Hirschhorn's identities

We prove a general identity between power series and use this identity to give proofs of a number of identities proposed by M.D. Hirschhorn. We also use the identity to give proofs of a well-known result of Jacobi, the quintuple-product identity and Winquist's identit

Christian education as a hermeneutical project with special reference to the ascension of Christ

This thesis offers a broad ranging overview of Adult Christian Education, approached from the standpoint of the facilitation of Understanding. We introduce nine questions central to this subject, and these form the thesis' overall structure and content. Continuous interaction is made with educationalists currently working in A.C.E., especially in the United States. We interact especially with J.M. Lee and T.H. Groome. Chapter I.l considers the nature of God's activity in A.C.E. programmes; and seeks to justify a moderate interventionist model of revelation; against M. Wiles particularly. Chapter I.2 propounds a matrix of twelve Aims possible in A.C.E. Our overall definition of A.C.E. focuses on Discipleship and Maturity (L.O. Richards).Chapter II.1 focuses on the content of A.C.E. We here concentrate upon Christian doctrine, illustrated in the Ascension. Detailed exegesis of the Ascension texts highlights the work of G. Lohfink. Chapter II.2 addresses the nature of the person being educated. Drawing on D. Cairns, J. Macquarrie we discuss the nature of the Imago Dei, and education into the Imago Christi. Chapter II.3 offers extensive justification for hermeneutical theory forming the underlying dynamic for learning theory pertinent to A.C.E. In dialogue initially with Heidegger, Bultmann and Gadamer we construct a model for A.C.E. with power to promote interpretative ability, and application of faith to daily life. A special place is reserved for the Holy Spirit's educative role. We utilize Narrative Theology as a powerful and practical hermeneutical bridge. (D.E. Miller)Chapter III features a particular small-scale educational programme carried out in a Church setting, using the model developed in Chapters I.II. The thesis concludes by re-emphasizing the multifaceted dimensions of A.C.E. necessary in order to be adequate to both Christian tradition and experience. Teaching that facilitates the release of students towards their own "meaning making" is far more demanding than traditionally required in education which transmits predetermined content. This is because of the teacher's need to understand in depth both the subject material (for hermeneutically distanced understanding) and his students (for hermeneutical fusion of horizons)