>Magister Scientiae - MSc / The aim of this dissertation is to calculate character tables of group extensions. There are several well developed methods for calculating the character tables of some selected group extensions. The method we study in this dissertation, is a standard application of Clifford theory, made efficient by the use of Fischer-Clifford matrices, as introduced by Fischer. We consider only extensions Ḡ of the normal subgroup N by the subgroup G with the property that every irreducible character of N can be extended to an irreducible character of its inertia group in Ḡ , if N is abelian. This is indeed the case if Ḡ is a split extension, by a well known theorem of Mackey. A brief outline of the classical theory of characters pertinent to this study, is followed by a discussion on the calculation of the conjugacy classes of extension groups by the method of coset analysis. The Clifford theory which provide the basis for the theory of Fischer-Clifford matrices is discussed in detail. Some of the properties of these Fischer-Clifford matrices which make their calculation much easier, are also given. We restrict ourselves to split extension groups Ḡ = N:G in which N is always an elementary abelian 2-group. In this thesis we are concerned with the construction of the character tables (by means of the technique of Fischer-Clifford matrices) of certain extension groups which are associated with the orthogonal group O+10(2), the automorphism groups U₆(2):2, U₆(2):3 of the unitary group U₆(2) and the smallest Fischer sporadic simple group Fi₂₂. These groups are of the type type 2⁸:(U₄(2):2), (2⁹ : L₃(4)):2, (2⁹:L₃(4)):3 and 2⁶:(2⁵:S₆).

M.V. Cerrillo, W.H. Kautz. / "November 15, 1951." / Bibliography: p. 11. / Army Signal Corps Contract DA36-039 SC-64637 Project 102B. Dept. of the Army Projects 3-99-10-022 and DA3-99-10-000.

Histories of medieval astronomy have brought to light a rich textual tradition, of treatises and tables composed and computed, transmitted and translated across Europe and beyond. These have been supplemented by fruitful inquiry into the material culture of astronomy, especially the instruments that served as models of the heavens, for teaching and for practical purposes. But even now we know little about the practices of medieval astronomers: how they obtained and passed on their knowledge; how they drew up and used mathematical tables; how they drafted the treatises in which they found words to express their ideas and inventions for their particular audiences. This thesis uses a case study approach to elucidate these medieval astronomical practices. Long thought to be a holograph manuscript in the hand of Geoffrey Chaucer, the Equatorie of the Planetis (Peterhouse, Cambridge MS 75.I) has recently been identified as the work of John Westwyk (d. c. 1400), a Benedictine monk of Tynemouth Priory and St Albans Abbey. His draft description of the construction and use of an astronomical instrument, with accompanying tables, provides an opportunity to reconstruct the practices of an unexceptional astronomer. The first chapter of this thesis reconstructs Westwyk’s astronomical reading and understanding, through an examination of the other manuscript that survives in his hand: a pair of instrument treatises by the outstanding monastic astronomer Richard of Wallingford. I show how Westwyk copied this manuscript in a monastic context, learning as he annotated texts and recomputed tables. In the second chapter I discuss the purposes of planetary instruments such as equatoria, their place among other astronomical instruments, and the physical constraints and possibilities experienced by their makers. Through this discussion I assess the craft environment in which Westwyk came to write his own instrument-making instructions. Chapters three and four assess Westwyk’s language, explaining the basis for his choice to write a technical work in the vernacular, and analysing how his innovative use of Middle English furthered his didactic objectives. In the final chapter, I undertake a technical reassessment of the Equatorie treatise, an integrated analysis of the instrument with the somewhat neglected tables that Westwyk compiled alongside it. The thesis thus applies a range of methodologies to examine the practices and products of a single inexpert astronomer from all angles. It aims to show what an in-depth case study approach can offer historians of the medieval sciences.