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Masters Degrees (Applied Mathematics)

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The Applied Mathematics group in the School of Mathematics at the University of Manchester has a long-standing international reputation for its research. Read more
The Applied Mathematics group in the School of Mathematics at the University of Manchester has a long-standing international reputation for its research. Expertise in the group encompasses a broad range of topics, including Continuum Mechanics, Analysis & Dynamical Systems, Industrial & Applied Mathematics, Inverse Problems, Mathematical Finance, and Numerical Analysis & Scientific Computing. The group has a strongly interdisciplinary research ethos, which it pursues in areas such as Mathematics in the Life Sciences, Uncertainty Quantification & Data Science, and within the Manchester Centre for Nonlinear Dynamics.

The Applied Mathematics group offers the MSc in Applied Mathematics as an entry point to graduate study. The MSc has two pathways, reflecting the existing strengths within the group in numerical analysis and in industrial mathematics. The MSc consists of five core modules (total 75 credits) covering the main areas of mathematical techniques, modelling and computing skills necessary to become a modern applied mathematician. Students then choose three options, chosen from specific pathways in numerical analysis and industrial modelling (total 45 credits). Finally, a dissertation (60 credits) is undertaken with supervision from a member of staff in the applied mathematics group with the possibility of co-supervision with an industrial sponsor.

Aims

The course aims to develop core skills in applied mathematics and allows students to specialise in industrial modelling or numerical analysis, in preparation for study towards a PhD or a career using mathematics within industry. An important element is the course regarding transferable skills which will link with academics and employers to deliver important skills for a successful transition to a research career or the industrial workplace.

Special features

The course features a transferable skills module, with guest lectures from industrial partners. Some dissertation projects and short internships will also be available with industry.

Teaching and learning

Students take eight taught modules and write a dissertation. The taught modules feature a variety of teaching methods, including lectures, coursework, and computing and modelling projects (both individually and in groups). The modules on Scientific Computing and Transferable Skills particularly involve significant project work. Modules are examined through both coursework and examinations.

Coursework and assessment

Assessment comprises course work, exams in January and May, followed by a dissertation carried out and written up between June and September. The dissertation counts for 60 credits of the 180 credits and is chosen from a range of available projects, including projects suggested by industrial partners.

Course unit details

CORE (75 credits)
1. Mathematical methods
2. Partial Differential Equations
3. Scientific Computing
4. Dynamical Systems
5. Transferrable skills for mathematicians

Industrial modelling pathway
1 Continuum mechanics
2. Stability theory
3. Conservation and transport laws

Numerical analysis pathway
1. Numerical linear algebra
2. Finite Elements
3. Optimization and variational calculus

Career opportunities

The programme will prepare students for a career in research (via entry into a PhD programme) or direct entry into industry. Possible subsequent PhD programmes would be those in mathematics, computer science, or one of the many science and engineering disciplines where applied mathematics is crucial. The programme develops many computational, analytical, and modelling skills, which are valued by a wide range of employers. Specialist skills in scientific computing are valued in the science, engineering, and financial sector.

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The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. Read more
The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. It is the medium for expressing knowledge about many physical phenomena and is concerned with patterns, systems, and structures unrestricted by any specific application, but also allows for applications across many disciplines.

Why this programme

-The University of Glasgow’s School of Mathematics and Statistics is ranked 4th in Scotland (Complete University Guide 2015).
-The School has a strong international reputation in pure and applied mathematics research and our PGT programmes in Mathematics offer a large range of courses ranging from pure algebra and analysis to courses on mathematical biology and fluids.
-You will be taught by experts across a wide range of pure and applied mathematics and you will develop a mature understanding of fundamental theories and analytical skills applicable to many situations.
-You will participate in an extensive and varied seminar programme, are taught by internationally renowned lecturers and experience a wide variety of projects.
-Our students graduate with a varied skill set, including core professional skills, and a portfolio of substantive applied and practical work.
-With a 94% overall student satisfaction in the National Student Survey 2014, the School of Mathematics and Statistics combines both teaching excellence and a supportive learning environment.

Programme structure

Modes of delivery of the Masters in Mathematics/Applied Mathematics include lectures, laboratory classes, seminars and tutorials and allow students the opportunity to take part in project work.

If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).

You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.

Level-H courses (10 or 20 credits)
-Algebraic & geometric topology
-Continuum mechanics & elasticity
-Differential geometry
-Fluid mechanics
-Functional analysis
-Further complex analysis
-Galois theory
-Mathematical biology
-Mathematical physics
-Numerical methods
-Number theory
-Partial differential equations
-Topics in algebra

Level-M courses (20 credits)
-Advanced algebraic & geometric topology
-Advanced differential geometry & topology
-Advanced functional analysis
-Advanced methods in differential equations
-Advanced numerical methods
-Biological & physiological fluid mechanics
-Commutative algebra & algebraic geometry
-Elasticity
-Fourier analysis
-Further topics in group theory
-Lie groups, lie algebras & their representations
-Magnetohydrodynamics
-Operator algebras
-Solitons
-Special relativity & classical field theory

SMSTC courses (20 credits)
-Algebra 1
-Algebra 2
-Applied analysis and PDEs 1
-Applied analysis and PDEs 2
-Applied mathematical methods 1
-Applied mathematical methods 2
-Geometry and topology 1
-Geometry and topology 2
-Mathematical modelling 1
-Mathematical modelling 2
-Pure analysis 1
-Pure analysis 2.

The project titles are offered each year by academic staff and so change annually

Career prospects

Career opportunities are diverse and varied and include academia, teaching, industry and finance.

Graduates of this programme have gone on to positions such as:
-Maths Tutor at a university.

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Applied Mathematics is concerned with mathematical methods used in industry, science, business and engineering. Studying this subject at doctoral level is an opportunity to become an specialist in the mathematics that powers business and society. Read more
Applied Mathematics is concerned with mathematical methods used in industry, science, business and engineering. Studying this subject at doctoral level is an opportunity to become an specialist in the mathematics that powers business and society.

As a researcher in the School of Mathematics and Physics, you have the opportunity to work with specialists in the field and may have the chance to develop national and international collaborations.

Research in the School follows two distinct strands: computational physics/applied mathematics and pure mathematics. Research in applied mathematics is focused on the development of numerical methods and algorithms for solving various equations found in materials science, specifically in the field of nanomaterials. This includes advanced parallelisation and adaptation of the methods for modern supercomputers.

Research Areas, Projects & Topics

Main Research Areas:
-Numerical Methods for non-linear Partial Differential Equations in Materials Science
-High Performance Computing in Materials Science

For information about the School’s research activity please visit: http://www.lincoln.ac.uk/home/smp/research/

How You Study

You can benefit from specialist computational facilities, training programmes to enhance your research skills and support from dedicated academic supervisors. You will be supported and encouraged to submit papers to international scientific journals, present your findings at conferences and share knowledge with colleagues across the University.

Due to the nature of postgraduate research programmes, the vast majority of your time will be spent in independent study and research. You will have meetings with your academic supervisors, however the regularity of these will vary depending on your own individual requirements, subject area, staff availability and the stage of your programme.

How You Are Assessed

A PhD is usually awarded based on the quality of your thesis and your ability in an oral examination (viva voce) to present and successfully defend your chosen research topic.

Career and Personal Development

Applied Mathematics students have the opportunity to develop the problem solving skills that may lead to careers in academia, research or industry. 

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An MSc by Research in Applied Mathematics gives students the opportunity to conduct research into areas of mathematics with practical applications in business and industry. Read more
An MSc by Research in Applied Mathematics gives students the opportunity to conduct research into areas of mathematics with practical applications in business and industry.

As a researcher in the School of Mathematics and Physics, you have the opportunity to work with specialists in the field and may have the chance to develop national and international collaborations.

Research in the School follows two distinct strands: computational physics/applied mathematics and pure mathematics. Research in applied mathematics is focused on the development of numerical methods and algorithms for solving various equations found in materials science, specifically in the field of nanomaterials. This includes advanced parallelisation and adaptation of the methods for modern supercomputers.

Research Areas, Projects & Topics

Main Research Areas:
-Numerical Methods for Non-Liner Partial Differential Equations in Materials Science
-High Performance Computing in Materials Science.

For detailed information about the School’s research activity please visit: http://www.lincoln.ac.uk/home/smp/research/

How You Study

You can benefit from specialist computational facilities, training programmes to enhance your research skills and support from dedicated academic supervisors. You will be supported and encouraged to submit papers to international scientific journals, present your findings at conferences and share knowledge with colleagues across the University.

Due to the nature of postgraduate research programmes, the vast majority of your time will be spent in independent study and research. You will have meetings with your academic supervisor, however the regularity of these will vary depending on your own individual requirements, subject area, staff availability and the stage of your programme.

How You Are Assessed

The MSc by Research involves writing a Master's thesis under the supervision of a member of academic staff on a topic to be agreed with your supervisor. The MSc by Research is usually awarded based on the quality of your thesis and your ability in an oral examination (viva voce) to present and successfully defend your chosen research topic.

Career and Personal Development

Applied Mathematics students have the opportunity to develop the problem solving skills that may lead to careers in academia, research or industry. 

The University Careers and Employability Team offer qualified advisors who can work with you to provide tailored, individual support and careers advice during your time at the University. As a member of our alumni we also offer one-to-one support in the first year after completing your course, including access to events, vacancy information and website resources; with access to online vacancies and virtual and website resources for the following two years.

This service can include one-to-one coaching, CV advice and interview preparation to help you maximise your future opportunities.
The service works closely with local, national and international employers, acting as a gateway to the business world.

Visit our Careers Service pages here http://bit.ly/1lAS1Iz.

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This course will provide you with the opportunity to learn a core of advanced pure and applied mathematics, together with a range of more specialised options. Read more
This course will provide you with the opportunity to learn a core of advanced pure and applied mathematics, together with a range of more specialised options.

These will equip you with a range of mathematical skills in problem solving, project work and presentation. This will enable you to take a prominent role in a wide spectrum of employment and research.

The very broad choice of modules available on this course will introduce you to a wide range of applications of mathematics.

They cover all areas of applied mathematics and mathematical physics, reflecting the research interests of the Applied Mathematics and Mathematical Physics section of the Department of Mathematics.

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Why does one car have more air resistance than another? How can a satellite be kept in an orbit around the earth? Applied mathematicians provide the necessary theoretical background to such questions. Read more
Why does one car have more air resistance than another? How can a satellite be kept in an orbit around the earth? Applied mathematicians provide the necessary theoretical background to such questions.

Applied Mathematics is concerned with the development and exploitation of mathematical tools for the analysis and control of technological problems. Mathematical modelling of the problem at hand plays a basic role, followed by (numerical) analysis and (computer) simulation. Interaction with other disciplines and with specialists in the fields of application is essential.

Two specialisations

- Systems and control
This specialisation deals with the mathematics behind designing stable controllers for satellites, purification plants or more general technical processes. Questions that arise include: is it possible to suppress perturbations in a system? Or, how can one stabilize and control a system without causing shocks?

- Computational science and numerical mathematics
This specialisation emphasizes modelling, analysis and the simulation of fluid flow problems. Although the applications can be quite diverse, the basic mathematical methods are much the same. If you are capable of computing the flow of air, you are able to predict the weather, and to design cars and aeroplanes. People who can simulate the flow of water can compute the optimal shape of ships, harbours and dikes.

Why in Groningen?

- Typical for Applied Mathematic in Groningen: the connection between mathematical theory and real-life problems
- You can combine courses from both Mathematics and Applied Mathematics
- Courses include related fields, e.g. Econometrics and Physics
- Internship and research opportunities

Job perspectives

A Master's degree in Applied Mathematics opens up many job opportunities. During the Master's programme you will learn to think in a logical, systematic, and problem-oriented way in a multidisciplinary environment. After having finished the programme you will be able to apply mathematics to a technical problem, and hence to work at the interface between theory and practice. These qualities are highly appreciated by employers.

Job opportunities are available in industrial companies, research institutes, as well as in universities. Examples of companies looking for applied mathematicians include Gasunie, Philips, Stork, Shell, Corus, KPN and small engineering bureaus. Examples of research institutes are the National Aerospace Laboratory (NLR, the picture on these pages comes from the NLR), WL/Delft Hydraulics, KNMI and TNO.You can start a university career by working as a PhD student, which means working for four years on a research project and writing a thesis. After having successfully defended this thesis, you will be awarded a PhD degree. Afterwards you can continue an academic career or start a career in industry.

Job examples

- Research institutes
- Engineering bureaus
- Industrial companies
- Universities

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The first intake for this course will be September 2015. The focus of this course is using mathematics to solve real world problems, such as in finance, energy, engineering or scientific research. Read more
The first intake for this course will be September 2015.

The focus of this course is using mathematics to solve real world problems, such as in finance, energy, engineering or scientific research. The combination of the applied nature of the mathematics that is taught, with the masters level of this course, makes this qualification highly attractive to employers.

Why study Applied Mathematics at Dundee?

Many of the topics taught are directly linked to the research that we do, so you will be learning at the cutting edge of applied mathematics.

We are a relatively small division and operate with an excellent staff/student ratio. One advantage of this is that we can get to know each student personally, and so can offer a friendly and supportive learning experience. Staff are ready and willing to help at all levels, and in addition, our Student-Staff Committee meets regularly to discuss matters of importance to our students.

We also offer students the chance to choose a selection of modules from other subject areas such as economics and finance.

Specialist software:
We have a wide selection of mathematical software packages such as MATLAB, Maple and COMSOL, which are used throughout the course.

Weekly seminar programme:
We have a weekly seminar programme in the mathematics division, which features talks in the areas of research strength in the division, Mathematical Biology, Applied Analysis, Magnetohydrodynamics and Numerical Analysis & Scientific Computing.

How you will be taught

You will learn by traditional methods such as lectures, tutorials, and workshops as well as via computer assisted learning. We teach the use of professional mathematical software packages in order to allow you to explore mathematics far beyond the limits of traditional teaching.

Individual reading and study takes a particularly important role in the Summer project. For the project, you will be guided to prepare your research project plan and to develop skills and competence in research including project management, critical thinking and problem solving, project reporting and presentation.

What you will study

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 eight of the following:

Dynamical Systems
Computational Modelling
Statistics & Stochastic Models
Inverse Problems
Mathematical Oncology
Mathematical Ecology & Epidemiology
Mathematical Physiology
Fluid Dynamics
Optimization in Finance and Energy
Personal Transferable Skills
We also offer the option of relacing one or two mathematics modules with modules from subjects such as Global Risk Analysis, Energy Economics, Quantitative Methods and Econometrics for Finance.

How you will be assessed

Assessment is via a mix of open book continual assessment and closed book examinations, with a substantial project completed over the Summer.

Careers

Mathematics is central to the sciences, and to the development of a prosperous, modern society. The demand for people with mathematical qualifications is considerable, and a degree in mathematics is a highly marketable asset.

Mathematics graduates are consistently amongst those attracting the highest graduate salaries and can choose from an ever widening range of careers in research, industry, science, engineering, commerce, finance and education.

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The College of Liberal Arts and Sciences is a thriving center of intellectual excellence that encompasses 14 academic departments and 80 degree programs. Read more
The College of Liberal Arts and Sciences is a thriving center of intellectual excellence that encompasses 14 academic departments and 80 degree programs. Its more than 2,500 students are engaged in a wide variety of challenging courses and hands-on learning experiences that extend across all areas of the humanities and sciences – from the great philosophers and classic literature to the world economy and environmental sustainability.

At the core of each department are faculty members who have garnered national acclaim for their best-selling books, ground-breaking research and creative endeavors. Together, students and their professors explore globally significant subjects and work towards the goal of improving every aspect of the way in which human beings live. To learn more about a specific area of study, click on the left-hand navigation bar for a full listing of academic departments.

The department

The Department of Mathematics provides numerous undergraduate and graduate level courses that will enable you to master the mathematical methods and sophisticated reasoning and problem-solving skills essential to a wide variety of fields. In addition, the department offers a program to become an actuary.

The bachelor’s and master’s degree programs are designed to provide flexibility while emphasizing mathematical reasoning and problem solving, preparing the student for graduate school or a career in mathematics in secondary school teaching, business, industry, government or academia. In addition, a degree in mathematics is regarded as excellent preparation for entrance to professional schools of law, medicine or business.

M.S. in Applied Mathematics

The Master of Science degree program in Applied Mathematics offers specializations in either Classical Mathematics or Computer Mathematics. Classical Mathematics focuses on the foundations of modern mathematical theory, covering linear algebra, numerical methods and complex analysis. Computer Mathematics combines the fields of mathematics and technology through courses such as logic and information, applications of analysis, linear programming and statistics.

The faculty members in the Department of Mathematics are experts in areas such as topological groups, probability theory, differential geometry, number theory, dynamical systems and computer graphics, real analysis, numerical analysis, abstract algebra, combinatorics and history of mathematics.

Many of our graduates have gone on to receive Ph.D.’s from prestigious institutions. LIU Post graduates also are qualified for rewarding positions in actuarial science, insurance, finance, engineering, manufacturing and education.

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This programme involves both taught classes in Applied Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree. Read more
This programme involves both taught classes in Applied Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree. The minimum period of registration is 12 months.

The MRes is an ideal preparation for entry into a PhD programme. Indeed, the MRes programme can be used as the first phase of our fast track PhD programme. This is an excellent option for well-qualified mathematics students who do not have all the necessary mathematical background to start immediately on a PhD in their area of choice. In the fast track programme the MRes thesis is extended over a further period of two years into a PhD thesis.

Each MRes student is assigned a project supervisor who will act as director and mentor in the preparation of the MRes thesis. This gives each student the opportunity to work one-to-one with mathematicians who are international experts in their fields.

In addition to the assessed elements of the course, students are expected to play a full part in the research life of the School. The School has an active seminar programme, and organises international conferences in all areas of mathematics.

About the School of Mathematics

The School of Mathematics is one of seven schools in the College of Engineering and Physical Sciences. The school is situated in the Watson Building on the main Edgbaston campus of the University of Birmingham. There are about 50 academic staff, 15 research staff, 10 support staff, 60 postgraduate students and 600 undergraduate students.
At the School of Mathematics we take the personal development and careers planning of our students very seriously. Jointly with the University of Birmingham's Careers Network we have developed a structured programme to support maths students with their career planning from when they arrive to when they graduate and beyond.

Funding and Scholarships

There are many ways to finance your postgraduate study at the University of Birmingham. To see what funding and scholarships are available, please visit: http://www.birmingham.ac.uk/pgfunding

Open Days

Explore postgraduate study at Birmingham at our on-campus open days.
Register to attend at: http://www.birmingham.ac.uk/pgopendays

Virtual Open Days

If you can’t make it to one of our on-campus open days, our virtual open days run regularly throughout the year. For more information, please visit: http://www.pg.bham.ac.uk

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This course, commonly referred to as Part III, is a one-year taught Master's course in mathematics. Read more
This course, commonly referred to as Part III, is a one-year taught Master's course in mathematics. It is an excellent preparation for mathematical research and it is also a valuable course in mathematics and in its applications for those who want further training before taking posts in industry, teaching, or research establishments.

Students admitted from outside Cambridge to Part III study towards the Master of Advanced Study (MASt). Students continuing from the Cambridge Tripos for a fourth year, study towards the Master of Mathematics (MMath). The requirements and course structure for Part III are the same for all students irrespective of whether they are studying for the MASt or MMath degree.

There are over 200 Part III (MASt and MMath) students each year; almost all are in their fourth or fifth year of university studies. There are normally about 80 courses, covering an extensive range of pure mathematics, probability, statistics and the mathematics of operational research, applied mathematics and theoretical physics. They are designed to cover those advanced parts of the subjects that are not normally covered in a first degree course, but which are an indispensable preliminary to independent study and research. Students have a wide choice of the combination of courses that they offer, though naturally they tend to select groups of cognate courses. Normally classes are provided as back-up to lecture courses.

See the website http://www.graduate.study.cam.ac.uk/courses/directory/maamasapm

Course detail

The structure of Part III is such that students prepare between six and nine lecture courses for examination. These lecture courses may be selected from the wide range offered by both Mathematics Departments. As an alternative to one lecture course, an essay may be submitted. Examinations usually begin in late May, and are scheduled in morning and afternoon sessions, over a period of about two weeks. Two or three hours are allocated per paper, depending on the subject. Details of the courses for the current academic year are available on the Faculty of Mathematics website. Details for subsequent years are expected to be broadly similar, although not identical.

Most courses in the Part III are self-contained. Students may freely mix courses offered by the two Mathematics Departments. Courses are worth either two or three credit units depending on whether they last for 16 or 24 lectures respectively. Candidates for Part III may offer a maximum of 19 credit units for examination. In the past it has been recommended that candidates offer between 17 and 19 units. An essay (should a candidate choose to submit one) counts for 3 credit units. Part III is graded Distinction, Merit, Pass or Fail. A Merit or above is the equivalent of a First Class in other Parts of the Mathematical Tripos.

Learning Outcomes

After completing Part III, students will be expected to have:

- Studied advanced material in the mathematical sciences to a level not normally covered in a first degree;
- Further developed the capacity for independent study of mathematics and problem solving at a higher level;
- Undertaken (in most cases) an extended essay normally chosen from a list covering a wide range of topics.

Format

Courses are delivered predominantly by either 16 or 24 hours of formal lectures, supported by additional examples classes. As an alternative to one lecture course, an essay may be submitted. There is also the possibility of taking a reading course for examination. There are normally additional non-examinable courses taught each year.

Twice a year students have an individual meeting with a member of academic staff to discuss their progress in Part III. Students offering an essay as part of their degree may meet their essay supervisor up to three times during the academic year.

Assessment

Candidates may substitute an essay for one lecture course. The essay counts for 3 credit units.

Lecture courses are assessed by formal examination. Courses are worth either two or three credit units depending on whether they are 16 or 24 hours in length respectively. A 16 hour course is assessed by a 2 hour examination and a 24 hour course, a 3 hour examination. Candidates for Part III may offer a maximum of 19 credit units for examination. In the past it has been recommended that candidates offer between 17 and 19 units.

Continuing

MASt students wishing to apply for the PhD must apply via the Graduate Admissions Office for readmission by the relevant deadline. Applicants will be considered on a case by case basis and offer of a place will usually include an academic condition on their Part III result.

How to apply: http://www.graduate.study.cam.ac.uk/applying

Funding Opportunities

There are no specific funding opportunities advertised for this course. For information on more general funding opportunities, please follow the link below.

General Funding Opportunities http://www.graduate.study.cam.ac.uk/finance/funding

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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. Read more
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.

The MSc, has at its core, fundamental courses in pure mathematics and students will be able to take options from both pure and applied mathematics.

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;
Functional Analysis;
Partial Differential Equations;
Pure Mathematics (recommended).

Optional Courses

Mathematical Ecology;
Optimization;
Numerical Analysis of ODEs;
Applied Mathematics;
Dynamical Systems;
Stochastic Simulation;
Applied Linear Algebra;
Partial Differential Equations;
Numerical Analysis;
Bayesian Inference and Computational Methods;
Geometry.

Typical project subjects

Domain Decomposition;
Mathematical Modelling of Crime;
The Geometry of Point Particles;
Can we Trust Eigenvalues on a Computer?;
Braess Paradox;
The Ising Model: Exact and Numerical Results;
Banach Alegbras.

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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Complex systems with a technological, biological or socio-economic background determine our everyday life. Read more

About the Program

Complex systems with a technological, biological or socio-economic background determine our everyday life. The challenge of modeling these complex systems mathematically demands the following prototypic profile of an "expert mastering a repertoire of modern mathematical and computer based methods for modeling, simulating and optimizing complex systems and knowing how to combine those methods for solving real-world problems".
The term expert is understood in the sense of generalist and not a specialist, since this program aims at teaching a broad spectrum of modern methods.

The two-years English-taught master program "Mathematical Modeling of Complex Systems" focuses on advanced techniques of modeling, simulation and optimization. A substantial set of elective courses allows concentration on areas of individual interest. A mobility window enables the students to study abroad and gain scientific and cultural experience at international partner universities. This program uses English as medium of instruction since its graduates will enter a highly globalized work and research community. Besides that, the participation and enrollment of international candidates is explicitly welcomed.

Application oriented, interdisciplinary seminars link the theoretical basics and concepts of modeling and simulation. Students work in small teams to solve real world problems. This teamwork reflects typical work in applied sciences and corresponds to our paradigm of an "expert mastering a repertoire of methods to solve problems".

Find out more about the program and our campus in Koblenz under:
https://www.uni-koblenz-landau.de/de/koblenz/fb3/mathe/studium/mmcs/

Aims/Career Perspectives

The Master degree in Mathematical Modeling of Complex Systems is to give those possessing extended skills in Mathematics, Physics and Computer Science in theory, experiment and practical application. These skills are complemented with further knowledge in additional topics, individually selected by each student. The degree entitles its holder to exercise professional work in the field of Applied Mathematics and/or Mathematical Modeling in science or industry or to pursue a PhD program in related fields.

Program Structure

The first three terms of the two-years master „Mathematical Modeling of Complex Systems“ consist of core courses in Applied Mathematics and Applied Physics. Elective courses in Applied Mathematics, Applied Physics and Computer Sciences allow each student to set its individual focus. Active use of the gained knowledge and its application to the solution of real-world problems is taught and practiced in a project seminar. This project seminar can be carried out in a three-month period at a research institution, enterprise or at university. The master thesis in the last term and dealing with modeling and simulating a real-world problem, shows the student’s ability to perform independent research work.
The core and elective courses typically include a written or oral exam, the project seminar is graded based an oral presentation and written report of the project results.

You can find an exemplary list of courses and can download a overview of the modules under:
https://www.uni-koblenz-landau.de/de/koblenz/fb3/mathe/studium/mmcs#curriculum

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

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

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

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

Research Foci

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

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

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

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

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

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

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

Facilities

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

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

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Do you have an aptitude and passion for mathematics and statistics, a keen interest in finance and insurance and want to work for a major financial organisation in finance, insurance or the money market? This course will provide you with a deep understanding of the world of finance, and give you the ability to speak its 'language'. Read more
Do you have an aptitude and passion for mathematics and statistics, a keen interest in finance and insurance and want to work for a major financial organisation in finance, insurance or the money market? This course will provide you with a deep understanding of the world of finance, and give you the ability to speak its 'language'. This course combines theory with hands-on practical skills via an industry placement or research project – ensuring you graduate with the right skills increasingly being sought by banks and other financial institutions.

The Master of Financial Mathematics offers advanced training in the core areas of stochastic, financial and insurance modelling, statistical analysis and computational methodology, as well as in a wide range of elective topics from economics, econometrics, finance, mathematics and probability.

Graduates of this course are likely to enter specialist careers in research departments within banks, insurance and consultancy firms or derivatives of valuation and portfolio management within investment houses.

The School of Mathematical Sciences sits within the leading Faculty of Science at Monash University. This vibrant, dynamic and successful School is undergoing a period of growth with the appointment of several new senior academic staff including Professor Gregoire Loeper, Course Director for the Masters of Financial Mathematics. With mathematics as the fundamental underpinning of so many subject areas, sectors and disciplines, the School is also building ever stronger collaborations with relevant industries, including the financial sector.

Visit the website http://www.study.monash/courses/find-a-course/2016/financial-mathematics-s6001?domestic=true

Course Structure

The course is structured in three Parts. Part A. Orientation studies, Part B. Specialist studies, Part C. Applied professional practice. All students complete Part B. Depending upon prior qualifications, you may receive credit for Part A or Part C or a combination of the two.

Part A. Orientation studies
These studies provide an orientation to the field of Financial Mathematics. You will choose studies that complement your current knowledge relevant to financial mathematics, including principles of econometrics, mathematical methods and stochastic processes.

Part B. Specialist studies
These studies will provide you with advanced knowledge and skills relevant to thoughtful, innovative and evidence-based practice in financial modelling and analysis. You will acquire core knowledge of and skills in financial econometrics, and advanced mathematical modelling and computational methods in finance. You will complement these with study in areas of your choice, including interest rate modelling, Markov processes, statistical learning in finance, and global financial markets.

Part C. Applied professional practice
These studies will provide you with the opportunity to apply your knowledge skills developed in Part A and B to "real life" problems, through completing an industry project or an industry internship. Students admitted to the course who have a recognised honours degree or graduate diploma or graduate certificate in a cognate discipline including mathematics or statistics, will receive credit for this part however, should they wish to complete a 24 point research project as part of Part B they should consult with the course convenor.

For more information visit the faculty website - http://www.study.monash/media/links/faculty-websites/science

About Mathematical Sciences

The School of Mathematical Sciences at Monash University is leading the way towards finding effective solutions to some of society's most pressing problems. Maths is the language of science and forms the basis of most of modern science and engineering. Our enthusiastic mathematicians love finding the true magic and beauty in maths and subsequently pass this passion on to their students.

Teaching

Studying maths equips you with a range of valuable, unique skills. Some of the exciting areas mathematicians at Monash are working on include mathematical modelling to predict behaviour, analysis using pure maths, and stochastic processes involving risk, randomness and change.

Mathematics and statistics are also the two cornerstones for decision making and various quantitative activities in commerce, industry, education and defence. From direct and daily experience, most companies and organisations have realised that success depends critically on the level of analytical, quantitative and statistical skills of their workforce and they therefore seek employees with a sound mathematical training.

By studying mathematics at Monash, you will also develop general skills in problem-solving, critical thinking, modelling, learning, analysis, research and creativity, which can be used wherever your career may take you.

Research

The School of Mathematical Sciences focuses on these main areas of research:

- Applied and Computational Mathematics
- Pure Mathematics
- Stochastic Processes

Find out how to apply here - http://www.study.monash/courses/find-a-course/2016/financial-mathematics-s6001?domestic=true#making-the-application

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The objective of this programme of study is to prepare professionals able to deal with complex systems using sophisticated mathematical tools, yet with an engineering attitude. Read more

Mission and goals

The objective of this programme of study is to prepare professionals able to deal with complex systems using sophisticated mathematical tools, yet with an engineering attitude. It harmonises a solid scientific background with a command of advanced methodologies and technologies. The programme is characterised by a continuous synergy between Applied Mathematics and Engineering disciplines- The students may choose among three specialisations:
- Computational Science and Engineering
- Applied Statistics
- Quantitative Finance

See the website http://www.polinternational.polimi.it/educational-offer/laurea-magistrale-equivalent-to-master-of-science-programmes/mathematical-engineering/

Career opportunities

The professional opportunities offered by this course are rather ample and varied: engineering consultancy companies that deal with complex computational problems; manufacturing or civil engineering companies where analyses based on the use of advanced mathematical tools are needed; banks, insurance companies and financial institutions making use of quantitative finance for risk analysis or forecast; companies that require statistical interpretation and the processing of complex data, or the simulation of different scenarios; public and private research institutes and laboratories.

Eligible students

Students holding a Bachelor degree in Mathematical Engineering, or in a related area with a solid background in the core disciplines of the programme, i.e. Applied Mathematics, Computer Science, Applied Physics or other Engineering disciplines are eligible for application. In particular, eligible students' past studies must include courses in different areas of Engineering (among Informatics, Economics & Business Organization, Electrotechnics, Automation, Electronics, Applied Physics, Civil Engineering) for at least 25% of the overall courses, as well as courses in different areas of Mathematics (Mathematical Analysis, Linear Algebra, Geometry, Probability, Statistics, Numerical Analysis, Optimization) for at least 33% of the overall courses.
The following tracks are available:
1. Computational Science and Engineering
2. Applied Statistics
3. Quantitative Finance

Eligible students must clearly specify the track they are applying for in their motivation letter.

Presentation

See http://www.polinternational.polimi.it/uploads/media/Mathematical_Engineering.pdf
The Master of Science in Mathematical Engineering (MSME) aims to form an innovative and flexible professional profile, endowed with a wide spectrum of basic scientific notions and engineering principles, together with a deep knowledge of modern pure and applied mathematical techniques. MSME is characterized by a continuous synergy between Mathematics and Engineering methods, oriented to the modelling, analysis and solution of complex planning, control and management problems, and provides the students with the possibility to face problems from various scientific, financial and/or technological areas. The MSME graduates can find employment in Engineering companies specialized in handling complex computational problems, requiring a multidisciplinary knowledge; in companies manufacturing industrial goods for which design analysis based on the use of advanced mathematical procedures are required; in service societies, banks, insurance companies, finance or consultant agencies for the statistical interpretation and the simulation of complex situations related to the analysis of large number of data (e.g. management and optimization of services, data mining, information retrieval) or for handling financial products and risk management; in public and private institutions. The programme is taught in English.

Subjects

Three main tracks available:
1. Computational Science for Engineering
Real and functional analysis; algorithms and parallel programming; numerical and theoretical analysis for partial differential equations; fluid mechanics; computational fluid dynamics advanced programming techniques for scientific computing;

2. Statistics
Real and functional analysis; algorithms and parallel programming; stochastic dynamical models; applied statistics, model identification and data analysis; Bayesian statistics

3. Mathematical Finance
Real and functional analysis; algorithms and parallel programming; stochastic differential equations; mathematical finance; financial engineering; model identification and data analysis.

In the motivation letter the student must clearly specify the track he/she is applying for.

See the website http://www.polinternational.polimi.it/educational-offer/laurea-magistrale-equivalent-to-master-of-science-programmes/mathematical-engineering/

For contact information see here http://www.polinternational.polimi.it/educational-offer/laurea-magistrale-equivalent-to-master-of-science-programmes/mathematical-engineering/

Find out how to apply here http://www.polinternational.polimi.it/how-to-apply/

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