Computers arechanging the way wethink. Of course,nearly all desk-workers have access to computers and use them to email their colleagues, search the Web for information and prepare documents. But I’m not referring to that. I mean that people have begun to think about what they do in compu- tional terms and to exploit the power of computers to do things that would previously have been unimaginable. This observation is especially true of mathematicians. Arithmetic c- putation is one of the roots of mathematics. Since Euclid’s algorithm for ?nding greatest common divisors, many seminal mathematical contributions have consisted of new procedures. But powerful computer graphics have now enabled mathematicians to envisage the behaviour of these procedures and, thereby, gain new insights, make new conjectures and explore new avenues of research. Think of the explosive interest in fractals, for instance. This has been driven primarily by our new-found ability rapidly to visualise fractal shapes, such as the Mandelbrot set. Taking advantage of these new oppor- nities has required the learning of new skills, such as using computer algebra and graphics packages.
Author(s): Michael Kohlhase (auth.)
Series: Lecture Notes in Computer Science 4180 : Lecture Notes in Artificial Intelligence
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2006
Language: English
Pages: 428
Tags: Artificial Intelligence (incl. Robotics); Information Storage and Retrieval; Mathematical Logic and Formal Languages; Symbolic and Algebraic Manipulation; Mathematics, general; Library Science
Front Matter....Pages -
Setting the Stage for Open Mathematical Documents....Pages 1-2
Document Markup for the Web....Pages 3-11
Markup for Mathematical Knowledge....Pages 13-23
OMDoc: Open Mathematical Documents....Pages 25-32
An OMDoc Primer....Pages 33-34
Mathematical Textbooks and Articles....Pages 35-48
OpenMath Content Dictionaries....Pages 49-53
Structured and Parametrized Theories....Pages 55-58
A Development Graph for Elementary Algebra....Pages 59-63
Courseware and the Narrative/Content Distinction....Pages 65-74
Communication with and Between Mathematical Software Systems....Pages 75-79
The OMDoc Document Format....Pages 81-81
OMDoc as a Modular Format....Pages 83-87
Document Infrastructure (Module DOC)....Pages 89-96
Metadata (Modules DC and CC)....Pages 97-105
Mathematical Objects (Module MOBJ)....Pages 107-120
Mathematical Text (Modules MTXT and RT)....Pages 121-131
Mathematical Statements (Module ST)....Pages 133-154
Abstract Data Types (Module ADT)....Pages 155-158
Representing Proofs (Module PF)....Pages 159-171
Complex Theories (Modules CTH and DG)....Pages 173-186
Notation and Presentation (Module PRES)....Pages 187-200
Auxiliary Elements (Module EXT)....Pages 201-208
Exercises (Module QUIZ)....Pages 209-211
Document Models for OMDoc....Pages 213-220
OMDoc Applications, Tools, and Projects....Pages 221-221
OMDoc Resources....Pages 223-225
Validating OMDoc Documents....Pages 227-233
Transforming OMDoc by XSLT Style Sheets....Pages 235-240
OMDoc Applications and Projects....Pages 241-316
Appendix....Pages 317-317
Changes to the Specification....Pages 319-331
Quick-Reference Table to the OMDoc Elements....Pages 333-338
Quick-Reference Table to the OMDoc Attributes....Pages 339-344
The RelaxNG Schema for OMDoc....Pages 345-359
The RelaxNG Schemata for Mathematical Objects....Pages 361-373
Back Matter....Pages -
