Computational Science Curriculum in Utrecht
H. A. van der Vorst
In 1993 Utrecht University has started a curriculum in Computational Science,
starting at the undergraduate level and leading to the Dutch `Doctorandus'
degree (wich is more or less comparable to the Master's degree). The
curriculum has been set up as a joint collaboration between the Departments
of Mathematics & Computer Science, and Physics. It aims at a complete
and self-contained educational program that should fulfill society's
growing demand for scientific computing, and it does so by trying to make
students familiar with computational models (physics), applied mathematics
(with emphasis on numerical analysis), and computer possibilities (computer
In our presentation we will discuss the ideas behind this new study, the
perspectives for students with respect to carreer, and we will report on
our experiences during the first two years of existence of the new
The Dutch Educational System
In order to understand how the CS-curriculum fits in the educational system
we will first briefly sketch the Dutch educational system in relation with
>From age 4 to 12 everyone attends the same type of primary school.
At age 12 the education splits in essentially three streams:
At each level the student can take a selection of courses, and typically
such a selection (the selection has to follow certain rules to make it a
proper one) contains Mathematics (Calculus), Physics, Biology, Dutch,
two foreign languages, history, and economics. For the higher levels
(VWO and HAVO) Mathematics comes in two flavours: Mathematics A and B.
Type A deals with statistics, type B has calculus and simple linear algebra.
The VWO type can be regarded as preparation for further education at
a University. Several combinations of courses can be taken and the choice
determines for what study the student qualifies. If one finishes the VWO
successfully then one is allowed to enter University without further
requirements than having followed the proper courses.
- MAVO (low to medium level)
- HAVO (medium to high level)
- VWO (high level)
The education at the University consists of two phases:
- The first phase takes in theory 4 years, but in practice often more
than 5, and ends with a so-called `Doctorandus (drs)' degree. This
degree can be compared to the American Masters Degree.
- The second phase takes again 4 years and ends with a PhD (Dr)-degree.
The Computational Science Curriculum starts right at the beginning of
phase 1, so when the students are at an age of about 18 years old.
The Circumstances in Utrecht
The main departments that are involved in Computational Science at Utrecht
Apart from these three Departments, computational activities take also
place in the Departments of Medicine, Chemistry, Biology, Pharmacy,
and Earth Sciences.
- Department of Mathematics, with chairs in Algebra, Analysis,
Numerical Analysis, Statistics & Probability, and Mathematical Pysics.
For Computational Science the chairs in Numerical Analysis and Statistics
& Probability are the most relevant ones. The chair in Mathematical
Physics became vacant in the last year and it is to be expected that
the new professor will also be involved at least partly in the Computational
Science curriculum. The Numerical Analysis section consists at this moment
of one full professor, three associate professors, four postdocs, and
a small number of PhD-students. This section played a key role in the
start of Computational Science, warmly supported by the other mathematicians
(including the pure mathematicians; in Utrecht there is no clear separation
between pure and applied).
- Department of Informatics. Although this Department played an
active role in getting Computational Science started in Utrecht, it became
more deeply involved only very recently. At this moment, July 1995, it
is very active in the participation as well as in the design of new courses.
The Department of Informatics is currently active in Algorithms and
Algorithmic design, Information Technology, Programming, and Software
- Department of Physics. This department has different subgroups, among
which we see Theoretical Physics, Experimental Physics,
Astronomy, Oceanography, and Informatics of Physics. The last one was most
actively involved in Computational Science, but the courses in Physics for
the new curriculum are not restricted to this group.
In 1990 a contact group was established, which acted as a forum for
discussions on Computational Science matters and for mutual help with large
scale computational work. This
group has organized Symposiums and it has also made a list of all those courses
that have strong emphasis on Computational aspects. Students
in various Departments are encouraged to select courses from this list.
Promotion of exact sciences
The number of students who enroll for exact sciences has decreased
dramatically over the last years, and this is seen as an alarming fact
by the Dutch Government. The State Department of Education and Science
has taken steps in order to help improve the situation, and together
with the encouraging attention and stimulances of the Board of Utrecht
University this has created an atmosphere in which the establishment
of a new Computational Science curriculum was facilitated. The University
Board has played a very active role in this by making money available,
partly for Physics and partly for Mathematics & Informatics, under
the condition that these Departments agreed to start the new curriculum
by September 1, 1993. This deadline was made known only one year earlier,
Furthermore, we received also warm support, in writing, from key industries
and large research laboratories. Some of these groups were willing to
help finance PhD positions (in fact, Philips Electronics is participating
in a program for financing PhD positions in Utrecht, as per September
This has culminated in the official approvement by the State Department
of the Computational Science curriculum as an independent study, of which
the name is privileged. This status becomes effective as per September
1995, and from then on we are allowed to grant a Doctorandus title
in Computational Science.
The Computational Science Curriculum
The goal of our Computational Science curriculum is to provide a complete
program for professional simulation of scientific processes. The ingredients
of this program are Mathematics, Numerical Analysis, Physics, and
Informatics. The students have, in the last two years, also a choice from
courses in Chemistry, Economics, etc.
The program of the first year leads to a `Propedeuse'-degree. Without this
degree students are formally not allowed to take 3-rd and 4-th year courses.
This first year program consists of the following elements:
After this first year the student has still the possibillity to switch
from Computational Science to a program in Mathematics or Physics with
no delay in the total program. We anticipated that this switch possibility
might make it easier for the student to select our new program, in the
sense of a reduced risk.
- Calculus (+/- 20%)
- Linear Algebra (+/- 16%)
- Introduction to Statistics (+/- 8%)
- Principles of Programming (+/- 10%)
- Algorithms & Datastructures (+/- 10%)
- Mechanics (+/- 10%)
- Electrodynamics (+/- 10%)
- CS Practical Work (+/- 16%)
The program of the second year includes
The practical work includes sessions in which the students becom
familiar with computer simulations of increasing complexity. The simplified
versions of the models are introduced in the first year. In these sessions
students use C, Matlab, Mathematica, and they make their reports
- Advanced Calculus (differential equations, partial differential
equations) (+/- 22%)
- Introduction Numerical Analysis, and
- Numerical Linear Algebra (together (+/- 18%))
- Introduction to Probability theory (+/- 8%)
- Knowledge Technology (+/- 8%)
- Parallel Programming (+/- 8%)
- Quantum Mechanics, and
- Waves + Optics (together +/- 16%)
- Coputational Science Practical Work (+/- 20%)
The 3-rd and 4-th year are rather diverse and we give here only an impression
of the most important elements:
- Numerical Algorithms for super and parallel computers
- Nonlinear PDE's and Dynamical Systems
- Theory of Programming
- Operations Research
- Artificial Intelligence
- A Project (in which the students work in small teams)
- Computer practice
- A seminar, in which the students have to give at least two
presentations of two times 45 minutes each.
- A selection upon choice from a list of courses in Physics, Chemistry,
Earth Sciences, Hydrodynamics, etc.
- Thesis work (6 months)
Of course we have undertaken actions to make sure that students at
secondary schools, as well as their teachers in mathematics and physics,
became aware of our program in Computational Sciences. Among our activities
in this direction we mention
- special brochures with information on the program, the purpose of
the program, career perspectives, and telephone numbers for further
- Utrecht University organizes each year in November two special days,
during which students in the final year of secondary school, get all sorts
of information on the various programs. Example lectures are given, computer
demonstrations, special introductions, and students have an opportunity
for contacts with staff.
These days are usually very lively events that are rather
popular for young students and their parents. Free lunches are provided.
Of course, also Computational Sciences presents itself at these occasions
with introductions, example courses, and videos.
- Our postdocs and some of our younger students present introductions
at schools (or at meetings where students of several schools attend). It
turns out that it is often more efficient to let younger persons do
this kind of propaganda.
- Since 1993 we have prepared, with professional help of editors
of a popular scientific journal, special inlays in full color for this
magazine. A significant number of the students in our program became
aware of the program through these inlays.
- Occasionally we give special lectures for secondary school teachers.
- We are in the process of providing information through WWW.
Our early experiences are quite encouraging. In the first year of existence,
'93-'94, we had 18 students enrolled in our program, and the same number
in the second year. We have no definitive numbers for this year but there
are indications that the number will be higher this time.
It is our impression that the best students are those with an interest
After two years we are now building up the necessary courses for the third
year and the involved Departments are willing to adjust their courses,
or to develop special variants for the Computational Science students.
This leads to further improvements in the program and it also leads to a better
identification of the curriculum.
Realted Research Project
We are convinced that the researchers who are involved in the new program,
should also be involved in related research projects, because of the
stimulating effect of this on students. This creates also positions for
students to participate for their thesis work and later on for their
The Dutch Organization for Scientific Research (NWO) has started a program
in Massively Parallel Computing and Networking. We got a fairly large
proposal granted, and this includes research in Plasma Physics (Tokamak
modeling), Earth Mantle convection, and studying the influence of the
Oceans on the long term climate.
Cray Research has also set up a grant program in the Netherlands from
which we received a grant for research on BSP-models for linear algebra.
Other projects, amongst others with Philips Eelctronics, are anticipated,
and this includes simulation studies for circuits and integrated circuits.
PROF. DR. HENK VAN DER VORST,
Mathematical Institute, University of Utrecht, P.O. Box 80010,
3508 TA Utrecht, the Netherlands. email: email@example.com
This paper is also available as a [ps-file, 90 kB].