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Register a new userThe Mathematics of Fels Sculptures
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We give a purely mathematical interpretation and construction of sculptures rendered by one of the authors, known herein as Fels sculptures. We also show that the mathematical framework underlying Fergusons sculpture, {it The Ariadne Torus}, may be considered a special case of the more general constructions presented here. More general discussions are also presented about the creation of such sculptures whether they be virtual or in higher dimensional space.
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We survey recent results on the mathematical stability of Bitcoin protocol. Profitability and probability of a double spend are estimated in closed form with classical special functions. The stability of Bitcoin mining rules is analyzed and several theorems are proved using martingale and combinatorics techniques. In particular, the empirical observation of the stability of the Bitcoin protocol is proved. This survey article on the mathematics of Bitcoin is published by the Newsletter of the European Mathematical Society, vol.115, 2020, p.31-37. Continuation of arXiv:1601.05254 (EMS Newsletter, 100, 2016 p.32).
Given the profound and uncritiqued changes that have been implemented in Aotearoa New Zealand education since the 1990s, this paper provides a critical commentary on the characterising features of the New Zealand mathematics curriculum in the context of the first stage of a study. The emphasis is on the importance of research design that begins with an explicit, evidence-based hypothesis. To that end, we describe evidence that informs and identifies the studys hypothesised problem and causes. The study itself will show whether or not the hypothesis is justified; that is, is the absence of standardised prescribed content in New Zealand mathematics curriculum the reason for the countrys declining mathematics rankings? The study aims to increase understanding in the field of mathematics education by exploring the effects on New Zealand year 7 public school teachers mathematics curriculum selection and design practices, teaching practices, and subsequently student achievement.
This is an expanded version of my review of Nina Engelhardts book Modernism, Fiction and Mathematics, Edinburgh University Press 2018. A considerably shortened version will appear in the Notices of the AMS.
An introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS, https://oeis.org) for graduate students in mathematics
I am an industrial mathematician. When asked to identify my profession or academic field of study, this is the most concise answer I can provide. However, this seemingly straightforward statement is commonly greeted by a blank stare or an uncomfortable silence, regardless of whether I am speaking to a fellow mathematician or a non-mathematician. I usually follow up with the clarification: I am an applied mathematician who derives much of my inspiration from the study of industrial problems that I encounter through collaborations with companies. This dispels some confusion, but unfortunately still leaves a great deal open to interpretation owing to the vagueness of the words mathematics, industry and company, each of which covers an extremely broad range of scientific or socio-economic activity. To those academics who actually work in the field of industrial mathematics (and whose perspective referred to in the title is the focus of this article) this ambiguity is familiar and untroubling. However, for anyone less acquainted with the work of industrial mathematicians, some clarification is desirable especially for anyone who might be considering entering the field. This essay therefore aims to shed light upon the nature of research being done at the interface between mathematics and industry, paying particular attention to the following questions: What is industrial mathematics? Where is industrial mathematics? How does one do industrial mathematics? Why (or more precisely, what value is there in doing) industrial mathematics? I will attempt to answer these questions by means of several case studies drawn from my own experience in tackling mathematical problems from industry.
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