of your degree at a foreign university.

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This programme is designed for graduates in mathematics, engineering, computer science and finance/economics wishing to pursue careers in the financial services and banking industry. The structure is of an interdisciplinary nature in which graduates coming from different disciplines collaborate to address the computational aspects of market risk. Our core philosophy is to equip our students with the appropriate knowledge in mathematical finance, focusing on a strong development of associated computational methods.

Our Royal Maritime (Heritage) London based campus, close to the financial district of Canary Wharf, enables the department to build ties with market practitioners permitting our students to become part of a wider financial group. Our seminar series, inviting both academics and practitioners, allows you to interact with our external links creating an advantageous learning experience. We provide the knowledge for you to build up your profile of understanding of current research practice in finance. You will be trained and equipped with the skills for derivatives pricing and make use of non-linear methods for quantitative analysis (programming in Matlab, R and VBA). Our classes include interactive applications that enhance your learning experience through innovative teaching. By utilising research expertise within the department you will graduate with a strong understanding of numerical methods. You will also develop an understanding for further applicability in relevant fields as in energy commodity markets, where part of our current research focuses on by combining the world leading Agent-Based research team with our Computational Finance applications for crude oil price modelling.

The programme welcomes both recent graduates as well as experienced professional practitioners who wish to further their skills. Programme assessments are all 100% coursework with problems relating to current market practice. A supervised dissertation project takes place after the end of the last teaching term during the summer months. Projects are allocated in March and students are encouraged to work on projects that provide genuine insight in financial markets analysis. The programme is also available on a part-time basis. For those already at employment the flexible part-time mode of study, two years typically but can be flexible, allows students to be committed to both the MSc programme and employment.

Visit the website http://www2.gre.ac.uk/study/courses/pg/maths/compfinance

Mathematics

Postgraduate mathematics students benefit from award-winning teaching and great facilities. Our programmes are informed by world-renowned research and our links with industry ensure our students develop the academic and practical skills that will enhance their career prospects.

What you'll study

Full time
- Year 1:
Students are required to study the following compulsory courses.

English Language Support Course (for Postgraduate Students in the School of Computing and Mathematical Sciences)
Financial Markets (Dual Award) (15 credits)
Masters Project (Maths) (60 credits)
Advanced Finite Difference Methods for Derivatives Pricing (15 credits)
Computational Methods (15 credits)
Mathematical Approaches to Risk Management (15 credits)
Mathematical Finance (30 credits)

Students are required to choose 15 credits from this list of options.

Scientific Software Design and Development (15 credits)
Inverse Problems (15 credits)

Students are required to choose 15 credits from this list of options.

Enterprise Software Engineering Development (15 credits)
Software Tools and Techniques (15 credits)
Actuarial Mathematics and Risk Modelling (15 credits)
Financial Time Series (15 credits)

Part time
- Year 1:
Students are required to study the following compulsory courses.

Computational Methods (15 credits)
Inverse Problems (15 credits)
Mathematical Finance (30 credits)

- Year 2:
Students are required to study the following compulsory courses.

Scientific Software Design and Development (15 credits)
Financial Markets (Dual Award) (15 credits)
Masters Project (Maths) (60 credits)
Advanced Finite Difference Methods for Derivatives Pricing (15 credits)
Mathematical Approaches to Risk Management (15 credits)

Fees and finance

Your time at university should be enjoyable and rewarding, and it is important that it is not spoilt by unnecessary financial worries. We recommend that you spend time planning your finances, both before coming to university and while you are here. We can offer advice on living costs and budgeting, as well as on awards, allowances and loans.

Find out more about our fees and the support available to you at our:
- Postgraduate finance pages (http://www.gre.ac.uk/finance/pg)
- International students' finance pages (http://www.gre.ac.uk/finance/international)

Assessment

100% coursework. Coursework assessment at the postgraduate level allows for better elaboration of ideas and expansion of knowledge. A supervised dissertation project takes places at the end of the teaching terms during the summer months. The Department is very keen to tackle dissertation topics.

Career options

Graduates are equipped with the tools needed to become quantitative analysts, work in risk and portfolio management as well as in the insurance sector. Our expert seminar series gives you the opportunity to interact with leading figures from industry and academia and undertake projects relating to current industry practice. A postgraduate qualification is a major achievement and a milestone in your specialised career path leading to a professional career. The Department also offers a PhD programme.

Find out how to apply here - http://www2.gre.ac.uk/study/apply

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This Masters degree provides you with knowledge of advanced finance concepts, whilst developing your quantitative, mathematical and research skills.

Taught by experienced academics based in both Leeds University Business School and the School of Mathematics, you’ll cover key topics including financial derivative pricing, discrete and continuous time models, risk management and portfolio optimisation, as well as statistical methods for finance.

You will be equipped with a rare combination of mathematical skills and the latest business finance knowledge, which is highly sought after in the financial sector by banks, investment and consultancy companies. It’s also excellent preparation if you’re interested in pursuing further academic research.

This course is ideal if you’ve previously studied finance, economics, mathematics, physics or computing, and are interested in applying your skills to financial markets.

Academic excellence

As a student, you will be able to access the knowledge of our advanced specialist research units, which also have strong links with leading institutions in the US, Europe and Asia. These include the Centre for Advanced Study in Finance (CASIF), the Institute of Banking and Investment (IBI) and the Credit Management Research Centre (CMRC).

This research makes an important contribution to your learning on the MSc Financial Mathematics; you will benefit from a curriculum that is informed by the latest knowledge and critical thinking.

You will also benefit from our strong relationships with the finance, credit and accounting professions. This provides a connection to the latest practitioner and policy developments, giving you a masters degree that is relevant to the contemporary environment.

Course content

In your first semester you’ll develop a broad understanding of corporate finance and how financial theory relates to practice in business and financial markets. This will put your mathematical studies into context while you develop your skills in applied statistics and probability, optimisation methods and discrete time finance.

You’ll build on these skills in topics such as continuous time finance, risk management and computational methods. You’ll also gain specialist knowledge in topics that suit your career ambitions such as risk and insurance, actuarial science and behavioural finance.

The programme will improve your research skills and allow you to study different research methodologies, including those employed by our own leading academics. This will prepare you for your dissertation – an independent research project on a topic of your choice that you’ll submit by the end of the year.

Course structure

Compulsory modules

You’ll take nine compulsory modules including your dissertation.

• Corporate Finance 15 credits
• Financial Mathematics Studies Dissertation 30 credits
• Applied Statistics and Probability 15 credits
• Discrete Time Finance 15 credits
• Continuous Time Finance 15 credits
• Research Methods in Financial Mathematics 15 credits
• Risk Management 15 credits
• Computations in Finance 15 credits
• Optimisation Methods for Finance 15 credits

Optional modules

You'll also take two optional modules.

• Security Investment Analysis 15 credits
• Portfolio Risk Management 15 credits
• Behavioural Finance 15 credits
• Financial Derivatives 15 credits
• International Investment 15 credits
• Models in Actuarial Science 15 credits

For more information on typical modules, read Financial Mathematics MSc in the course catalogue

Learning and teaching

We use a variety of teaching and learning methods to help you make the most of your studies. These will include lectures, seminars, workshops, online learning and tutorials. Independent study is also vital for this course allowing you to prepare for taught classes and sharpen your own research and critical skills.

In addition to the assessed modules and research dissertation, you benefit from professional training activities and employability workshops. Thanks to our links with major companies across the business world, you can also gain a practical understanding of key issues.

Recent activities have included CV building and interview sessions, professional risk management workshops and commercial awareness events. For example, students have developed their knowledge of financial markets through a one-week trading simulation. Read more about professional development activities for postgraduate finance students.

Assessment

Assessment methods emphasise not just knowledge, but essential skills development too. They include formal exams, group projects, reports, computer simulation exercises, essays and written assignments, group and individual presentations.

This diversity enables you to develop a broad range of skills as preparation for professional life.

Career opportunities

You have various opportunities open to you as a Financial Mathematics graduate, including: quantitative analysis, risk management, investment banking, financial consultancy, insurance, accounting and academia.

Previous graduates have gone on to secure employment with Allianz (London), AstraZeneca, Barclays, Cathay Life Insurance, CITIC Group, Commerzbank, Deloitte, First Direct, Gaz de France, HSBC, KPMG, Moody’s, PricewaterhouseCoopers, Royal Bank of Scotland, RSA and UK Government Actuary’s Department.

Careers support

We help you to achieve your career ambitions by providing professional development support and training as part of the course. You benefit from the support of a professional development tutor, who will work with you to develop the important professional skills that employers value.

Read more about our careers and professional development support.

The University of Leeds Careers Centre also provides a range of help and advice to help you plan your career and make well-informed decisions along the way, even after you graduate. Find out more at the Careers website

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Programme description

The MSc in Computational Mathematical Finance (CMF) is a dynamic new programme with the aim to deliver high quality training in the theory of Mathematical Finance with strong emphasis on computational methods.

Currently graduates in this field are expected to have a working knowledge of advanced computational finance (including construction of algorithms and programming skills) as well as a sound knowledge of the theory of Probability and Stochastic Analysis. These are the core theories needed in the modern valuation of complex financial instruments.

This MSc programme delivers:

• a flexible programme of study relevant to the needs of employers such as: top investment banks, hedge funds and asset management firms
• a solid knowledge in financial derivative pricing, risk management and portfolio management
• the transferable computational skills required by the modern quantitative finance world

Programme structure

You must obtain a total of 180 credits to be awarded the MSc. Over semesters 1 and 2, you will take compulsory courses worth a total of 85 credits and optional courses worth a further 35 credits. Successful performance in these courses (assessed through coursework or examinations or both) allows you to start work on a three-month dissertation project, worth 60 credits, for the award of the MSc degree.

There are two streams: the Financial stream and the Computational stream.

Compulsory courses (both streams):

• Stochastic Analysis in Finance (20 credits, semester 1)
• Discrete-Time Finance (10 credits, semester 1)
• Finance, Risk and Uncertainty (10 credits, semester 1)
• Object-Oriented Programming with Applications (10 credits, semester 1)
• Risk-Neutral Asset Pricing (10 credits, semester 2)
• Stochastic Control and Dynamic Asset allocation (10 credits, semester 2)
• Monte Carlo Methods (5 credits, semester 2)
• Research-Linked Topics (10 credits, semesters 1 and 2)

Optional courses - Computational stream:

• Numerical Methods for Stochastic Differential Equations [compulsory] (5 credits, semester 2)
• Numerical Partial Differential Equations [compulsory] (10 credits, semester 2)
• Programming Skills - HPC MSc (10 credits, semester 1)
• Parallel Numerical Algorithms - HPC MSc (10 credits, semester 1)

Optional courses - Financial stream:

• Financial Risk Theory [compulsory] (10 credits, semester 2)
• Optimization Methods in Finance [compulsory] (10 credits, semester 2)
• Advanced Time Series Econometrics (10 credits, semester 2)
• Credit Scoring (10 credits, semester 2)
• Computing for Operational Research and Finance (10 credits, semester 1)
• Financial Risk Management (10 credits, semester 2)
• Stochastic Optimization (5 credits, semester 2)

Learning outcomes

At the end of this programme you will have:

• developed personal communications skills, initiative, and professionalism within a mathematical context
• developed transferable skills that maximise your prospects for future employment, including writing, oral presentation, team-working, numerical and logical problem-solving, planning and time-management
• improved your ability to convey ideas in an articulate fashion, to build upon previous mathematical training and further develop logic and deductive skills
• mastered standard and advanced mathematical tools used to solve applied problems relevant to the mathematical finance industry
• developed quantitative and computational skills for the proficient fulfilment of tasks in the financial sector

Career opportunities

Graduates can expect to go on to work in major financial institutions or to continue their studies by joining PhD programmes.

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The MSc Computational Finance will provide you with mathematical and computational skills required to solve real problems in quantitative finance. Many areas of modern finance such as risk management and option pricing emphasise numerical and computational skills as well as an understanding of the mathematical background.

The programme brings together expertise from Mathematics and the Business School to ensure a balanced approach to many of the complex problems in modern quantitative finance.

On completion of the programme you will be able to review and implement complex financial models in a number of programming languages including C++, MATLAB and R.

Programme structure

Core modules

The compulsory modules can include; Methods for Stochastics and Finance; Analysis and Computation for Finance; Mathematical Theory of Optional Pricing; Introduction to C++; Computational Finance with C++; Numerical Finance; Research Methodology; Advanced Mathematics Project; Investment Analysis I; Investment Analysis II; Financial Modeling

Optional modules

Some examples of the optional modules are as follows; Topics in Financial Economics; Banking and Financial Services; Derivatives Pricing; Domestic and International Portfolio Management; Advanced Corporate Finance; Alternative Investments; Quantitative Research Techniques; Advanced Econometrics;

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Computational Life Science

In recent years, biological research has become increasingly interdisciplinary, focusing heavily on mathematical modeling and on the analysis of system-wide quantitative information. Sophisticated high-throughput techniques pose new challenges for data integration and data interpretation. The Computational Life Science (CompLife) MSc program at Jacobs University meets these challenges by covering computational, theoretical and mathematical approaches in biology and the life sciences. It is geared towards students of bioinformatics, computer science, physics, mathematics and related areas.

Program Features

The CompLife program is located at Jacobs University, a private and international English-language academic institution in Bremen, Germany. CompLife students at Jacobs University take a tailor-made curriculum comprising lectures, seminars and laboratory trainings. Courses cover foundational as well as advanced topics and methods. Core components of the program and areas of specialization include:

- Computational Systems Biology
- Computational Physics and Biophysics
- Bioinformatics
- RNA Biology
- Imaging and Modeling in Medicine
- Ecological Modeling
- Theoretical Biology
- Applied Mathematics
- Numerical Methods

For more details on the CompLife curriculum, please visit the program website at http://www.jacobs-university.de/complife.

Career Options

Graduates of the CompLife program are prepared for a career in biotechnology and biomedicine. Likewise, graduates of the program are qualified to move on to a PhD.

Application and Admission

The CompLife program starts in the first week of September every year. Please visit http://www.jacobs-university.de/graduate-admission or use the contact form to request details on how to apply. We are looking forward to receiving your inquiry.

Scholarships and Funding Options

All applicants are automatically considered for merit-based scholarships of up to € 12,000 per year. Depending on availability, additional scholarships sponsored by external partners are offered to highly gifted students. Moreover, each admitted candidate may request an individual financial package offer with attractive funding options. Please visit http://www.jacobs-university.de/study/graduate/fees-finances to learn more.

Campus Life and Accommodation

Jacobs University’s green and tree-shaded campus provides much more than buildings for teaching and research. It is home to an intercultural community which is unprecedented in Europe. A Student Activities Center, various sports facilities, a music studio, a student-run café/bar, concert venues and our Interfaith House ensure that you will always have something interesting to do.

For graduate students who would like to live on campus, Jacobs University offers accommodation in four residential colleges. Each college has its own dining room, recreational lounge, study areas, and common and group meeting rooms. Please visit http://www.jacobs-university.de/study/graduate/campus-life for more information.

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The MSc in Data and Computational Science is designed for students from highly quantitative disciplines who wish to work in data analytics or computational science.

Computational science is at the crossroads between modern applied mathematics and statistics, and our programme recognizes this fact by combining aspects of both in a unique set of tailored modules including scientific computing, mathematical modelling, and data analytics.

- The programme will equip you to solve complex scientific problems and analyse large data sets using a range of theoretical tools, from deterministic mathematical modelling to Bayesian analysis.

- The intensive programming modules will allow you develop a range of sought-after skills in practical programming and data analytics, including applications in high-performance computing.

- Topical application areas are offered each year, including cryptography, numerical weather prediction, and financial mathematics. The dissertation will give you further hands-on experience in computational science and will allow you to apply the key theoretical and practical skills by working on a challenging research topic.

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