This being a first draft, it is certain to have lots of errors and omissions. I welcome correspondence, additions, and corrections.
The new institute set up shop in a mansion in Copenhagen's Valby district, near the Carlsberg brewery, and went to work building a vacuum-tube computer named DASK (Dansk Algoritmisk Sekvens Kalkulator). This was an extension of the design of the BESK (Binär Elektrisk Sekvens Kalkulator) that had previously been built in Sweden. The computer took up the entire main floor of the mansion, and the cooling system was in the basement of Gammel Carlsbergvej 2. The speed was 18,000 instructions per second. 
DASK was the first computer in Denmark, and by 1957 had progressed far enough that coding classes were offered. Among the first students from DTH (Danmarks Tekniske Højskole, now Denmarks Technical University) to attend Christian Gram's classes were Helge Vilstrup, Gundorf K Kristiansen and Leif Hansson. 
The completion of the "electronic brain" caused quite a bit of excitement. I can remember listening to a popular science program on the radio with my grandfather, where Michael Schrøder visited Regnecentralen to have Christian Gram demonstrate how the computer could be used to calculate someone's income taxes with lightning speed. 
In the summer of 1958, Professor P L Ølgaard from the AEK's Risø research station offered 3 Master's thesis projects to develop DASK codes for reactor physics: "A two-group diffusion thery code, which calculates the reactivity, real - and adjoint flux in symmetrical homogeneous box-geometry", and also the same project is spherical and cylinder geometries. These projects were executed by Vibeke Hansen, G K Kristiansen and Helge Vilstrup, respectively. 
In February of 1959, Helge Vilstrup was hired by professor Ølgaard to write codes for the Reactor Physics group at Risø, and a few months later, G K Kristiansen joined him. 
At the same time that GIER was being designed, a the well-known astronomer, professor Peter Naur had joined Regnecentralen and was very active in the design of a new programming language to replace FORTRAN. When the committee issued its final report in early 1960, it was edited by Peter Naur. He immediately went to work building a compiler for the new language:
... one week after my return from Paris Regnecentralen's first course of the new language started. This course was given every day for a week, fortunately in the afternoon; this enabled me to finish the necessary parts of the ALGOL 60 Report on the same day in the morning, immediately before the teaching.
The GIER ALGOL project got its start signal on the day I returned to Copenhagen, 1962 January 5. Bech called us to a conference asking us (I don't know whether he thought we would refuse) to develop an ALGOL compiler for GIER. It had to be finished before the 1st September the same year, since it had to be ready for the beginning of the university semester. It did not matter whether it was poor or slow, or whether it included the complete language, if only it could be called by the name of ALGOL. At this last stipulation Jørn [Jensen] and I exchanged a glance: Bech would be shown something different. We accepted the task, on one condition: that we would be getting ample access to a machine during the testing.
The development of the GIER ALGOL compiler made fast progress during the spring. I myself went to the USA on the 21st June 1962 to tell about the work at a summer school in North Carolina. At that time the first five translator passes were running and the run time subroutines had been written. I took the input/output specifications of pass 6 along on the trip, Jørn took over pass 7, and passes 8 and 9 and the standard functions were in the hands of others in the group. When I came back from USA on the 26th of July everything was ready for testing except the machine language formulation of pass 6. Since we were now aiming at a demonstration of the compiler at the IFIP Congress in Munich from the 27th of August we had a busy month. We were in fact active from about 6 in the morning until midnight on most days.
The presentation of the GIER ALGOL at the exhibition in Munich was a success. The system could be demonstrated and put at the disposal of the guests, and it worked with only very few flaws that we managed to fix on the spot.
Although Regnecentralen was working on an Algol compiler which would allow researchers to write their own programs, GIER was originally programmed in an assembly language named "slip", and while waiting for delivery of their own machine, the programmers at Risø would punch their programs on 8-row papertape using Friden Flexo-Writers. The tapes were then sent to Valby, and a couple of days later, results (or error messages!) would be returned. But soon the compiler was ready and for many years to come, Algol-60 would be the preferred programming language for academic computing in Denmark. 
In an article written in Norvegian, Knut Skog from University of Trondheim describes how he was sent to Valby before his university took delivery of a GIER. He paints a vivid picture of life at the startup computer company:
"I don't know how the agreement to take delivery of a GIER, the first computer at NTH (Norway's Technical University) came about. But it caused to freshly graduated engineers, Niels Michelsen and myself, to be sent to Dansk Regnecentral A/S in Copenhagen in February of 1962. The job was to learn all that was necessary to maintain and use the new tool. A good-sized wardrobe cabinet with mahogany doors, and filled with wires and circuit boards awaited us on the first day we reported to work at Regnecentralen. The machine came fresh from the production floor, soldered and assembled by a half-dozen girls, but woefully filled with cold solder joints, miswires and defective components.
Our education from the university's electronics department was of limited use when trying to identify errors in microprograms and their underlying control circuits. With good assistance from assistant professor Sveigaard from Geodætisk Institut, the machine became ready to operate in a couple of months. Then I - who was designated to take control of the software - was transferred to Dr Peter Naur's ALGOL compiler group. There I wandered as a living question mark until I somewhat belatedly grasped some of the fundamentals of ALGOL. Later I learned that GIERs ALGOL compiler was the second complete implemetation of the language with the infamous recursive procedure calls. Edsgar Dijkstra had made the first one only a couple of months earlier. The contact between those groups was very good, however. So the machine we installed in the fall of 1962 was an ALGOL machine. Today (in 1987) it would be a small PC with 5 KB of main storage, 60 KB of mass core storage, and somewhat under 0.1 MIPS." 
According to another article in Norvegian, this sale was part of a contract to send at least two machines to Norway, with part of the payment being that the Norvegian universities sent 8-9 engineers to Copenhagen for 6-9 months. 
Around 1965, GIER was "mass-produced", and at least 3 more were delived to Copenhagen University: Two for the department of mathematics (Matematisk Institut) and one at the Niels Bohr Institute of Nuclear Physics. When I enrolled at University of Copenhagen in 1969, the twin GIER systems in the basement of the H C Ørsted building were still a major computing resource, used by both the math department and guests from other institutions, such as Meteorologisk Institut. 
The state government installed a large IBM 360 data center for income tax processing and motor vehicle registration. The state data center pioneered real-time remote transaction processing. As remote termional systems became practical, the national association of municipal governments established 6 regional centers for municipal data processing, linked to each other, to the state center and to terminal in each minicipal administration office in the country. In order to facilitate data exchanges between the various government systems, these systems were all very similar OS/360 systems. 
IBM was promoting APL\360 for high schools, and set up a system at their commercial service bureau, but it never took hold. The East Asiatic Company purchased a GE-635 timesharing system (all-BASIC, TTY-33 dial-up terminals) and was fairly successful in gaining acceptance for this service in engineering applications as well as a few schools. 
Many medium to large businesses installed IBM/360 systems. I remember looking into renting time on a 360/40 running DOS at Falck's rescue services, for a computer dating service I was playing with around 1973. When I was looking for a computer job at Claus Topsøe chemical engineering in early 1970, I remember they had a 360/44 running a locally modified PS-44 operating system. 
The three academic centers had very different flavors, due to their different systems.
The EXEC-8 operating system was an extremely well-rounded system. It would run batch jobs as efficiently as OS/360, but it also supported interactive timesharing users, providing a compatible environment for both user styles, with identical command languages. The scheduler would be given some general guidelines (give 25% of CPU cycles to interactive users) and then do a very good job of keeping the system productive with very little operator activity required. We generally switched to unattended operation every night sometime between 22:00 and 23:00, and the job queue kept running overnight. Some planning was required to ensure that the active job set could be drained by 7:00 AM so the machine could be turned over to the resident Univac service team for scheduled daily maintenance.
The telecommunications ports were fairly expensive, and a modem for a dial-up terminal took up one port, just like a CRT terminal cluster did, so we embarked on a project to build (on a PDP-11 minicomputer) a cluster controller that would accept TTY terminals (via modems) and look to the Univac like a cluster of CRTs or more precisely of DCT-1000 keyboard-printer terminals. This became my introduction to embedded systems programming.
The CDC operating system was designed to have a symbiotic relationship with the operator. The console allowed the operator to peek into (and patch) octal and alphanumeric views of system control structures in memory. The difference between unattended operation and a really smart operator could be as much as a factor 12 in user job throughput.
The CDC had inexpensive communication ports, so the campus was dotted with TTY terminals very early.
RECAU spawned a clone in Aalborg: When Aarhus upgraded to the next newer and bigger CDC system, Aalborg inherited the old one.
 Personal recollections of Lars Poulsen.
 from http://www.ntnu.no/itea.info/runit/skog.html - "I begynnelsen var GIER - og GIER var Regnesentret", Knut Skog, 1987.
 from "Elektronisk regnemaskin ved NTH", direktør Karl Stenstadvold, SINTEF, in Teknisk ukeblad, 25 oktober 1962.
Translated from "Regnecentralen og ALGOL 60" pp. 35-40 in
"Niels Ivar Bech--en Epoke i Edb-Udviklingen i Danmark".
DATA [magazine], Copenhagen, 1976.
"Noget om Dask"
by professor emeritus H B Hansen, Roskilde Universitetscenter, 1997.
DASK og GIER
Niels Ivar Bech
- en epoke i edb-udviklingen i Danmark
$Log: dan_hist.htm,v $
Revision 1.5 2006/06/28 23:18:05 lars
Periodic update, long overdue
Revision 1.4 2001/10/26 13:28:00 lars
Replaced CMC -> Beagle-Ears
Revision 1.3 2000/09/01 05:03:39 lars
Added the commercial 60s and the educational 70s.
Revision 1.2 2000/08/23 04:43:48 lars
*** empty log message ***
Revision 1.1 2000/08/15 21:02:55 lars
Added history of Danish computing as well as Naur's obituary for Bech.
 "Noget om Dask" by professor emeritus H B Hansen, Roskilde Universitetscenter, 1997.
 DASK og GIER
 Niels Ivar Bech - en epoke i edb-udviklingen i Danmark