Exact Sciences Master Guide2005/2006



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Part-time studying


It is possible to study Mathematics part-time. For more information ask the programme coordinator.
    1. Research areas


In the Mathematics Master the student may specialize in one of the research areas as covered by the Department of Mathematics of the Universiteit of Amsterdam or the Vrije Universiteit. Below you will find a short description of their scope. The master's programme is positioned adjacent to the masters' programmes Mathematical Physics and Stochastics and Financial Mathematics; courses from these programmes may be chosen. There is a great variety in the subjects of the courses that are offered.

 

Algebra and Geometry

Algebra and Geometry form a beautiful core part of mathematics, with a long and rich history, but also a very dynamic one with breath-taking new developments and applications. Geometry is also a very wide field with many diverse aspects ranging from algebraic geometry, non-commutative geometry, and differential geometry to topology.

Geometry always had many applications, from the applications of Euclidean geometry in Newtonian physics, through differential geometry in relativity theory to the more recent application of algebraic geometry in string theory.

 

Algebra and Geometry are represented in Amsterdam by algebraic geometry (both real and complex), non-commutative geometry, algebraic groups, topology, and discrete



mathematics. In this research area the emphasis in algebraic geometry is on moduli spaces algebraic groups and the topology of algebraic varieties, in non-commutative

geometry it is on quantum groups and knot-theory, while within topology it is on infinite-dimensional topological manifolds and convexity. Within Discrete Mathematics the emphasis is on the theory of graphs and on combinatorial optimisation.

 

Mathematical Analysis

Mathematical Analysis is a central part of mathematics with many aspects ranging from the pure to the very applied. It has connections to Algebra, Geometry, and Probability. At the same time Analysis provides the tools for the study of dynamical processes that occur in other sciences and in the real world. It has a strong numerical component in which the computer is an essential tool.

At the Amsterdam Universities the theory of Differential and Integral Equations, Harmonic Analysis, Special Functions, Numerical Analysis, Complex Analysis, Functional Analysis, and Operator Theory represent Analysis. The programme offers a wide range of advanced courses on these topics and adjacent ones.

 

Stochastics

Stochastics is a relatively young branch of mathematics, in which the key words are probability, randomness, and uncertainty. Stochastics comprises Probability Theory, Mathematical Statistics, and Operations Research. On the one hand, stochastics may be viewed and studied as a branch of pure mathematics with many links to analysis, topology, measure theory, and combinatorics; on the other hand, it aims at essential applications in biology, physics, economy, epidemiology and engineering, to name a few.

Probability Theory studies the mathematical properties of probability models with a focus on stochastic processes, and is often interested in what happens in the long run. Statistics is the science of learning from data; as such it is at the heart of all science. It generates and studies statistical procedures, aims for optimality, and is based on Probability Theory. Operations Research studies queues and networks, develops optimal strategies for them, and is also based on Probability Theory.

The Amsterdam Universities offer a wide range of advanced courses in Stochastics.

    1. Programme


At the start of the first year the student chooses a preliminary field of specialization. This leads naturally to the choice of a preliminary personal supervisor,

and a choice of the courses that the student will attend. Of course the student can change his mind about the field of specialization and the advisor until he starts his thesis work.

All decisions regarding the education of the student will be taken in consultation with advisor and coordinator.

The fields of specialization correspond with the research fields of the Institutes as described above.

 

There are no compulsory courses for master students. On the other hand, there are some 'central' courses of interest for the different fields of specialization.



 

Since September 2004 the nine Dutch Universities that have a master programme in Mathematics or Engineering Mathematics, offer a joint programme of courses. Each master student in mathematics is expected to attend four of these courses. Below you will find a list of courses. More details will be published on the web site

http://www.mastermath.nl

 

 



Students take part in a student seminar. It provides a possibility for individual study of a topic on which the student will present a lecture. Also it will be the forum where the student will present his master project.

 

The second year is largely devoted to advanced mathematics and ends in a master project. The subject of the project should be chosen at the end of the first or at the beginning of the second year. The supervisor will advise the student in choosing the subject.



 

The master project can be carried out under supervision of a member of one of the two mathematical institutes, or externally, within a company or research facility other than one of these two institutes.  In the latter case he/she will have a local advisor and a supervisor from one of the two institutes. The student chooses his master project with the help of the coordinator and the preliminary supervisor, and possibly the 'stagebureau' at the VU.



  • The project requires half a year of work, not including preparatory activities.

  •  A student can only start the actual project if he has obtained 75 cp . In exceptional cases the examination board may allow otherwise.
    1. Society oriented variant (M-variant)


The M-variant is the society-oriented variant of the programme. It aims at educating the student to become a mathematical professional, i.e., someone who will find a career in e.g. the commercial or strategic staff of companies or governmental institutions.

There are three versions, which are open for all students in the programme. Students who opt for version one will carry out a major part of the programme at the VU, while version two is UvA based. The versions are

 

1. At the VU the core of the M-variant is an internship of half a year at a company or institution outside the Faculty. The courses in this M-variant are courses in (applied) mathematics as well as courses taken from other programmes such as economics, computer science and the natural sciences.



 

2. At the Korteweg-de Vries Institute for Mathematics it is possible to decide for the M-variant in a so-called dual version. Instead of an internship it includes a full year of salaried work in companies. However, the dual master programme in Mathematics takes two and a half years. It is especially designed for students who aim for a job in business or industry, and pays attention to the demands of this sector.  It includes extra training in communicative and social skills and a training-on-the-job period during which students learn, among other things, to use their mathematical and statistical toolbox.  Both from the side of the company as from the side of the university there is much attention for coaching.

 

3. Both the Faculty of Sciences of the UvA and the Faculty of Exact Sciences of the VU offer an M-variant which consists for one half of courses in the main discipline and for the other half of society-oriented courses. Please consult the relevant section for detailed information on this variant.


    1. Mathematics with Life Sciences


Within the Mathematics programme, with either a M-variant or an O-variant the VU offers a specialization Mathematics with Life Sciences.

For more details one should contact dr. M.C.M. de Gunst, e-mail degunst@few.vu.nl.


    1. Course schedule of the joint national programme of courses


The list below describes the information as on May 1 2005. Updates and more details appear on the site www.mastermath.nl, which is dedicated to the joint programme in mathematics of the Dutch Universities.

Note: In spring 2006 there will be courses given at Zwolle/UT. See the site www.mastermath.nl




Courses given at VU




Course code

Course name

Cr.

Period

400383

Asymptotic Statistics

6

1 and 2

400244

Measure Theoretic Probability

8

1, 2 and 3

400339

Stochastic Processes

8

4, 5 and 6

400257

Semiparametrics Statistics

8

4, 5 and 6




Courses given at UVA




Course code

Course name

Cr.

Period

400329

Numerical Linear Algebra

8

1, 2 and 3

400328

Functional Analysis

8

1, 2 and 3

400400

Numerical Methods for PDE

8

4, 5 and 6

400399

Complex Analysis

8

4, 5 and 6



Courses given at UU




Course code

Course name

Cr.

Period

400332

Systems and Control

6

1 and 2

400411

Integer and Combinatorial Optimization

6

1 and 2

400406

Introduction to Stochastic Processes

6

1 and 2

400394

Geometry

8

1, 2 and 3

400324

Number Theory

8

1, 2 and 3

400326

Advanced Linear Programming

6

1, 2 and 3

400398

Nonlinear Programming

6

4 and 5

400397

Queueing Theory

6

4 and 5

400396

Scheduling

6

4 and 5

400403

Rational Points on Curves

8

4, 5 and 6

400401

Abelian Varieties

8

4, 5 and 6



    1. Course schedule of the local UvA-VU master programme


Note:

Students may extend any of the courses in the local schedule to 8-point courses. This requires some extra independent work related to the course. E.g., an oral or written report on a special topic, the presentation of additional exercises, etc.




Courses given at VU




Course code

Course name

Cr.

Period

400405

Topics in Finite Group Theory

6

1 and 2

400241

Groups of Homeomorphisms

6

1 and 2

400346

Caput Financial Stochastics

6

1 and 2

400392

Applied Stochastic Modeling

6

1 and 2

400337

Control of Stochastic Systems in Continuous-Time

6

1 and 2

400336

Caput Stochastic Optimization

6

1 and 2

400352

Stochastic Processes for Finance

6

1 and 2

400353

Coding and Complexity

6

1 and 2

400382

Topological Methods for Nonlinear Differential Equations

6

4 and 5

400393

Critical Percolation, Conformal Invariance and SLE

6

4 and 5

400395

Classical Dimension Theory

6

4 and 5

400260

Optimization of Business Processes

6

4 and 5

400135

Statistics and Probability Seminar

4

not fixed




Courses given at UVA




Course code

Course name

Cr.

Period

400341

Advanced Topics in Recursion Theory

6

1 and 2

400258

Simulation Methods in Statistics

6

1 and 2

400239

Recursion Theory

6

1 and 2

400408

Industrial Statistics

6

1, 2 and 3

400238

Scientific Computing

6

1, 2 and 3

400350

Lie Groups

6

1, 2 and 3

400240

Advanced Topics in Set Theory

6

1, 2 and 3

400340

Advanced Modal Logic

6

4 and 5

400253

Model Theory

6

4 and 5

400349

Fourier and Signal Analysis

6

4, 5 and 6

400297

Stochastic Integration

6

4, 5 and 6

400343

Knot Theory and Topological Quantum Field Theory

6

4, 5 and 6

400249

Student Seminar

6

the whole year; contact the lecturers




Courses given at UU




Course code

Course name

Cr.

Period

400247

Time Series

6

1, 2 and 3

400263

Ergodic Theory

6

1, 2 and 3

400402

Combinatorial Stochastic Processes

6

4, 5 and 6

400248

Quantum Stochastics

6

4, 5 and 6





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