Masters Degrees (Biomathematics)

Life Sciences is one of the strategic research fields at the University of Helsinki. The multidisciplinary Master’s Programme in Life Science Informatics (LSI) integrates research excellence and research infrastructures in the Helsinki Institute of Life Sciences (HiLIFE). As a student, you will gain access to active research communities on three campuses: Kumpula, Viikki, and Meilahti. The unique combination of study opportunities tailored from the offering of the three campuses provides an attractive educational profile. The LSI programme is designed for students with a background in mathematics, computer science and statistics, as well as for students with these disciplines as a minor in their bachelor’s degree, with their major being, for example, ecology, evolutionary biology or genetics.

As a graduate of the LSI programme you will:
-Have first class knowledge and capabilities for a career in life science research and in expert duties in the public and private sectors.
-Competence to work as a member of a group of experts.
-Have understanding of the regulatory and ethical aspects of scientific research.
-Have excellent communication and interpersonal skills for employment in an international and interdisciplinary professional setting.
-Understand the general principles of mathematical modelling, computational, probabilistic and statistical analysis of biological data, and be an expert in one specific specialisation area of the LSI programme.
-Understand the logical reasoning behind experimental sciences and be able to critically assess research-based information.
-Have mastered scientific research, making systematic use of investigation or experimentation to discover new knowledge.
-Have the ability to report results in a clear and understandable manner for different target groups.
-Have good opportunities to continue your studies for a doctoral degree.

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

Programme Contents

The Life Science Informatics Master’s Programme has six specialisation areas, each anchored in its own research group or groups.

Algorithmic Bioinformatics
Goes with the Genome-scale algorithmics, Combinatorial Pattern Matching, and Practical Algorithms and Data Structures on Strings research groups. This specialisation area educates you to be an algorithm expert who can turn biological questions into appropriate challenges for computational data analysis. In addition to the tailored algorithm studies for analysing molecular biology measurement data, the curriculum includes general algorithm and machine learning studies offered by the Master's Programmes in Computer Science and Data Science.

Applied Bioinformatics
Jointly with The Institute of Biotechnology and genetics. Bioinformatics has become an integral part of biological research, where innovative computational approaches are often required to achieve high-impact findings in an increasingly data-dense environment. Studies in applied bioinformatics prepare you for a post as a bioinformatics expert in a genomics research lab, working with processing, analysing and interpreting Next-Generation Sequencing (NGS) data, and working with integrated analysis of genomic and other biological data, and population genetics.

Biomathematics
With the Biomathematics research group, focusing on mathematical modelling and analysis of biological phenomena and processes. The research covers a wide spectrum of topics ranging from problems at the molecular level to the structure of populations. To tackle these problems, the research group uses a variety of modelling approaches, most importantly ordinary and partial differential equations, integral equations and stochastic processes. A successful analysis of the models requires the study of pure research in, for instance, the theory of infinite dimensional dynamical systems; such research is also carried out by the group.

Biostatistics and Bioinformatics
Offered jointly by the statistics curriculum, the Master´s Programme in Mathematics and Statistics and the research groups Statistical and Translational Genetics, Computational Genomics and Computational Systems Medicine in FIMM. Topics and themes include statistical, especially Bayesian methodologies for the life sciences, with research focusing on modelling and analysis of biological phenomena and processes. The research covers a wide spectrum of collaborative topics in various biomedical disciplines. In particular, research and teaching address questions of population genetics, phylogenetic inference, genome-wide association studies and epidemiology of complex diseases.

Eco-evolutionary Informatics
With ecology and evolutionary biology, in which several researchers and teachers have a background in mathematics, statistics and computer science. Ecology studies the distribution and abundance of species, and their interactions with other species and the environment. Evolutionary biology studies processes supporting biodiversity on different levels from genes to populations and ecosystems. These sciences have a key role in responding to global environmental challenges. Mathematical and statistical modelling, computer science and bioinformatics have an important role in research and teaching.

Systems Biology and Medicine
With the Genome-scale Biology Research Program in Biomedicum. The focus is to understand and find effective means to overcome drug resistance in cancers. The approach is to use systems biology, i.e., integration of large and complex molecular and clinical data (big data) from cancer patients with computational methods and wet lab experiments, to identify efficient patient-specific therapeutic targets. Particular interest is focused on developing and applying machine learning based methods that enable integration of various types of molecular data (DNA, RNA, proteomics, etc.) to clinical information.

Selection of the Major

During the first Autumn semester, each specialisation area gives you an introductory course. At the beginning of the Spring semester you are assumed to have decided your study direction.

Programme Structure

Studies amount to 120 credits (ECTS), which can be completed in two years according to a personal study plan.
-60 credits of advanced studies from the specialisation area, including a Master’s thesis, 30 credits.
-60 credits of other studies chosen from the programme or from other programmes (e.g. computer science, mathematics and statistics, genetics, ecology and evolutionary biology).

Internationalization

The Life Science Informatics MSc is an international programme, with international students and an international research environment. The researchers and professors in the programme are internationally recognized for their research. A significant fraction of the teaching and research staff is international.

As a student you can participate in an international student exchange programme, which offers the possibility to include international experience as part of your degree. Life Science Informatics itself is an international field and graduates can find employment in any country.

In the programme, all courses are given in English. Although the Helsinki region is very international and English is widely spoken, you can also take courses to learn Finnish via the University of Helsinki’s Language Centre’s Finnish courses. The Language Centre also offers an extensive programme of foreign language courses for those interested in learning new languages.

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If you are interested in the possibility of a research degree (PhD or Research Masters) in the School of Mathematical Sciences, we encourage you to become familiar with the range of research activity and expertise in the School. In particular, we would encourage you to approach or contact members of the academic staff whose research area may be of particular interest.

The research of the School covers a wide range of areas including:

Analysis (Infinite-dimensional analysis, Functional Analysis, Potential Theory)
Algebra (Matrix Theory, K-theory, Quadratic and Hermitian Forms)
Discrete Mathematics (Coding, Cryptography, Number Theory)
Applied Mathematics (Fluid Dynamics, Computational Science, Meteorology, Biomathematics, Information Theory)
Theoretical Physics (Astrophysics, General Relativity, Quantum Gravity, Statistical Mechanics, Quantum Field Theory)
Statistics (Bayesian Statistics, Pharmaceutical, Medical and Educational Statistics, Environmental and ecological modelling, Epidemiology, Econometrics).

Please see our School Website for more details:
http://www.ucd.ie/mathstat

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This MSc provides an ideal foundation for students wishing to advance their mathematical modelling skills. The programme teaches students the basic concepts which arise in a broad range of technical and scientific problems and illustrates how these may be applied in a research context to provide powerful solutions.

Degree information

Students develop an understanding of the processes undertaken to arrive at a suitable mathematical model and are taught the fundamental analytical techniques and computational methods used to develop insight into system behaviour. The programme introduces a range of problems - industrial, biological and environmental - and associated conceptual models and solutions.

Students undertake modules to the value of 180 credits.

The programme consists of five core modules (75 credits), three optional modules (45 credits), and a research dissertation (60 credits). The part-time option normally spans two years. The eight taught modules are spread over the two years. The research dissertation is taken in the summer of the second year.

Core modules
-Advanced Modelling Mathematical Techniques
-Nonlinear Systems
-Operational Research
-Computational and Simulation Methods
-Frontiers in Mathematical Modelling and its Applications

Optional modules
-Asymptotic Methods & Boundary Layer Theory
-Biomathematics
-Cosmology
-Evolutionary Game Theory and Population Genetics
-Financial Mathematics
-Geophysical Fluid Dynamics
-Mathematical Ecology
-Quantitative and Computational Finance
-Real Fluids
-Traffic Flow
-Waves and Wave Scattering

Dissertation/report
All MSc students undertake an independent research project, which culminates in a dissertation of approximately 15,000-words and a project presentation.

Teaching and learning
The programme is delivered through seminar-style lectures and problem and computer-based classes. Student performance is assessed through a combination of unseen examination and coursework. For the majority of courses, the examination makes up between 90–100% of the assessment. The project is assessed through the dissertation and an oral presentation.

Careers

Our graduates have found employment in a wide variety of organisations such as Hillier-Parker, IBM, Swissbank, Commerzbank Global Equities, British Gas, Harrow Public School, Building Research Establishment and the European Centre for Medium-Range Weather-Forecasting. First destinations of recent graduates include:
-R.T.E: Engineer
-Tower Perrins: Actuarist
-Deloitte: Quantitative Analyst
-UCL: Research Associate
-C-View: Quantitative Trader
-One-to-One: Maths Tutor
-UCL Research Degree - Mathematics
-Duff & Phelps Ltd: Financial Engineer
-Bank of Tokyo Mitsubishi: Assistant Compliance Officer

Employability
The finance, actuarial and accountancy professionals are constantly in demand for high-level mathematical skills and recent graduates have taken positions in leading finance-related companies such as UBS, Royal Bank of Scotland, Societe Generale, PricewaterhouseCoopers, Deloitte, and KPMG.

In the engineering sector, recent graduates from the MSc include a mathematical modeller at Steet Davies Gleave, a leading Transportation Planning Consultancy; and a graduate trainee at WesternGreco, a business segment of Schlumberger that provides reservoir imaging, monitoring, and development services. In addition, a number of graduates have remained in education either progressing to a PhD or entering the teaching profession.

Why study this degree at UCL?

UCL Mathematics is internationally renowned for its excellent individual and group research that involves applying modelling techniques to problems in industrial, biological and environmental areas.

The department hosts a stream of distinguished international visitors. In recent years four staff members have been elected fellows of the Royal Society, and the department publishes the highly regarded research journal Mathematika.

This MSc enables students to consolidate their mathematical knowledge and formulate basic concepts of modelling before moving on to case studies in which models have been developed for issues motivated by industrial, biological or environmental considerations.

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The Department of Mathematics offers graduate courses leading to M.Sc., and eventually to Ph.D., degree in Mathematics. The Master of Science program aims to provide a sound foundation for the students who wish to pursue a research career in mathematics as well as other related areas. The department emphasizes both pure and applied mathematics. Research in the department covers algebra, number theory, combinatorics, differential equations, functional analysis, abstract harmonic analysis, mathematical physics, stochastic analysis, biomathematics and topology.

Current faculty projects and research interests:

• Ring Theory and Module Theory, especially Krull dimension, torsion theories, and localization

• Algebraic Theory of Lattices, especially their dimensions (Krull, Goldie, Gabriel, etc.) with applications to Grothendieck categories and module categories equipped with torsion theories

• Field Theory, especially Galois Theory, Cogalois Theory, and Galois cohomology

• Algebraic Number Theory, especially rings of algebraic integers

• Iwasawa Theory of Galois representations and their deformations Euler and Kolyvagin systems, Equivariant Tamagawa Number
Conjecture

• Combinatorial design theory, in particular metamorphosis of designs, perfect hexagon triple systems

• Graph theory, in particular number of cycles in 2-factorizations of complete graphs

• Coding theory, especially relation of designs to codes

• Random graphs, in particular, random proximity catch graphs and digraphs

• Partial Differential Equations

• Nonlinear Problems of Mathematical Physics

• Dissipative Dynamical Systems

• Scattering of classical and quantum waves

• Wavelet analysis

• Molecular dynamics

• Banach algebras, especially the structure of the second Arens duals of Banach algebras

• Abstract Harmonic Analysis, especially the Fourier and Fourier-Stieltjes algebras associated to a locally compact group

• Geometry of Banach spaces, especially vector measures, spaces of vector valued continuous functions, fixed point theory, isomorphic properties of Banach spaces

• Differential geometric, topologic, and algebraic methods used in quantum mechanics

• Geometric phases and dynamical invariants

• Supersymmetry and its generalizations

• Pseudo-Hermitian quantum mechanics

• Quantum cosmology

• Numerical Linear Algebra

• Numerical Optimization

• Perturbation Theory of Eigenvalues

• Eigenvalue Optimization

• Mathematical finance

• Stochastic optimal control and dynamic programming

• Stochastic flows and random velocity fields

• Lyapunov exponents of flows

• Unicast and multicast data traffic in telecommunications

• Probabilistic Inference

• Inference on Random Graphs (with emphasis on modeling email and internet traffic and clustering analysis)

• Graph Theory (probabilistic investigation of graphs emerging from computational geometry)

• Statistics (analysis of spatial data and spatial point patterns with applications in epidemiology and ecology and statistical methods for medical data and image analysis)

• Classification and Pattern Recognition (with applications in mine field and face detection)

• Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives

• p-adic methods in arithmetical algebraic geometry, Ramification theory of arithmetic varieties

• Topology of low-dimensional manifolds, in particular Lefschetz fibrations, symplectic and contact structures, Stein fillings

• Symplectic topology and geometry, Seiberg-Witten theory, Floer homology

• Foliation and Lamination Theory, Minimal Surfaces, and Hyperbolic Geometry

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When you study mathematics and statistics at the University of Helsinki, some of the best mathematicians and statisticians in the world will be your instructors. Studies in this Master’s programme will give you a solid basis for maths and statistics applications. Graduates of this Master’s programme find employment as researchers, teachers, and in demanding expert posts in the public and private sectors in Finland and abroad.

The Master’s programme in mathematics and statistics is based on top research. The teaching within the sub-programmes at the University of Helsinki follows a high standard and is highly valued, not just within Finnish academia but in global university rankings. Upon graduating from this Master’s programme, you will:
-Be an expert in the methods of mathematics or statistics.
-Have mastered the basics of another scientific discipline.
-Be able to apply scientific knowledge and methods.
-Be able to follow developments in mathematics and statistics.
-Know how to think critically, argue a point, and solve problems.
-Have excellent interaction skills and be assertive and creative.
-Understand the principles of ethical and sustainable development.
-Be well prepared to work as an expert and developer in your field.
-Be prepared for scientific postgraduate studies.

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

Programme Contents

The Master’s programme consists of courses in mathematics, applied mathematics, and statistics. The courses include group and lecture instruction, exercises, literature, and workshops. Most courses also include exams or project assignments. In addition, you can complete some courses independently, by taking literature-based exams. The instructors in this programme have received prizes for their high standard of teaching. The teaching methods used in the subjects in this Master's programme have been widely recognised in the media.

Selection of the Major

The specialisation subjects within the programme are:
-Analysis
-Mathematical physics and stocastics
-Applied analysis
-Computational science
-Mathematical logic
-Mathematical modelling
-Insurance and financial mathematics
-Algebra and topology
-Statistics
-European Master in Official Statistics, EMOS (based on the statistics education in the Faculty of Social Sciences).

You will select your specialisation subject during your first year.

Programme Structure

The Master’s programme comprises 120 credits, which you can complete in two years. The degree in mathematics includes:
-85 credits of advanced courses, including the Master’s thesis (Pro gradu, 30 credits).
-35 credits of other courses from your own or other programmes.
-Working-life orientation and career planning.
-Personal study plan.

The degree in statistics includes:
-25 credits of advanced mathematics courses.
-60 credits of advanced statistics courses, including the Master’s thesis (Pro gradu, 30 credits).
-35 credits of other courses e.g. more advanced courses in statistics, or intermediate courses in some other subject, in which you included basic courses in your BSc degree, or, module/s from other university programmes.
-Working-life orientation and career planning.
-Personal study plan.

The European Master in Official Statistics sub-programme includes:
-85 credits of advanced courses in statistics or mathematics, including the Master’s thesis (Pro gradu, 30 credits) and a traineeship.
-35 credits of other courses from your own or other programmes.
-Working-life orientation and career planning.
-Personal study plan.

Career Prospects

Graduates of the Master’s programme can find employment outside the university or continue with one of the doctoral programmes in mathematics and statistics. The Master’s programme will give you excellent capabilities for work in the public or private sector as an expert in mathematics and statistics, skills that are very sought after in the job market both in Finland and abroad. The banking, investment, and insurance fields, for instance, value mathematicians and statisticians very highly internationally. Many of our graduates work in research and development or as teachers in various educational institutions. Graduates from this programme have excellent chances to find employment corresponding to their education.

Internationalization

The international nature of the programme is implemented in many ways:
-Research within the disciplines of the degree programme is of high international standard and is highly regarded.
-Teaching staff and research collaboration within the programme are international.
-The atmosphere of the programme is international, several international students are admitted each year.
-Theses and projects may be completed within international projects.
-There are opportunities for a student exchange period in many foreign universities.

Research Focus

The research focus within the disciplines in the degree programme are e.g.
-Geometric analysis and measurement theory
-Analysis in metric spaces
-Partial differential equations
-Functional analysis
-Harmonic analysis
-Mathematical physics
-Stochastics
-Inversion problems
-Mathematical logic and set theory
-Biomathematics
-Time series analysis
-Biometry
-Econometry
-Psychometrics
-Social statistics

The programme is part of the Analyysin ja dynamiikan (Analysis and dynamics) and the Inversio-ongelmien (Inversion problems) centres of excellence.

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

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

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

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

Modules

Modules on the MSc Mathematics include:

• Algebraic coding theory

• Biomathematics

• Black-Scholes theory

• Data science

• Differential geometry

• Fourier analysis

• Ito calculus

• Lie theory

• Numerical analysis

• Partial differential equations

• Stochastic processes

• Statistical mechanics

• Topology

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

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

Facilities

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

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

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

Careers

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

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

Research

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

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

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

Student Profile

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

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

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The M.A. in Mathematics at West Chester University is a thirty-three credit master’s program, eighteen credits of core courses and fifteen credits of electives, which offers great flexibility. Elective courses may be in mathematics education, statistics, computer science, pure mathematics, applied and computational mathematics, actuarial science, business, and others. By properly selecting their electives, our M.A. candidates may train for work in a large variety of fields, including, but not limited to, actuarial science, computer science, operations research, biomathematics, cryptography, teaching in a high school or a two-year college, research, economics, environmental mathematics, geophysical mathematics, air traffic control operations, photogrammetry, and many more. Upon completion of the M.A. in Mathematics, students are also well prepared to pursue a doctoral program in mathematics.

Curriculum

Required modules:

MAT 515 Algebra I
MAT 516 Algebra II
MAT 545 Real Analysis I
MAT 546 Real Analysis II
MAT 532 Geometry I
STA 505 Mathematical Statistics I

Electives:

A student may choose from among 500-level MAT course offerings, as well as MTE 507, MTE 508, MTE 512, and MTE 604. A student may select CSC or STA courses with approval of their advisor.

Capstone Experience:

A student may choose one of two different capstone experiences:

Thesis - Student selects MAT 609 and MAT 610, which replace 6 credits of electives.

Oral Comprehensive Exam in 3 different subject areas.

For more detailed information about the modules taught on this course, please visit the website:

http://catalog.wcupa.edu/graduate/sciences-mathematics/mathematics/#coursestext

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