Abstract: Personalizing Mathematical Textbooks

Ingo Dahn

Mathematical documents are usually well structured. They develop complex networks of concepts which are interrelated in various ways. To understand a certain mathematical theorem or example, the reader usually has to understand the environment in which it is stated. She has to understand the required definitions and the other theorems and lemmas that are eventually applied to explain it. Therefore, in different situations, different parts from a mathematical document are needed, which are frequently scattered over a large textbook. It will be shown in the talk, how Slicing Book Technology can support the reader in various such situations. This technology decomposes books into semantic units. Then the conditions under which these units can be reused are described by meta data. Automated inference procedures combine these meta data with declarative descriptions of intended documents and with information about the user to determine, how the document for the specific needs of the user should be composed. Based on this information, the document will be generated on the fly and delivered over the Web. This concept has been realized in the European project Trial-Solution (http://www.trial-solution.de) for several mathematical textbooks. We shall report on the experience gained in this project. Special attention will be paid to the implemented meta data system and how it is applied to combine content from different books for the benefit of the reader. Based on experience from the German project In2Math(http://www.uni-koblenz.de/ag-ki/PROJECTS/in2math/), an outlook will discuss the possibilities that arise when formalized mathematical objects are available as content descriptive meta data in Slicing Book Technology. Examples and demos are available from http://www.slicing.de/books/.