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In this paper we describe the compactification of the Drinfeld modular curve. This compactification is analogous to the compactification of the classical modular curve given by Katz and Mazur. We show how the Weil pairing on Drinfeld modules that we defined in earlier work gives rise to a map on the Drinfeld modular curve. We introduce the Tate-Drinfeld module and show how this describes the formal neighbourhood of the scheme of cusps of the Drinfeld modular curve.

Abstract. In the following, we describe a way of factoring polynomials in Fq [X] with Drinfeld modules. We furthermore analyse the complexity of the algorithm and compare it to the well-known Cantor-Zassenhaus algorithm. Defining F q [X]-module structures with Drinfeld modulesThroughout this paper we will denote A = F q [X], where q is a power of some prime p, and N ∈ A for the polynomial which is to be factored. Let B be an A-algebra coming from an F q -linear ring homomorphism γ : A −→ B.(1) B{τ } is the skew-polynomial ring which consists as set of all finite expres-and B{τ } has addition and multiplication defined bywhere b n + c n is addition and b i c q i j is multiplication in B. (2) We define a homomorphism on B{τ } as follows:This property implies that a Drinfeld module ϕ is F q -linear and hence is completely given by the image of X ∈ A. In the following we will write ϕ a instead of ϕ(a) for a ∈ A. If we denote ϕ X = r i=0 b i τ i , then b 0 = γ(X). If moreover b r is not nilpotent in B, then we call r ≥ 0 the rank of ϕ. In fact, without loss of generality we may assume that b r is not nilpotent; cf. [Mat97].Canonically B is an A-module via γ. This gives us a ring homomorphismB{τ } −→ End Fq (B).In particular this means that for all a ∈ A, ϕ a induces such a map. One checks easily that ϕ gives rise in this way to a new A-module structure on B via (a, b) → ϕ a (b).

Attention has been drawn to the concepts of Electronic Books and Electronic Study Books. Several publications have discussed some main ideas (paradigms) for both concepts. For the Electronic Study Book as a learning environment, it is essential to consider individual modes of learning, usually termed 'learning styles'. It is argued that Electronic Study Books should be adaptable in accordance with personal learning styles. Some options will be presented to link 'styles' and 'books'. One such option is a Style Initiating Module which we are currently investigating. Keywords: Courseware; Electronic books; Electronic study books;Electronic learning environment; Learning style. Electronic BooksIn a series of articles (Barker, 1990;Barker & Manji, 1989; Egan ef al., 1989) and in a special issue of Educational & Training Technology International (Barker, 1991) the nature and the educational potential of Electronic Books and Electronic Study Books (De Diana, 1991) have been discussed.By combining traditional book concepts with some of the advantages of electronic media, it is presumed that the Electronic Book could become a late 20th century successor of the Paper Book.In Barker (19901, hypermedia, reactive media, the principle of surrogation, learner control, and the composite screen are presented as paradigms for the Electronic Book. The hypermedia paradigm involves the nonlinear structuring of units of (multimedial) information. The units can be connected in several ways and thus become a network that can be travelled through ('navigated') by learners in different ways. Reactive media involve interaction between humans and computers; the dialogue can be initiated, responded to, or stopped by both partners. The principle of surrogation builds upon the capacity of the computer to simulate parts of the real world visually. Computer animation can be used to create visualisations of (small) explorable worlds. Learner control implies that the learner can control the learning process. The composite screen paradigm presumes the facility of opening simultaneously multiple windows and displaying different streams of information through these windows.The key distinction between the paper book and the electronic book is to be found in the additional cognitive support facilities that the electronic book could offer. Facilities, for example, to support information selection, information processing, information evaluation, and information approval or rejection. An electronic book then can be seen as an interactive 'mindtool', connected with a multimedia1 data base.Electronic Study Books Some facilities that could turn an Electronic Book into an Electronic Study Book are, according to De Diana (1991): information marking, annotation, support for group-based learning, information sequencing, and support for information distribution. Identifying scope and relevance of study materialIt is customary, though not always approved of, for readers to mark important passages in study books such as keywords, keyphrases, paragraphs ...

The sixteen essays in this volume reflect on, and discuss in detail important aspects of the threefold relation between Paul and continental philosophy, Paul and the Greco-Roman world, and Paul and political theology. Lookingb ack on these contributions,i nt his epilogue we wish to consider what conclusions mayb ed rawn from them and-by bringing these different interpretations into dialogue with one another-discuss what responses the volume mayo ffer to the line of inquiry set out at the startofthis project.Aswenoted in the introduction, our questions in this volume pertain first and foremost to the meaningand the impact of the notion of πίστις ("faith" or "belief")and Paul's πίστις language, both in the Greco-Roman world Paul inhabited and in the present-day philosophical discourse in which his letters are heavilyd ebated. In particular,w e are interested in how these two approaches to Paul's πίστις languagec an be brought into dialogue, and whether the essays in this volume indeeds upport ac onsonanceb etween ancient and modernt hought. The question of πίστις is as hared concern for all the contributions to this book, in which it is taken up in different ways and from different angles. Our introduction also suggested one specific direction the inquiry into the πίστις languageo fP aulm ight take, namelya ni nterrogation of πίστις or faith against the background of the (in)famous distinction, sometimes presented as an opposition, between faith and reason. How does πίστις,a nd the usage of this term in Paul'sl etters,i nt he Greco-Roman world, and in the present-day philosophicalreflection on Paul'sthought, relatet on otions such as reason, rationality,o rr ationalities?D ow ef ind an opposition, adifferent kind of relation or,perhaps, rather anon-relation since they belong to different fields altogether?If we consider how this more specific line of inquiry is addressed in this volume, we see asomewhat complex answer taking shape. The languageofπίστις in Paul and in the Greco-Roman world does indeed have an epistemological dimension; however,asT eresa Morgan argues in her contribution, it is also used in relation to other ethical, social, psychological, and spiritual dimensions, which are