With the globalisation in education, bridging cultural differences by making course material more accessible and adaptable to individual user needs becomes an important goal. In this paper we attack this goal for the field of mathematics where knowledge is abstract, highly structured, and extraordinarily interlinked. Modern representation formats like our OMDoc format allow us to capture, model, relate, and represent mathematical learning objects and thus make them context-aware and machine-adaptable to the respective learning contexts.

In the last two decades, the World Wide Web has become the universal information source. Search engines can efficiently serve daily information needs due to the enormous redundancy of relevant resources on the web. For educational and scientific information needs, the web functions much less efficiently: Scientific publishing is built on a culture of unique reference publications, and moreover documents abound with specialized structures such as technical nomenclature, notational conventions, references, tables, or graphs.

Hilbert's concept of formal proof is an ideal of rigour for mathematics which has important applications in mathematical logic, but seems irrelevant for the practice of mathematics. The advent, in the last twenty years, of proof assistants was followed by an impressive record of deep mathematical theorems formally proved. Formal proof is practically achievable. With formal proof, correctness reaches a standard that no pen-and-paper proof can match, but an essential component of mathematics --- the insight and understanding --- seems to be in short supply.

Several applications support the adaptation of course material. Even though most of these systems allow to specify interaction preferences or even employ user modeling techniques, every system is an island with this respect. In particular, different systems cannot share user models or predict preferences in the absence of prior interactions. We use ideas from the theory of Communities of Practice to consolidate user models and to extend current approaches towards a CoP-sensitive adaptation.

The problem of information overload has been addressed by several systems. However, many approaches are limited to informal artifacts and need to refer to the user for reference on the quality or usefulness of retrieved information. We make use of semantic technologies, which facilitate the reification and extraction of scientific practice. Based on semantic differences and similarities of semantically marked up artifacts, we identify clusters of users with shared practice, i.e. virtual communities of practice.

With the globalization in education, bridging cultural differences by making course material more accessible and adaptable to individual user needs becomes an important goal. In this paper we attack this goal for the field of mathematics where knowledge is abstract, highly structured, and extraordinary interlinked. Modern representation formats like our OMDOC format allow us to capture, model, relate, and represent mathematical learning objects and thus make them context-aware and machine-adaptable to the respective learning contexts.

We believe that mathematics is the language of science and has paved the way of many innovations. However, mathematical research is often said to be “non-practical” and “hard to digest”. Furthermore, experts have access to highly specialized results, but are often less aware of applications outside their own community.

Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent over the document and their own prior publications. In print media where notations are xed at publication time, this is an over-constrained problem. In living documents notations can be adapted at reading time, taking reader preferences into account.

Almost all aspects of scientific research and communication are now supported by software systems. Even though most of these systems
allow the user to specify interaction preferences or even employ user modeling techniques, every system is an island with this respect. In

At the Jacobs University Bremen we offer a lecture on General Computer Science to an international student body. We are challenged with the students' different mathematical backgrounds. The majority of our students believe that these mathematical discrepancies are very problematic, especially in the beginning of a course. Students reported that they had problems to get acquainted with the professor's notation systems; some had the feeling that the pace of the course was inappropriate, while others did not face any problems.