JohnFauvelRaymondFloodRobinWilsonOxford Figures: 800 Years of the Mathematical Sciences2000Oxford University PressOxford0-19-852309-2206 pp.

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A large discourse concerning algebra: John Wallis's 1685 <i>Treatise of algebra</i>

A treatise of algebra historical and practical (London 1685) by John Wallis (1616-1703) was the first full length history of algebra. In four hundred pages Wallis explored the development of algebra from its appearances in Classical, Islamic and medieval cultures to the modern forms that had evolved by the end of the seventeenth century. Wallis dwelt especially on the work of his countrymen and contemporaries, Oughtred, Harriot, Pell, Brouncker and Newton, and on his own contribution to the emergence of algebra as the common language of mathematics. This thesis explores why and how A treatise of algebra was written, and the sources Wallis used. It begins by analysing Wallis's account of mathematical learning in medieval England, never previously investigated. In his researches on the origins and spread of the numeral system Wallis was at his best as a historian, and initiated many modern historiographical techniques. His summary of algebra in Renaissance Europe was less detailed, but for Wallis this part of the story set the scene for the English flowering that was to be his main theme. The influence of Oughtred's Clavis on Wallis and his contemporaries, and Wallis's efforts to promote the book, are explored in detail. Wallis's controversial account of Harriot's algebra is also examined and it is argued that it was better founded than has sometimes been supposed and that Wallis had direct access to Harriot's algebra through Pell. Many other chapters of A treatise of algebra contain mathematics that can be linked or traced to Pell, a hitherto unsuspected secret of the book. The later chapters of the thesis, like the final part of A treatise of algebra, explore Wallis's Arithmetica infinitorum and the work which arose from it up to Newton's foundation of modern analysis, and include a discussion of Brouncker's treatment of the number challenges set by Fermat. The thesis ends with a summary of contemporary and later reactions to A treatise of algebra and an assessment of Wallis's view of algebra and its history

Editing and reading early modern mathematical texts in the digital age

The advent of digital technology has brought a world of new possibilities for editors of historical texts. Though much has been written about conventions for digital editing, relatively little attention has been paid to the particular question of how best to deal with texts with heavily mathematical content. This essay outlines some ways of encoding mathematics in digital form, and then discusses three recent digital editions of collections of early modern mathematical manuscripts

Computer simulations of the growth of synthetic peptide fibres

Abstract. We present a coarse-grained computer model designed to study the growth of fibres in a synthetic self-assembling peptide system. The system consists of two 28 residue α-helical sequences, denoted AB and CD, in which the interactions between the half peptides, A, B, C and D, may be tuned individually to promote different types of growth behaviour. In the model, AB and CD are represented by double ended rods, with interaction sites distributed along their lengths. Monte Carlo simulations are performed to follow fibre growth. It is found that lateral and longitudinal growth of the fibre are governed by different mechanisms -the former is diffusion limited with a very small activation energy for the addition of units, whereas the latter occurs via a process of secondary nucleation at the fibre ends. As a result, longitudinal growth generally proceeds more slowly than lateral growth. Furthermore, it is shown that the aspect ratio of the growing fibre may be controlled by adjusting the temperature and the relative strengths of the interactions. The predictions of the model are discussed in the context of published data from real peptide systems