Samuels, P

English

Brunel University Research Archive

                  TR/09/92 November 1992 A Personal Response to the Euromath Project: Towards the Specification of an IT Infrastructure for the European Mathematical Community  Peter Samuels  graphical user interfaces and Boolean Algebra search options. The closest existing sys-tems are those for selecting mathematical software (eg. GAMSIC - [5]). Once the re-quired information has been found, should we provide the user with the technology to do something with it, more than just accessing it {as in the case of mathematical software libraries)? The creation of personal and group databases is strongly connected with the idea of producing large hypertext networks, called Intermedia [17]. This more clearly focusses a potential problem that the creation of a network of objects contains information in the links as well as in the nodes [10]. 2.4 Online Encyclopedia 1 again approve of the idea of creating an online encyclopedia of mathematical concepts. The most natural medium is clearly hypertext. I am not aware of a sizeable system having been implemented, only small systems such as in [26]. It would be a massive project to produce one from sratch (taking hundreds or perhaps thousands of man years). The best book source is probably [15]. I wonder if the authors are thinking along the same lines (yet)? An online encyclopedia could be used as a front-end to a database network and could also tie into computer aided learning material (see later). 2.5 Algebraic Manipulation There are several powerful and usable systems currently on the market (eg. Axiom, Derive, Macsyma, Maple, Mathematica and REDUCE). It would be a large (and not necessarily successful) task to attempt to produce a new and better system. An interesting approach might be to classify the functionality required and offered by algebraic manipulator in a similar way to mathematical software algorithms. This might help to centralise and coordinate research in the area. There is a need for a standard interface language. 3 Other Specified Infrastructure Components 3.1 Theorem Proving The use of theorem-provers by mathematicians is increasing. A generally avaialble theorem-prover supporting standard mathematical logics and theories with a graphi-cal user interface would be of benefit. The need for compatability with formal languages is also clearly important. 3.2 Numerical Computation A significant proportion of numerical computation is based on using large libraries of proven numerical algorithms. These libraries need to be made accessible and usable to  4 the general mathematical community. The current research in this area is the develop-ment of knowledge-based front-ends, with the long-term goal of creating problem solving environments [11]. I do not feel sufficiently experienced to comment on the use of mathematical programming languages for the computational modelling of mathematical problems, but this is clearly another important area. 3.3 Visualisation Many mathematicians need to be able to represent and interact with graphical infor-mation, including data, functions and images. The science related to this area is called Visualisation or VISC (Visualisation In Scientific Computing). A foundational article on the subject is [20]. 3.4 Computer-Aided Learning Education plays an important role in the working lives of most mathematicians. IT in the form of Computer Aided Learning (CAL) seems destined to play a greater role in mathematical education due to the needs for: increased computer literacy; larger classes; cost reduction; and automation. Computers may even prove to be a more effective medium for education for aspects of the curriculum such as the repetitive acquisition of skills. The use of the computer terminal for multi-media appears to be a likely future devel-opment [2]. Work is underway to produce such material at the first year undergraduate level [14], for which it appears to be particularly suited. There are moves to develop a standard syllabus at this level [3]. Modules of mathematical CAL 'Courseware' could be made available within the math-ematician's working environment as an educational or reference resource (linked to the database and the encyclopedia). 4 Infrastructure Design Criteria The design criteria I would identify are: Component Identification - I propose the utility of the metaphor of building different system components which correspond to different mathematical processes or modes of working. I have attempted to identify separate components in the classification I have used above. Integration - the separate components need to be integrated within a single integrated computer environment (eg. using a blackboard architecture). Accessibility - information needs to be made accessible and manipulatable.   5 Standards Setting - standards cannot be prescribed too far in advance, but with thought and planning, the overall movement of the technological community can be anticipated. Maintenance - the need to maintain any implemented system has already been identi-fied by the Euromath Project. Extendability - versions of ‘the system’ need designed in such a way that new and more sophisticated components can be easily integrated at a future date. For this reason, we need to have a clear idea of where we are heading. User Interface - all components need to be implemented with sophisticated graphical user interfaces. 5 Future Trends 5.1 Supporting Mathematical Research It is hard to define what mathematical research is and how it is best done. People seem to need space and time to think to do it. The classification of Mathematical Knowledge (eg. in creating an online encyclopedia) may help in identifying connections (analogies, models, etc.) between hitherto diverse and unrelated areas. If such hypertext systems are user modifiable, they may actually provide a new medium for mathematical research. Creativity [13] and problem-solving heuristics [18] are not well understood and may never be satisfactorily automated. However, it may be possible for IT to support them in some (more direct) way. 5.2 Modern Technologies The development and use of new technologies may alter the infrastructure specification. Some such possible technologies are: Long-Distance Working - the development of technologies to support the formation of working communities separated by physical distance. Parallel Computing - mathematical programming itself may be affected by the in-creased power provided by certain kinds of new computer architectures. Virtual Reality - currently only a highly speculative area [4]. 5.3 Knowledge-Based Systems The development of an IT infrastructure could be viewed as the creation of a massive knowledge-based system incorporating computer networks and reserach communities. This may be a useful metaphor during specification and give insight into long-term objec-tives. Knowledge acquisition methodologies (such as KADS [7]) could play an important role in this process, due to the recurrence of the ‘knowledge acquisition bottleneck’ in various guises. 6 5.4 Artifical Intelligence I somewhat reluctantly mention AI because I see it, along with IT, as very much as the servant of Mathematics, rather than its master. Computers seem to be much better at doing the boring repetitive tasks, leaving people to concentrate in the intelligent tasks [21]. However, attempts at generating artificial intelligence may help us to understand more clearly what doing Mathematics and being a mathematician is all about in order to support the process with different technologies. 6 Conclusions A substantial investment is required to produce an IT infrastructure for working math-ematicians in which the depth and power of existing Mathematical Knowledge is made accessible and the tasks of mathematicians are most helpfully supported. The Euromath Project represents a valiant start, but there is much that still needs to be achieved. References [1] W. P. J. M. van Asseldonk. User interface development software. Technical Report FOCUS/Philips/4/2-P, Esprit 2 Project 2620, November 1989. [2] J. Barker and R. N. Tucker, editors. The Intercative Learning Revolution: Multime-dia in Education and Training. Kogan Page, London, 1990. [3] M. D. J. Barry and N. C. Steele. A core curriculum in Mathematics for the European engineer. Technical report, The European Society for Engineering Education (SEFI), 1990. [4] L. Blackwell. The virtual reality learning paradigm in real time curriculum: A new beginning? In The Ninth International Conference on Technology and Education, pages 811-813, The University of Texas at Austin, Texas 78712, 1992. [5] R. F. Boisvert. Toward an intelligent system for mathematical software selection. Technical report, National Institute of Standards and Technology, Gaithersburg, MD 20899, 1990. [6] R. F. Boisvert, S. E. Howe, and D. K. Kahaner. The Guide to Available Mathe-matical Software problem classification system. Technical Report NISTIR 90-4475, National Institute of Standards and Technology, Gaithersburg, MD 20899, Novem-ber 1990. [7] J. Breuker and R. Wielinga. Knowledge acquisition as modelling expertise: the KADS methodology. In T. R. Addis, J. Boose, and B. R. Gaines, editors, Proceedings of the First European Workshop on Knowledge Acquisition for Knowledge-Based Systems. Reading University, 1987. [8] The British Library, National Bibliographic Service, Wetherby. UK MARC Manual, 1990. The British Library Board. 7 [9] E. W. Dijkstra. On a cultural gap. The Mathematical Intelligencer, 8(l):48-52, 1986. [10] V. M. Doland Hypermedia as an interpretive act. Hypermedia, 1(1):6-19, Spring 1989. [11] B. Ford, S. J, Hague, R. M. J. lies, and I. Reid. A framework for combining reason-ing components with mathematical software. In Proceedings of IMA conference on Artificial Intelligence in Mathematics, University of Strathclyde, 1991. [12] J. Galegher. Technology for intellectual teamwork: Perspectives on research and design. In J. Galegher, R. E. Kraut, and C. Egido, editors, Intellectual Teamwork: Social and Technological Foundations of Cooperative Work, chapter 1, pages 1-20. Lawrence Erlbaum Associates, London, 1990. [13] J. Hadamard. The Psychology of Invention in the Mathematical Field. Princeton University Press, New Jersey, 1945. [14] R. D. Harding, S. W. Lay, H. Moule, and D. A. Quinney. Multimedia Interac-tive Mathematics Courseware: The Mathematics experience within the Renaissance Project. Draft paper presented at CTI Mathematics Courseware Consortium Work-shop, Birmingham, 2 November 1992. [15] Kiyosi Itô, editor. Encyclopedic Dictionary of Mathematics. MIT Press, London, second edition, 1987. [16] J. H. Johnson and M. Loomes, editors. The Mathematical Revolution Inspired by The Computer. Number 30 in The Institute of Mathematics & its Applications; New Series. Oxford University Press, 1991. [17] G. P. Landow. Hypertext and collaborative work: The example of Intermedia. In J. Galegher, R. E. Kraut, and C. Egido, editors, Intellectual Teamwork: Social and Technological Foundations of Cooperative Work, chapter 15, pages 407-428. Lawrence Erlbaum Associates, London, 1990. [18] D. B. Lenat. The nature of heuristics. Artificial Intelligence, 19:189-249, 1982. [19] H. Lenzing. The Euromath Project. Euromath Bulletin, 1:13-20, 1992. [20] J. Lohse, H. Rueter, K. Biolsi, and N. Walker. Classifying visual knowledge repre-sentations: A foundation for visualization research. Cognitive Science and Machine Intelligence Laboratory, University of Michigan, Ann Arbor, Michigan 48109-1234, 1990. [21] A. G. J. MacFarlane. Interactive computing: A revolutionary medium for teaching and design. IEE Computing & Control Engineering Journal, pages 149-158, July 1990. [22] A. Muir. Are computers changing mathematics?  City University, London, 1991. [23] A. Muir. How mathematicians work: Newsletter no. 1. Department of Mathematics, City University, London EClV OHB, July 1992. 8 [24] H. Reichgelt. Knowledge Representation: An AI Perspective. Ablex Publishing Corporation, Norwood, New Jersey, 1991. [25] P. C. Samuels. Representations for scientific and mathematical knowledge. Knowl-edge Systems Group, Department of Computer Science, University of Reading, Eng-land, UK; Presented at BSPS Conference on Evolving Knowledge, held at Reading University, September 1989. [26] P. C. Samuels. Hypertext for computational mathematics. In Proceedings of IMA Conference on Artificial Intelligence in Mathematics, 1991. [27] J. M. Spivey. The Z Notation. International Series in Computer Science. Prentice Hall, London, 1989. [28] N. Yankelovich, N. Meyrowitz, and A. van Dam. Reading and writing the electronic book. IEEE Computer, 18(10):15-30, October 1985.                    9              NOT TO BE REMOVED  FROM THE LIBRARY                            

A core curriculum in Mathematics for the European engineer. Technical report, The European Society for Engineering Education (SEFI),

A framework for combining reasoning components with mathematical software.

Are computers changing mathematics?

Classifying visual knowledge representations: A foundation for visualization research.

Doland Hypermedia as an interpretive act.

How mathematicians work: Newsletter no.

Hypertext and collaborative work: The example of Intermedia. In

Hypertext for computational mathematics.

Interactive computing: A revolutionary medium for teaching and design.

Knowledge acquisition as modelling expertise: the KADS methodology. In

Multimedia Interactive Mathematics Courseware: The Mathematics experience within the Renaissance Project. Draft paper presented at CTI Mathematics Courseware Consortium Workshop,

On a cultural gap. The Mathematical Intelligencer,

Reading and writing the electronic book.

Representations for scientific and mathematical knowledge.

Technology for intellectual teamwork: Perspectives on research and design.

The Euromath Project.

The Guide to Available Mathematical Software problem classification system.

The nature of heuristics.

The Psychology of Invention in the Mathematical Field.

The virtual reality learning paradigm in real time curriculum: A new beginning?

The Z Notation.

Toward an intelligent system for mathematical software selection.

User interface development software.

A personal response to the euromath project: Towards the specification of an it infrastructure for the European mathematical community

A personal response to the euromath project: Towards the specification of an it infrastructure for the European mathematical community

Abstract

Similar works

Full text

Available Versions

Brunel University Research Archive