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Masters Degrees (Mathematical Analysis)

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The University of Dundee has a long history of mathematical biology, going back to Professor Sir D'Arcy Wentworth Thompson, Chair of Natural History, 1884-1917. Read more

Mathematical Biology at Dundee

The University of Dundee has a long history of mathematical biology, going back to Professor Sir D'Arcy Wentworth Thompson, Chair of Natural History, 1884-1917. In his famous book On Growth and Form (where he applied geometric principles to morphological problems) Thompson declares:

"Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, molded and conformed. They are no exceptions to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science."

Current mathematical biology research in Dundee continues in the spirit of D'Arcy Thompson with the application of modern applied mathematics and computational modelling to a range of biological processes involving many different but inter-connected phenomena that occur at different spatial and temporal scales. Specific areas of application are to cancer growth and treatment, ecological models, fungal growth and biofilms. The overall common theme of all the mathematical biology research may be termed"multi-scale mathematical modelling" or, from a biological perspective, "quantitative systems biology" or"quantitative integrative biology".

The Mathematical Biology Research Group currently consists of Professor Mark Chaplain, Dr. Fordyce Davidson and Dr. Paul Macklin along with post-doctoral research assistants and PhD students. Professor Ping Lin provides expertise in the area of computational numerical analysis. The group will shortly be augmented by the arrival of a new Chair in Mathematical Biology (a joint Mathematics/Life Sciences appointment).

As a result, the students will benefit directly not only from the scientific expertise of the above internationally recognized researchers, but also through a wide-range of research activities such as journal clubs and research seminars.

Aims of the programme

1. To provide a Masters-level postgraduate education in the knowledge, skills and understanding of mathematical biology.
2. To enhance analytical and critical abilities and competence in the application of mathematical modeling techniques to problems in biomedicine.

Prramme Content

This one year course involves taking four taught modules in semester 1 (September-December), followed by a further 4 taught modules in semester 2 (January-May), and undertaking a project over the Summer (May-August).

A typical selection of taught modules would be:

Dynamical Systems
Computational Modelling
Statistics & Stochastic Models
Inverse Problems
Mathematical Oncology
Mathematical Ecology & Epidemiology
Mathematical Physiology
Personal Transferable Skills

Finally, all students will undertake a Personal Research Project under the supervision of a member of staff in the Mathematical Biology Research Group.

Methods of Teaching

The programme will involve a variety of teaching formats including lectures, tutorials, seminars, journal clubs, case studies, coursework, and an individual research project.

Taught sessions will be supported by individual reading and study.

Students will be guided to prepare their research project plan and to develop skills and competence in research including project management, critical thinking and problem solving, project reporting and presentation.

Career Prospects

The Biomedical Sciences are now recognizing the need for quantitative, predictive approaches to their traditional qualitative subject areas. Healthcare and Biotechnology are still fast-growing industries in UK, Europe and Worldwide. New start-up companies and large-scale government investment are also opening up employment prospects in emerging economies such as Singapore, China and India.

Students graduating from this programme would be very well placed to take advantage of these global opportunities.

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International Master's in Statistics - MSc. https://www.kent.ac.uk/courses/postgraduate/163/international-masters-statistics. Read more
International Master's in Statistics - MSc: https://www.kent.ac.uk/courses/postgraduate/163/international-masters-statistics

Overview

The International Master’s in Statistics develops your practical, statistical and computing skills to prepare you for a professional career in statistics or as a solid basis for further research in the area.

The programme has been designed to provide a deep understanding of the modern statistical methods required to model and analyse data. You will benefit from a thorough grounding in the ideas underlying these methods and develop your skills in key areas such as practical data analysis and data modelling.

It has been accredited by the Royal Statistical Society (RSS) and equips aspiring professional statisticians with the skills they need for posts in industry, government, research and teaching. It also enables you to develop a range of transferable skills that are attractive to employers within the public and private sectors.

Students whose mathematical and statistical background is insufficient for direct entry on to the appropriate programme, may apply for this course. The first year of the programme gives you a strong background in statistics, including its mathematical aspects, equivalent to the Graduate Diploma in Statistics. This is followed by the MSc in Statistics.

International Master's in Statistics with Finance - MSc: https://www.kent.ac.uk/courses/postgraduate/164/international-masters-statistics-finance

Overview

This programme, accredited by the Royal Statistical Society (RSS), equips aspiring professional statisticians with the skills they will need for posts in industry, government, research and teaching. It is suitable preparation too for careers in other fields requiring a strong statistical background.

Students whose mathematical and statistical background is insufficient for direct entry on to the appropriate programme, may apply for this course. The first year of the programme gives you a strong background in statistics, including its mathematical aspects, equivalent to the Graduate Diploma in Statistics. This is followed by the MSc in Statistics with Finance.

About the School of Mathematics, Statistics and Actuarial Science (SMSAS)

The School has a strong reputation for world-class research and a well-established system of support and training, with a high level of contact between staff and research students. Postgraduate students develop analytical, communication and research skills. Developing computational skills and applying them to mathematical problems forms a significant part of the postgraduate training in the School. We encourage all postgraduate statistics students to take part in statistics seminars and to help in tutorial classes.

The Statistics Group is forward-thinking, with varied research, and received consistently high rankings in the last two Research Assessment Exercises.

Statistics at Kent provides:

- a programme that gives you the opportunity to develop practical, mathematical and computing skills in statistics, while working on challenging and important problems relevant to a broad range of potential employers

- teaching and supervision by staff who are research-active, with established reputations and who are accessible, supportive and genuinely interested in your work

- advanced and accessible computing and other facilities

- a congenial work atmosphere with pleasant surroundings, where you can socialise and discuss issues with a community of other students.

Research areas

Biometry and ecological statistics
Specific interests are in biometry, cluster analysis, stochastic population processes, analysis of discrete data, analysis of quantal assay data, overdispersion, and we enjoy good links within the University, including the School of Biosciences and the Durrell Institute of Conservation and Ecology. A recent major joint research project involves modelling the behaviour of yeast prions and builds upon previous work in this area. We also work in collaboration with many external institutions.

Bayesian statistics
Current work includes non-parametric Bayes, inference robustness, modelling with non-normal distributions, model uncertainty, variable selection and functional data analysis.
Bioinformatics, statistical genetics and medical statistics
Research covers bioinformatics (eg DNA microarray data), involving collaboration with the School of Biosciences. Other interests include population genetics, clinical trials and survival analysis.

Nonparametric statistics
Research focuses on empirical likelihood, high-dimensional data analysis, nonlinear dynamic analysis, semi-parametric modelling, survival analysis, risk insurance, functional data analysis, spatial data analysis, longitudinal data analysis, feature selection and wavelets.

Careers

Students often go into careers as professional statisticians in industry, government, research and teaching but our programmes also prepare you for careers in other fields requiring a strong statistical background. You have the opportunity to attend careers talks from professional statisticians working in industry and to attend networking meetings with employers.

Recent graduates have started careers in diverse areas such as the pharmaceutical industry, financial services and sports betting.

Professional recognition

The taught programmes in Statistics and Statistics with Finance provide exemption from the professional examinations of the Royal Statistical Society and qualification for Graduate Statistician status.

Find out how to apply here - https://www.kent.ac.uk/courses/postgraduate/apply/

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What do Facebook, the financial system, Internet or the brain have in common?. "Everything is connected, all is network". Read more
What do Facebook, the financial system, Internet or the brain have in common?

"Everything is connected, all is network"
From the underlying skeleton of social relations, the interdependent evolution of our financial system, to the emergent collective computation in the brain, most of the complex systems that appear in society, technology, and nature are ultimately characterised by a nontrivial pattern of inter-relations. This underlying architecture is in turn shaping how information diffuses and spreads, how resilient the system is against attacks or perturbations, or how complex patterns emerge at the systemic level from the aggregation of seemingly simple individuals.

Our MSc Network Science will provide a thorough grounding in the core principles of modelling and analysis of complex and networked systems, along with the principal analytical and numerical methodologies. This will open to students a host of career opportunities in systems and networks modelling industries, spanning the IT, financial, and biomedical sectors, that are now requiring such specialist knowledge and skills.

Network Science is a very active and rapidly evolving research field with high societal impact, which stands at the crossroads of graph theory, complexity and data analysis. Addressing the description and modelling of the architecture and dynamics of complex systems -systems composed by many interacting units that show collective behaviour- it stands as a new kind of science to cope with some of the most challenging endeavours we face today, in an ever increasingly more connected society.
Its impact and applications outside academia pervades technological sectors such as communications and infrastructures (Internet, transportation networks, energy networks, urban mobility), finance (financial risk and systemic instability, financial networks, interbank cross-correlations), marketing and IT (social media, data analytics), public health (epidemic spreading models), or biostatistics and network biology (brain modelling, protein interaction networks, postgenomic era), to cite a few. This specialist masters programme aims at providing graduate students and professionals with a rigorous training in the underlying mathematical concepts, the analysis and modelling of complex networks and networked systems, complemented with training in computing, numerical simulations and massive data analysis. It is aimed towards students with a mathematical background who wish to enter a career involving analysis and optimisation of diverse kinds of networks, networked dynamics and models.

Why study your MSc Network Science at Queen Mary?
This is a pioneering MSc in the UK, a joint programme, taught by our Schools of Mathematical Sciences, and Electronic Engineering and Computer Science, drawing on their strengths in research and teaching in the area of complex networks, mathematical modelling of complex systems, and data mining.

We teach what we know and what we do best. Within the School of Mathematics, the Complex Systems & Networks group is one of the biggest hubs in Network Science within the UK, where we address both fundamental and applied challenges in the mathematical modelling of complex systems with clear societal impact, in collaboration with several industrial stakeholders. Within the School of Electronic Engineering, the Networks group was founded in 1987, and has hugely expanded ever since, bringing their expertise in online social networks, data mining and cloud computing. The coalescence of both groups expertises has fostered the creation of this unique MSc.

More about our two schools

Queen Mary is a member of the prestigious Russell Group of leading UK universities, combining world-class research, teaching excellence and unrivalled links with business and the public sector. The School of Mathematical Sciences has a distinguished history on itself. We have been conducting pioneering mathematical research since the 1950s, and as one of the largest mathematical departments in the UK, with over 50 members of staff, the school can offer diverse postgraduate study opportunities across the field, from pure and applied mathematics, to finance and statistics. Along with the MSc in Network Science, our cohort of postgraduate students specialise in Mathematics and Statistics, Mathematical Finance and Financial Computing. We are one of the UK’s leading universities in the most recent national assessment of research quality, we were placed ninth in the UK (REF 2014) amongst multi-faculty universities. This means that the teaching on our postgraduate programmes is directly inspired by the world-leading research of our academics. Our staff includes international leaders in many areas of mathematical research, and the School is a hive of activity, providing a vibrant intellectual space for postgraduate study.

The School of Electronic Engineering and Computer Science is internationally recognised for their pioneering and ground-breaking research in several areas including machine learning and applied network analysis. This expertise uniquely complements the more theoretical knowledge offered by the School of Mathematical Sciences, providing a well balanced mix of theory and applications and offering a deep and robust programme that combines the foundations of the mathematics of networks with the latest cutting edge applications in real world problems.

Additionally, Queen Mary holds a university-level Bronze Award for the Athena SWAN Charter, which recognises and celebrates good employment practice for women working in mathematics, science, engineering and technology in higher education and research.

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Studying Mathematics at postgraduate level gives you a chance to begin your own research, develop your own creativity and be part of a long tradition of people investigating analytic, geometric and algebraic ideas. Read more
Studying Mathematics at postgraduate level gives you a chance to begin your own research, develop your own creativity and be part of a long tradition of people investigating analytic, geometric and algebraic ideas.

If your mathematical background is insufficient for direct entry to the MSc in Mathematics and its Applications, you may apply for this course. The first year of this Master's programme gives you a strong background in mathematics, equivalent to the Graduate Diploma in Mathematics, with second year studies following the MSc in Mathematics and its Applications.

Visit the website https://www.kent.ac.uk/courses/postgraduate/148/international-masters-in-mathematics-and-its-applications

About the School of Mathematics, Statistics and Actuarial Science (SMSAS)

The School has a strong reputation for world-class research and a well-established system of support and training, with a high level of contact between staff and research students. Postgraduate students develop analytical, communication and research skills. Developing computational skills and applying them to mathematical problems forms a significant part of the postgraduate training in the School.

The Mathematics Group at Kent ranked highly in the most recent Research Assessment Exercise. With 100% of the Applied Mathematics Group submitted, all research outputs were judged to be of international quality and 12.5% was rated 4*. For the Pure Mathematics Group, a large proportion of the outputs demonstrated international excellence.

The Mathematics Group also has an excellent track record of winning research grants from the Engineering and Physical Sciences Research Council (EPSRC), the Royal Society, the EU, the London Mathematical Society and the Leverhulme Trust.

Course structure

At least one modern application of mathematics is studied in-depth by each student. Mathematical computing and open-ended project work forms an integral part of the learning experience. You strengthen your grounding in the subject and gain a sound grasp of the wider relevance and application of mathematics.

There are opportunities for outreach and engagement with the public on mathematics.

Modules

The following modules are indicative of those offered on this programme. This list is based on the current curriculum and may change year to year in response to new curriculum developments and innovation. Most programmes will require you to study a combination of compulsory and optional modules. You may also have the option to take modules from other programmes so that you may customise your programme and explore other subject areas that interest you.

MA552 - Analysis (15 credits)
MA553 - Linear Algebra (15 credits)
MA588 - Mathematical Techniques and Differential Equations (15 credits)
MA591 - Nonlinear Systems and Mathematical Biology (15 credits)
MA593 - Topics in Modern Applied Mathematics (30 credits)
MA549 - Discrete Mathematics (15 credits)
MA572 - Complex Analysis (15 credits)
MA563 - Calculus of Variations (15 credits)
MA587 - Numerical Solution of Differential Equations (15 credits)
MA577 - Elements of Abstract Analysis (15 credits)
MA576 - Groups and Representations (15 credits)
MA574 - Polynomials in Several Variables (15 credits)
MA961 - Mathematical Inquiry and Communication (30 credits)
MA962 - Geometric Integration (15 credits)
MA964 - Applied Algebraic Topology (15 credits)
MA965 - Symmetries, Groups and Invariants (15 credits)
MA968 - Mathematics and Music (15 credits)
MA969 - Applied Differential Geometry (15 credits)
MA970 - Nonlinear Analysis and Optimisation (15 credits)
MA971 - Introduction to Functional Analysis (15 credits)
MA972 - Algebraic Curves in Nature (15 credits)
MA973 - Basic Differential Algebra (15 credits)
CB600 - Games and Networks (15 credits)
MA562 - Nonlinear Waves and Solitons (15 credits)
MA960 - Dissertation (60 credits)

Assessment

Closed book examinations, take-home problem assignments and computer lab assignments (depending on the module).

Programme aims

This programme aims to:

- provide a Master’s level mathematical education of excellent quality, informed by research and scholarship

- provide an opportunity to enhance your mathematical creativity, problem-solving skills and advanced computational skills

- provide an opportunity for you to enhance your oral communication, project design and basic research skills

- provide an opportunity for you to experience and engage with a creative, research-active professional mathematical environment

- produce graduates of value to the region and nation by offering you opportunities to learn about mathematics in the context of its application.

Study support

Postgraduate resources
The University’s Templeman Library houses a comprehensive collection of books and research periodicals. Online access to a wide variety of journals is available through services such as ScienceDirect and SpringerLink. The School has licences for major numerical and computer algebra software packages. Postgraduates are provided with computers in shared offices in the School. The School has two dedicated terminal rooms for taught postgraduate students to use for lectures and self-study.

Support
The School has a well-established system of support and training, with a high level of contact between staff and research students. There are two weekly seminar series: The Mathematics Colloquium at Kent attracts international speakers discussing recent advances in their subject; the Friday seminar series features in-house speakers and visitors talking about their latest work. These are supplemented by weekly discussion groups. The School is a member of the EPSRC-funded London Taught Course Centre for PhD students in the mathematical sciences, and students can participate in the courses and workshops offered by the Centre. The School offers conference grants to enable research students to present their work at national and international conferences.

Dynamic publishing culture
Staff publish regularly and widely in journals, conference proceedings and books. Among others, they have recently contributed to: Advances in Mathematics; Algebra and Representation Theory; Journal of Physics A; Journal of Symbolic Computations; Journal of Topology and Analysis. Details of recently published books can be found within the staff research interests section.

Global Skills Award
All students registered for a taught Master's programme are eligible to apply for a place on our Global Skills Award Programme (http://www.kent.ac.uk/graduateschool/skills/programmes/gsa.html). The programme is designed to broaden your understanding of global issues and current affairs as well as to develop personal skills which will enhance your employability.

Careers

A postgraduate degree in Mathematics is a flexible and valuable qualification that gives you a competitive advantage in a wide range of mathematically oriented careers. Our programmes enable you to develop the skills and capabilities that employers are looking for including problem-solving, independent thought, report-writing, project management, leadership skills, teamworking and good communication.

Many of our graduates have gone on to work in international organisations, the financial sector, and business. Others have found postgraduate research places at Kent and other universities.

Find out how to apply here - https://www.kent.ac.uk/courses/postgraduate/apply/

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How can different kinds of data inform us on economic issues? On this course you learn how economic data analysis can address practical problems within business, accounting, and development. Read more
How can different kinds of data inform us on economic issues? On this course you learn how economic data analysis can address practical problems within business, accounting, and development.

Our MSc Applied Economics and Data Analysis is run jointly between our Department of Economics and our Institute for Social and Economic Research (ISER), which specialises in the analysis of household and labour market data.

On our course you will be provided the tools for analysing and implementing some of the models that are present in theory modules. You study data-orientated, applied modules, exploring topics including:
-Techniques used in the analysis of panel data
-The specification of models and the tests of their validity
-Methods for analysing persistence over time in economic variables
-Handling different types of datasets,
-Survey methodology and sampling frames, and how to deal with problems of response rates and attrition

We are top 5 in the UK for research, with over 90% of our research rated as “world-leading” or “internationally excellent”. Much of this world-class research is related to policy, and we have particular strengths in the areas of:
-Game theory and strategic interactions
-Theoretical and applied econometrics
-Labour economics

The quality of our work is reflected in our stream of publications in high-profile academic journals, including American Economic Review, Econometrica, and Review of Economic Studies.

Our University is one of only 21 ESRC-accredited Doctoral Training Centres in the UK. This means that our course can form part of a prestigious 1+3 funding opportunity worth up to £21,575.

Our expert staff

Study and work alongside some of the most prominent economists of our time.

Our researchers are at the forefront of their field and have even received MBEs, with students coming from across the globe to study, research or work with us.

Many of our researchers also provide consultancy services to businesses in London and other major financial centres, helping us to develop research for today's society as well as informing our teaching for the future.

For a full list of research interests, see our Department’s staff pages.

Specialist facilities

Take advantage of our wide range of learning resources to assist you in your studies:
-Extensive software for quantitative analysis is available in all computer labs across the university
-Access a variety of economics databases and multiple copies of textbooks and e-books in the Albert Sloman Library

Your future

After completing your masters, you may wish to extend your knowledge with a research degree – many Essex graduates decide to stay here for further study.

Alternatively, our course also prepares you for employment; recent surveys have shown that higher degree graduates are more likely to obtain jobs at professional or managerial level.

You will develop key employability skills including analytical reasoning, mathematical techniques, model building and data analysis.

Our graduates find employment in roles such as business and financial analysts, management consultants, government officials, and economists for banks and other financial organisations.

We also work with the university’s Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

Example Structure

Postgraduate study is the chance to take your education to the next level. The combination of compulsory and optional modules means our courses help you develop extensive knowledge in your chosen discipline, whilst providing plenty of freedom to pursue your own interests. Our research-led teaching is continually evolving to address the latest challenges and breakthroughs in the field, therefore to ensure your course is as relevant and up-to-date as possible your core module structure may be subject to change.

MSc Applied Economics and Data Analysis
-Dissertation
-Applications of Data Analysis
-Mathematical Methods
-Microeconomics
-Panel Data Methods
-Banking (optional)
-Behavioural Economics I: Individual Decision Making (optional)
-Behavioural Economics II: Games and Markets (optional)
-Computational Agent-Based Macro-Economics, Financial Markets and Policy Design (optional)
-Econometric Methods (optional)
-Economic Development Theory (optional)
-Economics of Financial Markets (optional)
-Estimation and Inference in Econometrics (optional)
-Game Theory and Applications (optional)
-International Finance (optional)
-International Trade (optional)
-Macroeconomics (optional)
-Monetary Economics (optional)
-Political Economy (optional)
-Theory of Industrial Organisation (optional)
-Time Series Econometrics (optional)
-Topics in Financial Economics (optional)
-Economics of Incentives, Contracts and the Firm (optional)

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Candidates who have a good undergraduate (BSc) degree or equivalent but whose mathematical background is insufficient for direct entry to the MSc programme may apply for a place on the conversion year for the MSc in Mathematical Finance. Read more
Candidates who have a good undergraduate (BSc) degree or equivalent but whose mathematical background is insufficient for direct entry to the MSc programme may apply for a place on the conversion year for the MSc in Mathematical Finance.

A place on the conversion year is normally offered together with a conditional offer for the MSc in Mathematical Finance in the following year, subject to successfully completing the conversion year. The normal progression requirement for progression from the conversion year to the MSc in Mathematical Finance is a final weighted average at 2:1 level (60% or above) for the modules taken in the conversion year.

Programme structure

The conversion year consists of a selection of modules to the value of 120 credits being part of the undergraduate degree in Mathematics and Finance at the University of York, with emphasis on the mathematical aspects of the course. Module choice is subject to prerequisites, timetabling constraints, availability of modules, and is subject to approval by the programme director.

The available modules may vary from year to year but are likely to include:

Term 1 (Autumn)
-Calculus (30 credits) (continues into Spring and Summer Terms)
-Algebra (20 credits) (continues into Spring and Summer Terms)
-Introduction to Probability and Statistics (20 credits)
-Statistics I (10 credits)
-Applied Probability (10 credits)
-Differential Equations (10 credits)
-Mathematical Finance I MAT00015H (10 credits)

Terms 2 and 3 (Spring and Summer Terms)
-Calculus (30 credits) (starts in Autumn, continues through Spring and completes in Summer Term)
-Algebra (20 credits) (starts in Autumn, continues through Spring and completes in Summer Term)
-Introduction to Applied Mathematics (20 credits) (starts in Spring Term, continues into Summer Term)
-Real Analysis (20 credits) (starts in Spring Term, continues into Summer Term)
-Linear Algebra (20 credits) (starts in Spring Term, continues into Summer Term)
-Vector Calculus (20 credits) (starts in Spring Term, continues into Summer Term)
-Statistics II (20 credits) (starts in Spring Term, continues into Summer Term)
-Numerical Analysis (10 credits) (Spring Term only)
-Mathematical Finance II (10 credits) (Spring Term only)

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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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Working at a frontier of mathematics that intersects with cutting edge research in physics. Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. Read more
Working at a frontier of mathematics that intersects with cutting edge research in physics.

Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. History shows us as much. Mathematical physics began with Christiaan Huygens, who is honoured at Radboud University by naming the main building of the Faculty of Science after him. By combining Euclidean geometry and preliminary versions of calculus, he brought major advances to these areas of mathematics as well as to mechanics and optics. The second and greatest mathematical physicist in history, Isaac Newton, invented both the calculus and what we now call Newtonian mechanics and, from his law of gravity, was the first to understand planetary motion on a mathematical basis.

Of course, in the Master’s specialisation in Mathematical Physics we look at modern mathematical physics. The specialisation combines expertise in areas like functional analysis, geometry, and representation theory with research in, for example, quantum physics and integrable systems. You’ll learn how the field is far more than creating mathematics in the service of physicists. It’s also about being inspired by physical phenomena and delving into pure mathematics.

At Radboud University, we have such faith in a multidisciplinary approach between these fields that we created a joint research institute: Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). This unique collaboration has lead to exciting new insights into, for example, quantum gravity and noncommutative geometry. Students thinking of enrolling in this specialisation should be excellent mathematicians as well as have a true passion for physics.

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

Why study Mathematical Physics at Radboud University?

- This specialisation is one of the few Master’s in the world that lies in the heart of where mathematics and physics intersect and that examines their cross-fertilization.
- You’ll benefit from the closely related Mathematics Master’s specialisations at Radboud University in Algebra and Topology (and, if you like, also from the one in Applied Stochastics).
- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that at Radboud University you’ll get plenty of one-on-one time with your thesis supervisor.
- You partake in the Mastermath programme, meaning you can follow the best mathematics courses, regardless of the university in the Netherlands that offers them. It also allows you to interact with fellow mathematic students all over the country.
- As a Master’s student you’ll get the opportunity to work closely with the mathematicians and physicists of the entire IMAPP research institute.
- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating. About half of our PhD’s continue their academic careers.

Career prospects

Mathematicians are needed in all industries, including the industrial, banking, technology and service industry and also within management, consultancy and education. 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 indeed and is 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 Mathematical Physics Department, emphasise operator algebras and noncommutative geometry, Lie theory and representation theory, integrable systems, and quantum field theory. Below, a small sample of the research our members pursue.

Gert Heckman's research concerns algebraic geometry, group theory and symplectic geometry. His work in algebraic geometry and group theory concerns the study of particular ball quotients for complex hyperbolic reflection groups. Basic questions are an interpretation of these ball quotients as images of period maps on certain algebraic geometric moduli spaces. Partial steps have been taken towards a conjecture of Daniel Allcock, linking these ball quotients to certain finite almost simple groups, some even sporadic like the bimonster group.

Erik Koelink's research is focused on the theory of quantum groups, especially at the level of operator algebras, its representation theory and its connections with special functions and integrable systems. Many aspects of the representation theory of quantum groups are motivated by related questions and problems of a group representation theoretical nature.

Klaas Landsman's previous research programme in noncommutative geometry, groupoids, quantisation theory, and the foundations of quantum mechanics (supported from 2002-2008 by a Pioneer grant from NWO), led to two major new research lines:
1. The use of topos theory in clarifying the logical structure of quantum theory, with potential applications to quantum computation as well as to foundational questions.
2. Emergence with applications to the Higgs mechanism and to Schroedinger's Cat (aka as the measurement problem). A first paper in this direction with third year Honours student Robin Reuvers (2013) generated worldwide attention and led to a new collaboration with experimental physicists Andrew Briggs and Andrew Steane at Oxford and philosopher Hans Halvorson at Princeton.

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

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From geometry, analysis, partial differential equations and mathematical physics to fluid dynamics, meteorology and modelling in life sciences – our Masters in Mathematics offers you an extraordinary range of research opportunities that lie at the heart of tackling the key scientific questions of our age. Read more
From geometry, analysis, partial differential equations and mathematical physics to fluid dynamics, meteorology and modelling in life sciences – our Masters in Mathematics offers you an extraordinary range of research opportunities that lie at the heart of tackling the key scientific questions of our age.

PROGRAMME OVERVIEW

This programme reflects and benefits from the strong research activities of the Department of Mathematics.

The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups:
-Mathematics of Life and Social Sciences
-Dynamical Systems and Partial Differential Equations
-Fields, Strings and Geometry
-Fluids, Meteorology and Symmetry

During the first two semesters you will take a range of taught modules from an extensive list of options, followed by an extended research project conducted over the summer under the supervision of a member of the department, culminating in the writing of a dissertation.

PROGRAMME STRUCTURE

This programme is studied full-time over one academic year. It consists of eight taught modules and a dissertation. The following modules are indicative, reflecting the information available at the time of publication. Please note that not all modules described are compulsory and may be subject to teaching availability and/or student demand.
-Maths of Weather
-Graphs and Networks
-Manifolds and Topology
-Quantum Mechanics
-Numerical Solutions of PDEs
-Functional Analysis and Partial Differential Equations
-Nonlinear Wave Equations
-Representation Theory
-Advanced Techniques in Mathematics
-Lie Algebras
-Nonlinear Patterns
-Geometric Mechanics
-Relativity
-Ecological and Epidemiological Modelling
-Mathematical Biology and Physiology
-Topology
-Non-Commutative Algebra
-Dissertation

CAREERS

Mathematics is not only central to science, technology and finance-related fields, but the logical insight, analytical skills and intellectual discipline gained from a mathematical education are highly sought after in a broad range of other areas such as law, business and management.

There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.

As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied.

EDUCATIONAL AIMS OF THE PROGRAMME

-To provide graduates with a strong background in advanced mathematical theory and its applications to the solution of real problems
-To develop students understanding of core areas in advanced mathematics including standard tools for the solution of real life applied mathematical problems
-To develop the skill of formulating a mathematical problem from a purely verbal description
-To develop the skill of writing a sophisticated mathematical report and, additionally, in presenting the results in the form of an oral presentation
-To lay a foundation for carrying out mathematical research leading to a research degree and/or a career as a professional mathematician in an academic or non-academic setting

PROGRAMME LEARNING OUTCOMES

Knowledge and understanding
-Knowledge of the core theory and methods of advanced pure and applied mathematics and how to apply that theory to real life problems
-An in-depth study of a specific problem arising in a research context

Intellectual / cognitive skills
-Ability to demonstrate knowledge of key techniques in advanced mathematics and to apply those techniques in problem solving
-Ability to formulate a mathematical description of a problem that may be described only verbally
-An understanding of possible shortcomings of mathematical descriptions of reality
-An ability to use software such as MATLAB and IT facilities more generally including research databases such as MathSciNet and Web of Knowledge

Professional practical skills
-Fluency in advanced mathematical theory
-The ability to interpret the results of the application of that theory
-An awareness of any weaknesses in the assumptions being made and of possible shortcomings with model predictions
-The skill of writing an extended and sophisticated mathematical report and of verbally summarising its content to specialist and/or non-specialist audiences

Key / transferable skills
-Ability to reason logically and creatively
-Effective oral presentation skills
-Written report writing skills
-Skills in independent learning
-Time management
-Use of information and technology

GLOBAL OPPORTUNITIES

We often give our students the opportunity to acquire international experience during their degrees by taking advantage of our exchange agreements with overseas universities.

In addition to the hugely enjoyable and satisfying experience, time spent abroad adds a distinctive element to your CV.

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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. Read more

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 course has been developed to enable you to develop advanced knowledge and skills in the following areas. i) Business Analytical Methods and Information Technology. Read more
The course has been developed to enable you to develop advanced knowledge and skills in the following areas:
i) Business Analytical Methods and Information Technology
ii) Business Problem Structuring and Solving
iii) Consultancy Skills in the Business Environment

These themes are explored through modules in Business Analytics, Computer Simulation, Creative Problem Solving, Consultancy Skills and Business Statistics. The course also includes a project based module where you will solve a problem for a client using the knowledge and skills acquired during your study. There is then a further applied consultancy project, which allows you to independently research, investigate and analyse a current business problem.

About the course

The course focuses on:
-Computational, mathematical, philosophical and management science approaches to business analysis
-Developing problem solving skills
-Enhancing your ability to use business software and other information technology
-Encouraging independent and creative thinking
-Effective communication in all formats appropriate to a business environment

Why choose this course?

This Master's in Business Analysis and Consultancy aims to provide you with the analytical knowledge and skills required to be a successful consultant in the modern business environment.

Three key reasons to study Business Analysis and Consultancy at the Hertfordshire Business School:
-It is a hands-on, practical programme
-It is client-facing so it counts as work experience
-It is a unique programme, informed by the latest research and consultancy in the area

You will gain experience of applying these skills to real consultancy (working with a local organisation) in the complex context in which organisations operate. You will also experience a range of teaching, learning and assessment methods, which will enable you to gain - and be confident in - the skills of modelling, analysis and consulting. All this should directly improve your employment prospects.

The programme is delivered by the Business Analysis and Statistics (BAS) group at Hertfordshire Business School. The BAS group is very strong in the areas of Business Analytics and Consultancy, and its members have diverse experience and expertise in mathematical, computational and philosophical methods of analysis. The group is home to the Statistical Services and Consultancy Unit which does commercial consultancy carried out by members of the group. The course is informed by the cutting edge research undertaken by members of the group.

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Applied Mathematical Sciences offers a clear and relevant gateway into a successful career in business, education or scientific research. Read more
Applied Mathematical Sciences offers a clear and relevant gateway into a successful career in business, education or scientific research. The programme arms students with the essential knowledge required by all professional mathematicians working across many disciplines. You will learn to communicate their ideas effectively to peers and others, as well as the importance of research, planning and self-motivation.

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;
Optimization;
Dynamical Systems;
Applied Mathematics (recommended);
Applied Linear Algebra (recommended).

Optional Courses

:

Mathematical Ecology;
Functional Analysis;
Numerical Analysis of ODEs;
Pure Mathematics;
Statistical Methods;
Stochastic Simulation;
Software Engineering Foundations;
Mathematical Biology and Medicine;
Partial Differential Equations;
Numerical Analysis;
Geometry.

Typical project subjects

:

Pattern Formation of Whole Ecosystems;
Climate Change Impact;
Modelling Invasive Tumour Growth;
Simulation of Granular Flow and Growing Sandpiles;
Finite Element Discretisation of ODEs and PDEs;
Domain Decomposition;
Mathematical Modelling of Crime;
The Geometry of Point Particles;
Can we Trust Eigenvalues on a Computer?

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Climate change is recognised as having potentially huge impacts on the environment and on human society. Read more
Climate change is recognised as having potentially huge impacts on the environment and on human society. This programme aims to provide an understanding of climate change causes, impacts, mitigation and adaptation measures from a life science perspective in conjunction with developing a wide variety of mathematical modelling skills that can be used to investigate the impacts of climate change.

The programme closely follows the structure of our Applied Mathematical Sciences MSc. Two of the mandatory courses will specifically focus on understanding the issues related to climate change and are taught by the School of Life Sciences.

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;
Mathematical Ecology;
Climate Change: Causes and Impacts;
Climate Change: Mitigation and Adaptation Measures;
Dynamical Systems (recommended);
Stochastic Simulation (recommended)

Optional Courses

Optimization;
Mathematical Biology and Medicine;
Numerical Analysis of ODEs;
Applied Mathematics;
Statistical Methods;
Applied Linear Algebra;
Partial Differential Equations;
Numerical Analysis;
Geometry;
Bayesian Inference.

Typical project subjects

Population Cycles of Forest Insects;
Climate Change Impact;
The replacement of Red Squirrels by Grey Squirrels in the UK;
Vegetation Patterns in Semi-arid Environments;
Daisyworld: A Simple Land Surface Climate Model.

The final part of the MSc is an extended project in mathematical modelling the impacts of climate change on environmental systems, giving the opportunity to investigate a topic in some depth guided by leading research academics.

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The School of Mathematics and Alliance Manchester Business School at the University of Manchester have combined their academic strength and practical expertise to deliver the 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 Alliance Manchester Business School at the University of Manchester have combined their academic strength and practical expertise to deliver the 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.

Coursework and assessment

Teaching is shared by the School of Mathematics and Alliance Manchester Business School, and delivered through lectures, case studies, seminars and group project-based work.

Career opportunities

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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Our MSc in Mathematical Sciences is a flexible and challenging programme, taught by leading experts in the field. It allows you to develop a wide range of mathematical techniques and gives you a solid foundation to progress to research and employment at the highest levels. Read more
Our MSc in Mathematical Sciences is a flexible and challenging programme, taught by leading experts in the field. It allows you to develop a wide range of mathematical techniques and gives you a solid foundation to progress to research and employment at the highest levels.

Under the guidance of an academic mentor, you will be offered a choice of units spanning the breadth of mathematics. The programme offers a huge variety of possible combinations of units and themes, allowing you to add units from other schools to create an MSc which matches your interests. Its taught element is followed in June by your chosen research project, which is supervised by an experienced research academic.

The programme gives you the opportunity to increase your understanding of mathematical theory and equips you with fundamental skills in the modelling and analysis of problems. Our graduates are highly sought-after by employers for their strong analytical, communication and organisational skills.

Programme structure

Structure
The MSc in Mathematical Sciences comprises a taught component of 120 credit points (October to May), followed by a 60-credit research project (June to September).

Units
There is an extensive range of possible combinations of units and themes. An academic mentor will advise you on these units and meet regularly with you individually or in small groups throughout the taught component. You are also invited to participate in the wider academic life of the school, including research seminars.

Research project
Research themes include:
-Algebra and Representation Theory
-Applied Probability in Biology and Communications
-Bayesian Modelling and Analysis
-Dynamical systems and Statistical Mechanics
-Ergodic Theory and Dynamical Systems
-Fluid Dynamics
-Geometric Analysis
-Logic and Set Theory
-Material Science
-Monte Carlo Methods
-Nonparametric Regression
-Number Theory
-Probability: Scaling limits and Statistical Physics
-Quantum Information
-Quantum Chaos
-Random Matrix Theory
-Time Series and Finance

Careers

This programme provides you with quantitative research, reasoning and problem solving skills that will be valuable in your future career. Mathematics graduates find employment in finance, accountancy, research, teaching and management.

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