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Masters Degrees (Scientific Computation)

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Scientific computing is a new and growing discipline in its own right. It is concerned with harnessing the power of modern computers to carry out calculations relevant to science and engineering. Read more

Overview

Scientific computing is a new and growing discipline in its own right. It is concerned with harnessing the power of modern computers to carry out calculations relevant to science and engineering.
By its very nature, scientific computing is a fundamentally multidisciplinary subject. The various application areas give rise to mathematical models of the phenomena being studied.

Examples range in scale from the behaviour of cells in biology, to flow and combustion processes in a jet engine, to the formation and development of galaxies. Mathematics is used to formulate and analyse numerical methods for solving the equations that come from these applications.

Implementing the methods on modern, high performance computers requires good algorithm design to produce efficient and robust computer programs. Competence in scientific computing thus requires familiarity with a range of academic disciplines. The practitioner must, of course, be familiar with the application area of interest, but it is also necessary to understand something of the mathematics and computer science involved.

Whether you are interested in fundamental science, or a technical career in business or industry, it is clear that having expertise in scientific computing would be a valuable, if not essential asset. The question is: how does one acquire such expertise?

This course is one of a suite of MScs in Scientific Computation that are genuinely multidisciplinary in nature. These courses are taught by internationally leading experts in various application areas and in the core areas of mathematics and computing science, fully reflecting the multidisciplinary nature of the subject. The courses have been carefully designed to be accessible to anyone with a good first degree in science or engineering. They are excellent preparation either for research in an area where computational techniques play a significant role, or for a career in business or industry.

Key facts:
- This course is offered in collaboration with the School of Computer Science.
- It is one of a suite of courses focusing on scientific computation.
- The School of Mathematical Sciences is one of the largest and strongest mathematics departments in the UK, with over 50 full-time academic staff.
- In the latest independent Research Assessment Exercise, the school ranked 8th in the UK in terms of research power across the three subject areas within the School of Mathematical Sciences (pure mathematics, applied mathematics, statistics and operational research).

Modules

Advanced Techniques for Differential Equations

Computational Linear Algebra

Operations Research and Modelling

Programming for Scientific Computation

Scientific Computation Dissertation

Simulation for Computer Scientists

Stochastic Financial Modelling

Variational Methods

Vocational Mathematics

Data Mining Techniques and Applications

Mathematical Foundations of Programming

English language requirements for international students

IELTS: 6.0 (with no less than 5.5 in any element)

Further information



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The MPhil programme in Scientific Computing is a full-time 12-month course which aims to provide education of the highest quality at Master’s level. Read more
The MPhil programme in Scientific Computing is a full-time 12-month course which aims to provide education of the highest quality at Master’s level. Covering topics of high-performance scientific computing and advanced numerical methods and techniques, it produces graduates with rigorous research and analytical skills, who are well-equipped to proceed to doctoral research or directly into employment in industry, the professions, and the public service. It also provides training for the academic researchers and teachers of the future, encouraging the pursuit of research in computational methods for science and technology disciplines, thus being an important gateway for entering PhD programmes containing a substantial component of computational modelling.

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

Course detail

The MPhil in Scientific Computing has a research and a taught element. The research element is a project on a science or technology topic which is studied by means of scientific computation. The taught element comprises of core lecture courses on topics of scientific computing and elective lecture courses relevant to the science or technology topic of the project. Most of the projects are expected to make use of the University’s High Performance Computing Service.

The students will attend lecture courses during Michaelmas Term (some courses may be during Lent Term) and then they will undertake a substantial Research Project over the next 6 months (from March to the end of August) in a participating Department. The research element aims to provide essential skills for continuation to a PhD programme or employment, as well as to assess and enhance the research capacity of the students. It is based on a science or technology topic which is studied by means of scientific computation. Research project topics will be provided by academic supervisors or by the industrial partners who are working with the participating Departments and may be sponsoring the research project.

There is equal examination credit weighting between the taught and the research elements of the course, which is gained by submitting a dissertation on the project and by written assignments and examinations on the core and elective courses, respectively.

Weighting of the assessed course components is as follows: Dissertation (research) 50%; written assignments on the core courses 25%; written examinations on the elective courses 25%.

Learning Outcomes

By the end of the course, students will have:

- a comprehensive understanding of numerical methods, and a thorough knowledge of the literature, applicable to their own research;
- demonstrated originality in the application of knowledge, together with a practical understanding of how research and enquiry are used to create and interpret knowledge in their field;
- shown abilities in the critical evaluation of current research and research techniques and methodologies;
- demonstrated self-direction and originality in tackling and solving problems, and acted autonomously in the planning and implementation of research.

Format

The taught element comprises core lecture courses on topics of all aspects of scientific computing, and elective lecture courses relevant to the topic of the research project.

The taught element comprises core lecture courses on topics of all aspects of scientific computing, and elective lecture courses relevant to the topic of the research project. There is equal examination credit weighting between the taught and the research elements of the course, which is gained by submitting a dissertation on the project and by written assignments and examinations on the core and elective courses, respectively. Weighting of the assessed course components is as follows: Dissertation (research) 50%; written assignments 25%; written examinations 25%.

The core lectures are on topics of high performance scientific computing numerical analysis and advanced numerical methods and techniques. They are organized by the Centre for Scientific Computing and are taught and examined during the first five months (October-February). Their purpose is to provide the students with essential background knowledge for completing their dissertation and for their general education in scientific computing.

In particular, their objective is to introduce students to the simulation science pipeline of problem identification, modelling, simulation and evaluation - all from the perspective of employing high-performance computing. Numerical discretisation of mathematical models will be a priority, with a specific emphasis on understanding the trade-offs (in terms of modelling time, pre-processing time, computational time, and post-processing time) that must be made when solving realistic science and engineering problems. Understanding and working with computational methods and parallel computing will be a high priority. To help the students understand the material, the lecturers will furnish the courses with practical coursework assignments.

The lectures on topics of numerical analysis and HPC are complemented with hands-on practicals using Linux-based laptops provided by the course (students may bring their own), as well as on the University’s High Performance Computing Service.

Appropriate elective lecture courses are selected from Master’s-level courses offered by the Departments of the School of Physical Sciences, Technology or Biological Sciences. The choice of courses will be such as to provide the students with essential background knowledge for completing their theses and for their general education in the materials science application of the project. They are decided in consultation with the project supervisor. While every effort is made within the Departments to arrange the timetable in a coherent fashion, it is inevitable that some combinations of courses will be ruled out by their schedule, particularly if the choices span more than one department.

Continuing

For continuation to a PhD programme in Scientific Computing, students are required to gain a Distinction (overall grade equal or greater than 75%).

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

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

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

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

Research Foci

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

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

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

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

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

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

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

Facilities

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

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

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The MRes is a Masters degree by research. This means that you are taught core principles and then develop these skills by doing interesting, innovative research, supported by academic staff and peers. Read more
The MRes is a Masters degree by research. This means that you are taught core principles and then develop these skills by doing interesting, innovative research, supported by academic staff and peers. This is structured so that you learn how to plan, organise and manage your time; you learn what it is to be a scientific researcher; you help contribute to the development of new knowledge; you learn intellectual skills such as argumentation, exposition, and reasoning; and you develop as an individual by improving your communication skills, writing, collaborative working and creativity.

The programme is designed for highly competent students who are keen on research-oriented Masters programmes. It consists of a mini-project in the first semester and a major research project, which will be two-thirds of the entire Masters programme. You will also study essential Research Skills, and a further 20 credits of optional modules from the following list:

Introduction to Evolutionary Computation
Introduction to Neural Computation
Intelligent Robotics (Extended)
Intelligent Data Analysis (Extended)
Planning (Extended)

Breakdown of course

Natural computation is the study of computational systems that use ideas and gain inspiration from natural systems, including biological, ecological and physical systems. It is an emerging interdisciplinary area in which appropriate techniques and methods are studied for dealing with large, complex, and dynamic problems. The aims of this programme are to:

Meet the increasing need from industry for graduates equipped with knowledge of natural computation techniques.
Provide a solid foundation in natural computation for graduates to pursue a research and development career in industry or to pursue further studies (e.g. PhD).
Give up-to-date coverage of current topics in natural computation (such as evolutionary algorithms, co-evolution, evolutionary design, nature-inspired optimisation techniques, evolutionary games, novel learning algorithms, artificial neural networks, theory of natural computation).

About the School of Computer Science

The School of Computer Science at University of Birmingham has consistently been ranked in the Top 10 in UK league tables and has regularly achieved high satisfaction scores in National Student Surveys. 95% of our students go into graduate employment (Destination of Leavers from Higher Education Survey 2014/15), and our School is ranked 8th nationally for research quality in the '2014 Research Excellence Framework'.
Our work is regularly presented in international conferences and journals, indicating the high standards we achieve in research. In 2008, the UK Funding Councils undertook a national assessment of the quality of research at British universities, the RAE. Among 81 submissions nationally for computer science, the School is equal 7th in the proportion of 4* awards, for research quality that is world-leading in terms of originality, significance and rigour.

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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Learn how to create artificial information systems that mimic biological systems as well as how to use theoretical insights from AI to better understand cognitive processing in humans. Read more
Learn how to create artificial information systems that mimic biological systems as well as how to use theoretical insights from AI to better understand cognitive processing in humans.
The human brain is a hugely complex machine that is able to perform tasks that are vastly beyond current capabilities of artificial systems. Understanding the brain has always been a source of inspiration for developing artificially intelligent agents and has led to some of the defining moments in the history of AI. At the same time, theoretical insights from artificial intelligence provide new ways to understand and probe neural information processing in biological systems.
On the one hand, the Master’s in Computation in Neural and Artificial Systems addresses how models based on neural information processing can be used to develop artificial systems, probing of human information processing in closed-loop online settings, as well as the development of new machine learning techniques to better understand human brain function.
On the other hand it addresses various ways of modelling and understanding cognitive processing in humans. These range from abstract mathematical models of learning that are derived from Bayesian statistics, complexity theory and optimal control theory to neural information processing systems such as neural networks that simulate particular cognitive functions in a biologically inspired manner. We also look at new groundbreaking areas in the field of AI, like brain computer interfacing and deep learning.

See the website http://www.ru.nl/masters/ai/computation

Why study Computation in Neural and Artificial Systems at Radboud University?
- Our cognitive focus leads to a highly interdisciplinary AI programme where students gain skills and knowledge from a number of different areas such as mathematics, computer science, psychology and neuroscience combined with a core foundation of artificial intelligence.

- Together with the world-renowned Donders Institute, the Behavioural Science Institute and various other leading research centres in Nijmegen, we train our students to become excellent researchers in AI.

- Master’s students are free to use the state-of-the-art facilities available on campus, like equipment for brain imaging as EEG, fMRI and MEG.

- Exceptional students who choose this specialisation have the opportunity to study for a double degree in Artificial Intelligence together with the specialisation in Brain Network and Neuronal Communication. This will take three instead of two years.

- This specialisation offers plenty of room to create a programme that meets your own academic and professional interests.

- To help you decide on a research topic there is a semi-annual Thesis Fair where academics and companies present possible project ideas. Often there are more project proposals than students to accept them, giving you ample choice. We are also open to any of you own ideas for research.

- Our AI students are a close-knit group; they have their own room in which they often get together to interact, debate and develop their ideas. Every student also receives personal guidance and supervision from a member of our expert staff.

Our research in this field

The programme is closely related to the research carried out in the internationally renowned Donders Institute for Brain, Cognition and Behaviour. This institute has several unique facilities for brain imaging using EEG, fMRI and MEG. You will be able to use these facilities for developing new experimental research techniques, as well as for developing new machine learning algorithms to analyse the brain data and integrate them with brain-computer interfacing systems.

Some examples of possible thesis subjects:
- Deep learning
Recent breakthroughs in AI have led to the development of artificial neural networks that achieve human level performance in object recognition. This has led companies like Google and Facebook to invest a lot of research in this technology. Within the AI department you can do research on this topic. This can range from developing deep neural networks to map and decode thoughts from human brain activity to the development of speech recognition systems or neural networks that can play arcade games.

- Brain Computer Interfacing
Brain computer interfaces are systems which decode a users mental state online in real-time for the purpose of communication or control. An effective BCI requires both neuro-scientific insight (which mental states should we decode?) and technical expertise (which measurement systems and decoding algorithms should be used?). A project could be to develop new mental tasks that induce stronger/easier to decode signals, such as using broadband stimuli. Another project could be to develop new decoding methods better able to tease a weak signal from the background noise, such as adaptive-beam forming. Results for both would assessed by performing empirical studies with target users in one of the EEG/MEG/fMRI labs available in the institute.

Career prospects

Our Artificial Intelligence graduates have excellent job prospects and are often offered a job before they have actually graduated. Many of our graduates go on to do a PhD either at a major research institute or university with an AI department. Other graduates work for companies interested in cognitive design and research. Examples of companies looking for AI experts with this specialisation: Google, Facebook, IBM, Philips and the Brain Foundation. Some students have even gone on to start their own companies.

Job positions

Examples of jobs that a graduate of the specialisation in Computation in Neural and Artificial Systems could get:
- PhD researcher on bio-inspired computing
- PhD researcher on neural decoding
- PhD researcher on neural information processing
- Machine learning expert in a software company
- Company founder for brain-based computer games
- Hospital-based designer of assistive technology for patients
- Policy advisor on new developments in neurotechnology
- Software developer for analysis and online visual displays of brain activity

Internship

Half of your second year consists of an internship, giving you plenty of hands-on experience. We encourage students to do this internship abroad, although this is not mandatory. We do have connections with companies abroad, for example in China, Sweden and the United States.

See the website http://www.ru.nl/masters/ai/computation

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The Architectural Computation MRes offers a self-directed route which concentrates on research skills, for those intending to take a doctoral degree or those looking to take their existing architecture and computating experience to a higher level. Read more
The Architectural Computation MRes offers a self-directed route which concentrates on research skills, for those intending to take a doctoral degree or those looking to take their existing architecture and computating experience to a higher level. The programme can be taken alone or as the first year of the EngD VEIV.

Degree information

On completion of the programme, students will be able to use computational techniques in architecture, understand and predict the consequences of their design actions through computational processes, integrate their predictions into the design process, and carry out self-sufficient research into new methods and processes.

Students undertake modules to the value of 180 credits.

The programme consists of taught modules (30 credits), research skills modules (30 credits) and research projects (120 credits).

Core modules:
-Computational Analysis
-Computational Synthesis
-Research Skills (A)
-Research Skills (B)
-Computational Research Project

Optional modules - stand-alone MRes students take:
-Extended Personal Research Project
-First-year EngD VEIV students take:
-Interdisciplinary Group Project
-Personal Research Project

Dissertation/report
Students complete project reports for the research projects listed above.

Teaching and learning
The programme is delivered through a combination of lectures, workshops and seminars as well as individual and collaborative projects. Time is dedicated to studio sessions with experienced tutors who have a track record of research into architecture and computation. Assessment is through unseen examination, 3,000-word term paper and project reports.

Careers

After completing the programme, many graduates go on to join leading architectural and engineering practices, either directly with design teams or with specialist modelling groups. In the past three years, graduates have joined Foster and Partners, Zaha Hadid Architects, KPF Associates, Aedas, Arup and Mott MacDonald.

Employability
Our MRes concentrates on your research skills, offering a self-directed route if you are intending to undertake a doctoral degree or are looking to take your existing architecture and computing experience to a higher level. Alumni have joined (or founded) cutting-edge emerging digital design practices such as United Visual Artists and Moving Brands, or they have moved into academic research.

Why study this degree at UCL?

The UCL Bartlett is the UK's largest multidisciplinary Faculty of the Built Environment, bringing together dozens of scientific and professional specialisms required to research, understand, design, construct and operate the buildings and urban environments of the future. Located in London, it is at the heart of the world's largest cluster of creative architects and engineering firms and has all the resources of a world city to hand.

The Architectural Computation programme at UCL offers a unique perspective on the application of technology to the built environment. The course team, drawn from the world-leading Space Syntax Laboratory, comprises both architects and experts in artificial intelligence.

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This programme trains you in the methods and techniques to apply mathematics to the real world, with a particular emphasis on problem solving and an exposure to different disciplines and industrial problems. Read more
This programme trains you in the methods and techniques to apply mathematics to the real world, with a particular emphasis on problem solving and an exposure to different disciplines and industrial problems.

The programme aims to provide innovative training in interdisciplinary applied mathematics and modern scientific computing. It links mathematics with engineering, biology and other sciences, and gives students direct contact with industry.

It develops an awareness of modern applications of mathematics in an interdisciplinary environment, provides training in mathematical methods, mathematical modelling, scientific computation and other applied techniques, and bridges the gap between theory and applications.

Why study Mathematical Sciences with us?

- Consistently ranked in the top ten of Mathematics league tables
- The most recent assessment of the quality of research being done in academic departments across the UK, (RAE 2008), confirms that our research activity is at the forefront of international excellence
- We have a fully-supported professional placement programme.

Visit the website http://www.bath.ac.uk/science/graduate-school/taught-programmes/msc-modern-application-of-mathematics/

What will I learn?

The MSc Modern Applications of Mathematics specialises in interdisciplinary applications of mathematics, notably in industry and mathematical biology. There is the possibility of a six month placement with industry.

The MSc combines a thorough education in core areas of applied mathematics with interdisciplinary training; there is a wide range of interdisciplinary units to choose from, ranging from astrophysics over cryptography to computational chemistry.

The theory elements will be developed in context, with the students doing an applications based project.

The MSc benefits strongly from close interactions with many industrial companies who come to meet the students and to offer projects. Recent project partners have included:

BAE systems
Airbus
the Met Office
SERCO
Schlumberger
BT
RHM Food Technology
QinetiQ
Hoare-Lea Acoustics

We offer a six month industrial placement as alternative to a three-month project, both leading to a dissertation.

This placement gives the opportunity to work in a company for an extended period of time and to gain in this way first-hand experience in industrial applications of mathematics. Several companies have funded places on offer.

For further information please visit our department pages (http://www.bath.ac.uk/math-sci/).

Career opportunities

Our graduates have gone on to further research in Lausanne, Berlin, Brussels, Frankfurt, and academic posts in Malaysia, Sweden, Germany, Canada, the US and in the UK. Recent employers of Bath graduates include:

British Aerospace
Network Rail
Powergen
Barclays Capital
BNP Paribas
Pfizer
AstraZenaca
MBDA UK Ltd
ATASS

Find out more about the department here - http://www.bath.ac.uk/math-sci/

Find out how to apply here - http://www.bath.ac.uk/science/graduate-school/taught-programmes/how-to-apply/

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This course is designed for students from a mathematical background who wish to apply their skills to understanding the complex behaviour of Earth's atmosphere and oceans. Read more
This course is designed for students from a mathematical background who wish to apply their skills to understanding the complex behaviour of Earth's atmosphere and oceans. This is an exciting interdisciplinary subject, of increasing importance to a society facing climate change.

The focus of the course is on analysing the equations of fluid dynamics and thermodynamics, via mathematical and numerical modelling. Training is thus offered in both modern applied mathematics and atmosphere-ocean science, combining teaching resources from both the School of Mathematics and the School of Earth and Environment. The latter are provided by members of the School's Institute for Climate and Atmospheric Science, part of the National Centre for Atmospheric Science. Only a handful of UK universities are positioned to offer similar interdisciplinary training.

Two-thirds of the course consists of taught modules involving lectures and some computer workshops. Beyond a compulsory core of atmosphere-ocean fluid dynamics, students may choose options from applied maths (e.g., wave and stability theory), atmosphere-ocean science (e.g., climate change processes, weather forecasting), numerical methods and scientific computation. The final third of the course consists of an intensive summer project, in which students conduct an in-depth investigation of a chosen subject related to the course.

Careers
Students will be prepared for postgraduate research in applied mathematics or atmosphere-ocean science, or employment in the environmental sector.

However, given the interdisciplinary nature of the programme, graduates will have expertise and skills in a number of different areas, and should be attractive to wider range of employers.

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The development of new materials lies at the heart of many of the technological challenges we currently face, for example creating advanced materials for energy generation. Read more

Overview

The development of new materials lies at the heart of many of the technological challenges we currently face, for example creating advanced materials for energy generation. Computational modelling plays an increasingly important role in the understanding, development and optimisation of new materials. This four year Doctoral Training Programme on computational methods for material modelling aims to train scientists not only in the use of existing modelling methods but also in the underlying computational and mathematical techniques. This will allow students to develop and enhance existing methods, for instance by introducing new capabilities and functionalities, and also to create innovative new software tools for materials modelling in industrial and academic research. The first year of the CDT is a materials modelling option within the MPhil in Scientific Computing (please see the relevant entry) at the University of Cambridge and a range of additional training elements.

The MPhil in Scientific Computing is administered by the Department of Physics, but it serves the training needs of the Schools of Physical Sciences, Technology and Biological Sciences. The ability to have a single Master’s course for such a broad range of disciplines and applications is achieved by offering core (i.e. common for all students) numerical and High Performance Computing (HPC) lecture courses, and complementing them with elective courses relevant to the specific discipline applications.

In this way, it is possible to generate a bespoke training portfolio for each student without losing the benefits of a cohort training approach. This bespoke course is fully flexible in allowing each student to liaise with their academic or industrial supervisor to choose a study area of mutual interest.

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

Learning Outcomes

By the end of the course, students will have:
- a comprehensive understanding of numerical methods, and a thorough knowledge of the literature, applicable to their own research;
- demonstrated originality in the application of knowledge, together with a practical understanding of how research and enquiry are used to create and interpret knowledge in their field;
- shown abilities in the critical evaluation of current research and research techniques and methodologies;
- demonstrated self-direction and originality in tackling and solving problems, and acted autonomously in the planning and implementation of research.

Teaching

The first year of the CDT has a research as well as a taught element. The students attend lecture courses during the first five months (October-February) and then they will undertake a substantial Research Project over the next 6 months (from March to the end of August) in a participating Department. The research element aims to provide essential skills for a successful completion of the PhD, as well as to assess and enhance the research capacity of the students. It is based on a materials science topic which is studied by means of scientific computation. Research project topics will be provided by academic supervisors or by the industrial partners. Most of the projects are expected to make use the University’s High Performance Computing Service (for which CPU time for training and research has been budgeted for every student).

The taught element comprises core lecture courses on topics of all aspects of scientific computing, and elective lecture courses relevant to the topic of the research project. There is equal examination credit weighting between the taught and the research elements of the course, which is gained by submitting a dissertation on the project and by written assignments and examinations on the core and elective courses, respectively. Weighting of the assessed course components is as follows: Dissertation (research) 50%; written assignments 25%; written examinations 25%.

The core courses are on topics of high-performance scientific computing and advanced numerical methods and techniques; they are taught and examined during the first five months (October-February). Their purpose is to provide the students with essential background knowledge for completing their theses and for their general education in scientific computing.

Appropriate elective courses are selected from Master’s-level courses offered by the Departments of the School of Physical Sciences, Technology or Biological Sciences. The choice of courses will be such as to provide the students with essential background knowledge for completing their theses and for their general education in the materials science application of the project. They are decided in consultation with the project supervisor.

Depending on the materials science application of the research topic, students will follow one of the following two numerical methodology options: a) Continuum methods based on systems of partial differential equations (PDEs, e.g. finite-difference, element or volume methods); or b) atomistic approaches, which can be based on classical particle-based modelling (e.g. molecular dynamics) or on electronic structure- based methods (e.g. density functional theory). The students who take the atomistic modelling options will attend a 12-lecture course before continuing to classical particle-based methods or electronic structure methods. Irrespective of the numerical methodology option, students will attend lecture courses on High Performance Computing topics and elements of Numerical Analysis.

In addition to the comprehensive set of Masters-level courses provided by the MPhil and across the University in the field, which will be available to the CDT students, it will also be possible for students to take supplementary courses (not for examination) at undergraduate level, where a specific need is identified, in order to ensure that any prerequisite knowledge for the Masters courses is in place.

Moreover, depending on their background and circumstances, students may be offered places in the EPSRC-funded Autumn Academy, which takes place just before the start of the academic year (two weeks in September).

Funding Opportunities

Studentships funded by EPSRC and/or Industrial and other partners are available subject to eligibility criteria.

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

Find out how to apply here http://www.graduate.study.cam.ac.uk/courses/directory/pcphpdcms/apply

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

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The techniques we use to model and manipulate data guide the political, financial and social decisions that shape our modern society and are the basis of growth of the economy and success of businesses. Read more
The techniques we use to model and manipulate data guide the political, financial and social decisions that shape our modern society and are the basis of growth of the economy and success of businesses. Technology is growing and evolving at an incredible speed, and both the rate of growth of data we generate and the devices we use to process it can only increase.

Data science is a growing and important field of study with a fast-growing number of jobs and opportunities within the private and public sector. The application of theory and methods to real-world problems and applications is at the core of data science, which aims especially to use and to exploit big data.

If you are interested in solving real-world problems, you like to develop skills to use smart devices efficiently, you want to use and to foster your understanding of mathematics, and you are interested and keen to use statistical techniques and methods to interpret data, MSc Data Science at Essex is for you. You study a balance of solid theory and practical application including:
-Computer science
-Programming
-Statistics
-Data analysis
-Probability

Our Department of Mathematical Sciences has an international reputation in many areas including semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology.

You also benefit from being taught in our School of Computer Science and Electronic Engineering, who are ranked Top 10 in the UK in the 2015 Academic Ranking of World Universities, with more than two-thirds of their research rated ‘world-leading’ or ‘internationally excellent’ (REF 2014).

The collaborative work between our departments has resulted in well-known research in areas including artificial intelligence, data analysis, data analytics, data mining, data science, machine learning and operations research.

Our expert staff

Our Department of Mathematical Sciences is a small but influential department, so our students and staff know each other personally. You never need an appointment to see your tutors and supervisors, just knock on our office doors – we are one of the few places to have an open-door policy, and no issue is too big or small.

The academic staff in our School of Computer Science and Electronic Engineering are conducting world-leading research in areas such as evolutionary computation, brain-computer interfacing, intelligent inhabited environments and financial forecasting.

Specialist staff working on data analytics include Dr Paul Scott, who researches data mining, models of memory and attention, and artificial intelligence, and Professor Maria Fasli, who researches data exploration, analysis and modelling of complex, structured and unstructured data, big data, cognitive agents, and web search assistants.

Specialist facilities

-Unique to Essex is our renowned Maths Support Centre, which offers help to students, staff and local businesses on a range of mathematical problems. Throughout term-time, we can chat through mathematical problems either on a one-to-one or small group basis
-We have our own computer labs for the exclusive use of students in the Department of Mathematical Sciences – in addition to your core maths modules, you gain computing knowledge of software including Matlab and Maple
-We have six laboratories that are exclusively for computer science and electronic engineering students
-All computers run either Windows 7 or are dual boot with Linux
-Software includes Java, Prolog, C++, Perl, Mysql, Matlab, DB2, Microsoft Office, Visual Studio, and Project
-You have access to CAD tools and simulators for chip design (Xilinx) and computer networks (OPNET)
-We also have specialist facilities for research into areas including non-invasive brain-computer interfaces, intelligent environments, robotics, optoelectronics, video, RF and MW, printed circuit milling, and semiconductors
-We host regular events and seminars throughout the year
-Collaborate with the Essex Institute of Data Analytics and Data Science (IADS) and the ESRC Business and Local Government (BLoG) Data Research Centre of the University of Essex
-The UK Data Archive and the Institute for Social and Economic Research (ISER) at Essex contribute to our internationally outstanding data science environment

Your future

With a predicted shortage of data scientists, now is the time to future-proof your career. Data scientists are required in every sector, carrying out statistical analysis or mining data on social media, so our course opens the door to almost any industry, from health, to government, to publishing.

Our graduates are highly sought after by a range of employers and find employment in financial services, scientific computation, decision making support and government, risk assessment, statistics, education and other sectors.

We also offer supervision for PhD, MPhil and MSc by Dissertation. We have an international reputation in many areas such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology, and our staff are strongly committed to research and to the promotion of graduate activities.

We additionally work with our Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

Example structure

-Dissertation (optional)
-MSc Project and Dissertation (optional)
-Applied Statistics
-Machine Learning and Data Mining
-Modelling Experimental Data
-Text Analytics
-Artificial Neural Networks (optional)
-Bayesian Computational Statistics (optional)
-Big-Data for Computational Finance (optional)
-Combinatorial Optimisation (optional)
-High Performance Computing (optional)
-Natural Language Engineering (optional)
-Nonlinear Programming (optional)
-Professional Practice and Research Methodology (optional)
-Programming in Python (optional)
-Information Retrieval (optional)
-Data Science and Decision Making (optional)
-Research Methods (optional)
-Statistical Methods (optional)
-Stochastic Processes (optional)

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Discrete mathematics underlies some vital situations in practical life. Game theory, with roots in mathematics, statistics and economics, is routinely applied to understanding and predicting human behaviour. Read more
Discrete mathematics underlies some vital situations in practical life.

Game theory, with roots in mathematics, statistics and economics, is routinely applied to understanding and predicting human behaviour. Problems of protection of digital information against piracy are closely related to aspects of set systems. And the RSA cryptosystem, used on computers all over the world, depends on classical results of number theory.

Our MSc Discrete Mathematics and its Applications covers many aspects of discrete mathematics and their potential use in practice, and provides you with options in:
-Optimisation
-Machine learning
-Data mining
-Statistics

Our interdisciplinary research recognises that mathematics, including what can be very abstract mathematics, is an essential part of research in many other disciplines.

Our Department of Mathematical Sciences has an international reputation in many areas including semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology.

This course can also be studied to a PGDip level - for more information, please view this web-page: http://www.essex.ac.uk/courses/details.aspx?mastercourse=PG00538&subgroup=2

Our expert staff

Our Department of Mathematical Sciences is a small but influential department, so our students and staff know each other personally. You never need an appointment to see your tutors and supervisors, just knock on our office doors – we are one of the few places to have an open-door policy, and no issue is too big or small.

Our staff have published several well-regarded text books and are world leaders in their individual specialisms, with their papers appearing in learned journals like Communications in Algebra, Studia Logica, International Journal of Algebra and Computation, SIAM Journal in Optimization, IEEE Evolutionary Computation, Computers and Operations Research, Ecology, Journal of Mathematical Biology, and Journal of Statistical Applications in Genetics and Molecular Biology.

Specialist facilities

-Unique to Essex is our renowned Maths Support Centre, which offers help to students, staff and local businesses on a range of mathematical problems. Throughout term-time, we can chat through mathematical problems either on a one-to-one or small group basis
-We have our own computer labs for the exclusive use of students in the Department of Mathematical Sciences – in addition to your core maths modules, you gain computing knowledge of software including Matlab and Maple
-We host regular events and seminars throughout the year
-Our students run a lively Mathematics Society, an active and social group where you can explore your interest in your subject with other students

Your future

Key employability skills you gain from this course include analytic reasoning, problem solving, techniques of discrete mathematics and an understanding of application areas of these techniques, algorithm design and implementation, and data analysis.

Our graduates are highly sought after by a range of employers and find employment in financial services, scientific computation, decision making support and government, risk assessment, statistics, education and other sectors.

We also offer supervision for PhD, MPhil and MSc by Dissertation. We have an international reputation in many areas such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology, and our staff are strongly committed to research and to the promotion of graduate activities.

We additionally work with our Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

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In recent years, finance has been one of the areas where high-calibre mathematicians have been in great demand. Read more
In recent years, finance has been one of the areas where high-calibre mathematicians have been in great demand. With the advent of powerful and yet economically accessible computing, online trading has become a common activity, but many have realised that a certain amount of mathematics is necessary to be successful in such fields.

One of our most popular courses, MSc Mathematics and Finance allows those with a background in mathematics to study finance. Since finance routinely involves modelling and evaluating risk, asset pricing and price forecasting, mathematics has become an indispensable tool for this study.

You explore topics including:
-Models and mathematics in portfolio management
-Risk management in modern banking
-Financial modelling
-Actuarial modelling
-Applied statistics

Our interdisciplinary research recognises that mathematics, including what can be very abstract mathematics, is an essential part of research in many other disciplines.

Our Department of Mathematical Sciences has an international reputation in many areas including semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology.

This course can also be studied to a PGDip level - for more information, please view this web-page: http://www.essex.ac.uk/courses/details.aspx?mastercourse=PG00610&subgroup=2

Our expert staff

Our Department of Mathematical Sciences is a small but influential department, so our students and staff know each other personally. You never need an appointment to see your tutors and supervisors, just knock on our office doors – we are one of the few places to have an open-door policy, and no issue is too big or small.

Our staff have published several well-regarded text books and are world leaders in their individual specialisms, with their papers appearing in learned journals like Communications in Algebra, Studia Logica, International Journal of Algebra and Computation, SIAM Journal in Optimization, IEEE Evolutionary Computation, Computers and Operations Research, Ecology, Journal of Mathematical Biology, and Journal of Statistical Applications in Genetics and Molecular Biology.

Specialist facilities

-Unique to Essex is our renowned Maths Support Centre, which offers help to students, staff and local businesses on a range of mathematical problems. Throughout term-time, we can chat through mathematical problems either on a one-to-one or small group basis
-We have our own computer labs for the exclusive use of students in the Department of Mathematical Sciences – in addition to your core maths modules, you gain computing knowledge of software including Matlab and Maple
-We host regular events and seminars throughout the year
-Our students run a lively Mathematics Society, an active and social group where you can explore your interest in your subject with other students

Your future

There is undoubtedly a shortage of mathematicians in general, and an even greater one of those with knowledge of finance.

Our course produces graduates with a sound background in mathematics and finance. Key employability skills include computing, use of algorithms, data analysis, mathematical modelling and understanding financial statements.

Our graduates are highly sought after by a range of employers and find employment in financial services, scientific computation, decision making support and government, risk assessment, statistics, education and other sectors.

We also offer supervision for PhD, MPhil and MSc by Dissertation. We have an international reputation in many areas such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology, and our staff are strongly committed to research and to the promotion of graduate activities.

We additionally work with our Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

Example structure

-Dissertation
-Research Methods
-Financial Modelling
-Mathematics of Portfolios
-Research Methods in Finance: Empirical Methods in Finance
-Stochastic Processes
-Applied Statistics (optional)
-Bank Strategy and Risk (optional)
-Bayesian Computational Statistics (optional)
-Combinatorial Optimisation (optional)
-Derivative Securities (optional)
-Economics of Financial Markets (optional)
-Financial Derivatives (optional)
-Ordinary Differential Equations (optional)
-Partial Differential Equations (optional)
-Statistical Methods (optional)
-Metric Spaces

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Mathematics is the language that underpins the rest of science. Our Department of Mathematical Sciences has an international reputation in many areas like such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology. Read more
Mathematics is the language that underpins the rest of science. Our Department of Mathematical Sciences has an international reputation in many areas like such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology.

Graduate Diplomas last for six to nine months (full-time) and include the modules and assessed work of a Masters, without a dissertation. Our Graduate Diploma in Mathematics gives you training in basic mathematics techniques if your first degree contained only a modest amount of mathematics, so that you can proceed to a Masters in mathematics.

At Essex, Mathematics has truly broad reach; we are working on projects ranging from the economic impact of the behaviour of dairy cows, to understanding crowd behaviour through modelling a zombie apocalypse, to circular Sudoku and other puzzles. Our interdisciplinary research recognises that mathematics, including what can be very abstract mathematics, is an essential part of research in many other disciplines.

You therefore gain an exceptional range of knowledge and skills that are currently in demand in mathematically oriented employment; in business, commerce, industry, government service, education and in the wider economy.

Our expert staff

Our Department of Mathematical Sciences is a small but influential department, so our students and staff know each other personally. You never need an appointment to see your tutors and supervisors, just knock on our office doors – we are one of the few places to have an open-door policy, and no issue is too big or small.

Our staff have published several well-regarded text books and are world leaders in their individual specialisms, with their papers appearing in learned journals like Communications in Algebra, Studia Logica, International Journal of Algebra and Computation, SIAM Journal in Optimization, IEEE Evolutionary Computation, Computers and Operations Research, Ecology, Journal of Mathematical Biology, and Journal of Statistical Applications in Genetics and Molecular Biology.

Specialist facilities

-Unique to Essex is our renowned Maths Support Centre, which offers help to students, staff and local businesses on a range of mathematical problems. Throughout term-time, we can chat through mathematical problems either on a one-to-one or small group basis
-We have our own computer labs for the exclusive use of students in the Department of Mathematical Sciences – in addition to your core maths modules, you gain computing knowledge of software including Matlab and Maple
-We host regular events and seminars throughout the year
-Our students run a lively Mathematics Society, an active and social group where you can explore your interest in your subject with other students

Your future

Our graduates are highly sought after by a range of employers and find employment in financial services, scientific computation, decision making support and government, risk assessment, statistics, education and other sectors.

We also offer supervision for PhD, MPhil and MSc by Dissertation. We have an international reputation in many areas such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology, and our staff are strongly committed to research and to the promotion of graduate activities.

We additionally work with our Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

Example structure

-Applied Statistics (optional)
-Bayesian Computational Statistics (optional)
-Combinatorial Optimisation (optional)
-Complex Variables and Applications (optional)
-Contingencies I
-Contingencies II
-Cryptography and Codes
-Finance and Financial Reporting (optional)
-Financial Derivatives (optional)
-Graph Theory (optional)
-Introduction to Numerical Methods (optional)
-Linear Algebra (optional)
-Mathematical Biology (optional)
-Mathematical Methods (optional)
-Mathematics of Portfolios (optional)
-Modelling Experimental Data (optional)
-Nonlinear Programming (optional)
-Ordinary Differential Equations (optional)
-Partial Differential Equations (optional)
-Project: Mathematics (optional)
-Quantum Mechanics (optional)
-Real Analysis (optional)
-Statistical Methods (optional)
-Statistics II (optional)
-Stochastic Processes (optional)
-Survival Analysis (optional)
-The Laws of Physics (optional)
-Vector Calculus (optional)

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Mathematics is an indispensible subject for quantitative understanding and logical thinking. It is employed as a formidable and powerful tool in science, engineering, and finance, and as such the learning and teaching of mathematics is of vital importance. Read more
Mathematics is an indispensible subject for quantitative understanding and logical thinking. It is employed as a formidable and powerful tool in science, engineering, and finance, and as such the learning and teaching of mathematics is of vital importance. The aim of the Master of Science in Mathematics for Educators (MAED) is to enrich a mathematics educator’s knowledge of mathematics. It will particularly benefit teachers in secondary schools and tutorial educational institutions. The degree is meant to allow these teachers to enhance their mathematical knowledge and teaching skills with the dual benefit of: (i) Career advancement facilitation of the individual, and (ii) Better teachers for society.

Strengths of the HKUST MAED Program

The HKUST Mathematics Department is a diverse department with strengths in the three areas of Applied Mathematics, Pure Mathematics, and Statistics/Financial Mathematics. The Department is leveraging its subject diversity to offer a program which both broadens and deepens an educator's appreciation and comprehension of mathematics with the goal of making them better teachers of mathematics. The courses of the program cover topics ranging from number theory and combinatorics, to geometry, to frontiers in application of mathematics, to training in mathematics problem solving. They promote student intellectual development, and teaching craft, and they provide a basis for student achievement of academic and professional goals.

Curriculum

Students must complete 26 credits consisting of 24 credits from 8 lecture courses and 2 credits from a project course. The requirements are: (i) 5 core courses comprising 15 credits, (ii) 3 elective courses comprising 9 credits, and (iii) 1 project course of 2 credits.

Core courses:
-MAED 5021 Mathematical analysis and its applications I
-MAED 5111 Classical and abstract algebra
-MAED 5121 Algebra and its applications I
-MAED 5211 Classical and modern geometry
-MAED 5731 Problem solving strategies

Elective courses:
-MAED 5031 Mathematical analysis and its applications II
-MAED 5131 Algebra and its applications II
-MAED 5321 Combinatorics
-MAED 5421 Probablity and Statistics
-MAED 5821 Topics in Mathematics
-MAED 5851 Scientific computation

Project course:
-MAED 6980 MSc Project

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Memorial’s Department of Mathematics and Statistics is one of the institution’s youngest – half our faculty have been hired since 2005 – and most recognized – 20% of us hold the university's highest rank, University Research Professor. Read more
Memorial’s Department of Mathematics and Statistics is one of the institution’s youngest – half our faculty have been hired since 2005 – and most recognized – 20% of us hold the university's highest rank, University Research Professor. Although the Department of Mathematics and Statistics has offered graduate degrees for many years, the past decade has seen an explosion of interest in these programs, adding invaluable new voices to the Department's community of researchers.

Among the research areas studied by our faculty and graduate students are the following: Numerical Analysis and Scientific Computation, Analysis, Combinatorics, Topology, Applied Statistics, Differential Equations and Dynamical Systems, Mathematical Models and Modeling / Numerical Optimization, Algebra, Mathematical Physics, Mathematical Statistics, and Fluid Mechanics.

MAS -The MAS is a highly structured program incorporating both courses and practicum (an applied statistics project). A full-time student with an honours degree in statistics normally requires two years to complete the degree requirements. This program accepts new students only in the Fall semester.

MSc – The MSc program has two options. The research-based program consists of graduate courses and a thesis. A full-time student is expected to complete the degree requirements in two years. The course-based program is an intensive three semester (one-year) program based on graduate courses and a project. This program accepts new students only in the Fall semester.

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