Rodney Nillsen University of Wollongong NSW, AUSTRALIA 2522 email: nillsen@uow.edu.au Mathematical books and seminars Mathematical research and exposition Book reviews Thecurrent commentspage University policy and academic culture Teaching and Learning Ideas and opinion School mathematics and social policy Research ethics
  RECENT RESEARCH & SCHOLARSHIP DOWNLOAD a preprint of the article Infinitesimal Knowledges, DOI 10.1007/s10516-021-09540-z. You can also READ THIS ARTICLE ON-LINE as published in the journal Axiomathes. Here is an edited excerpt from the abstract: "The notion of indivisibles and atoms arose in ancient Greece. The continuum -- that is, the collection of points in a straight line segment, appeared to have paradoxical properties, arising from the `indivisibles' that remain after an infinite process of division. In the seventeenth century, Italian mathematicians were using new methods, and the paradoxes of the continuum appeared in a new context. This article discusses aspects of these and subsequent events with reference to the book Infinitesimal by Amir Alexander and to other sources. Also discussed are wider issues including: the changes in cultural sensibility associated with the growth of new mathematical and scientific knowledge in the seventeenth century, the changes in language concomitant with these changes, what constitutes valid methods of enquiry in various contexts, and the question of authoritarianism in knowledge. Key words: infinitesimals; indivisibles; paradox; axiomatic method; Euclid; Aristotle; history of mathematics; Jesuits; uncertainty in knowledge; language and knowledge; historical method, authoritarianism and knowledge. *** Read the paper Higher education policy and cultural change in universities, Proceedings of the 2016 Annual Conference of the Independent Scholars Association of Australia, pp.93-112, Independent Scholars Association of Australia, 2020. *** The paper Quadratic functions and public policy has appeared in The Australian Mathematics Education Journal 1(1), 2019, 4-9. The paper aims to illustrate how mathematical thinking can clarify problems in business and public policy. The paper Vanishing Fourier coefficients and the expression of functions as sums of generalised differences in ${L}^{2}\left(-\pi ,\pi \right)$ appeared in the Journal of Mathematical Analysis and Applications, 455 (2017), pp.1425-1443. Read an abstract of this paper. You may also read a short slide presentation of this paper. The graph above illustrates a function of the type $x⟼{\left(\mathrm{cos}x-\mathrm{cos}nx\right)}^{2}$, and such functions are important in obtaining the results of this paper. *** Read the abstract of the paper: Vanishing Fourier transforms and generalised differences in ${L}^{2}\left(ℝ\right),$ published in The Canadian Mathematical Bulletin 62(2), (2019), 393-404. *** Read the abstract of the paper with Susumu Okada: Sharpness results concerning finite differences in Fourier analysis on the circle group. The paper has appeared in Acta Scientiarum Mathematicarum (Szeged), 84 (2018), 591-609. *** The paper A comparison of two types of bank investments was published in The Australian Senior Mathematics Journal, volume 31 (2017), pp.5-18. The analysis is a comparison of two types of compound interest investment. The main aim is to establish the time at which the second type of investment becomes superior to the first, thus assisting in investment decision making. *** Read a review of the book by Matthew Inglis and Nina Attridge: Does Mathematical Study Develop Logical Thinking? Testing the Theory of Formal Discipline. The review appeared in the Gazette of the Australian Mathematical Society, volume 44, no.3, July 2017. *** The year 2012 was the bicentenary of the birth of the celebrated English writer Charles Dickens (d. 1870). Go to the Charles Dickens Page to read about his life and work. *** Read about pentagons and the golden ratio, and the irrationality of the square root of five. Read about an elegant result in Fourier analysis of Gary H. Meisters and Wolfgang M. Schmidt. To read a description of the result at undergraduate level, click here. Read some mathematical quotations. The book Randomness and Recurrence in Dynamical Systems was published by the Mathematical Association of America in 2010. Read reviews of this book by David Hand, Svitlana P. Rogovchenko and James A. Walsh. Read further reviews and more about this book. *** Read about the Slovak-Australian mathematician Igor Kluvánek, and read some of his quotations. Also,you may read a paper given in Badin, Slovakia, at the conference "The University: place of meeting and confrontation between faith and reason" held in September 2011. Read about Richard Dawkins and the God hypothesis. Read about the research-teaching nexus. Leading-edge your objectives -- read a (rather unorthodox) submission to the Bradley enquiry on universities. ***