Tikaram and Chandrakala Dhananjaya: A collaborative couple in mathematics from Nepal

Within the history of mathematics and mathematics education in Nepal, Tikaram and Chandrakala Dhananjaya are relatively well-known figures for their two books Śiśubodha Taraṅgiṇī and Līlāvatī. This is despite there being almost no archival or manuscript materials offering a window into their lives: we have no letters, notebooks, diaries, or school records. Rather than focusing on either individual in isolation, in this article we present an argument for considering the Dhananjayas as an analytically indivisible collaborative couple in mathematics. Of the two aforementioned books, one is attributed to Chandrakala and the other to Tikaram; but in fact, both are translations of the same Sanskrit source text, Līlāvatī, into Nepali. By comparing the mathematical contents of these two works, which were published within a few years of each other, we explore what it means to be an author or translator of a mathematical text and propose different models of spousal collaboration which could plausibly have been adopted by the Dhananjayas. In the absence of documentary evidence, the impossibility of delineating each individual’s contributions removes the temptation to focus exclusively on apportioning credit. Instead, we offer the alternative perspective of considering what labour must have been undertaken to bring their books to publication. This article was published Open Access through the CCU Libraries Open Access Publishing Fund. The article was first published in Endeavour: https://doi.org/10.1016/j.endeavour.2023.10089

Cosmic Statistics of Statistics

The errors on statistics measured in finite galaxy catalogs are exhaustively investigated. The theory of errors on factorial moments by Szapudi & Colombi (1996) is applied to cumulants via a series expansion method. All results are subsequently extended to the weakly non-linear regime. Together with previous investigations this yields an analytic theory of the errors for moments and connected moments of counts in cells from highly nonlinear to weakly nonlinear scales. The final analytic formulae representing the full theory are explicit but somewhat complicated. Therefore as a companion to this paper we supply a FORTRAN program capable of calculating the described quantities numerically (abridged).Comment: 18 pages, 9 figures, Latex (MN format), published in MNRAS 310, 428 with slight correction

Pandey\u27s Method of Cube Root Extraction: Is it Better than Aryabhata’s Method?

We compare two methods of cube root extraction: one proposed by the Nepali mathematician Gopal Pandey in the 19th century, which uses proportionality, and another one provided by the Indian mathematician and astronomer Aryabhata

Engaging Students with High-stakes Problems

Engaging students in meaningful mathematics problem-solving is the intention of many education stakeholders around the world. Research suggests that the implementation of high-stakes problems in mathematics teaching is one way to strengthen students’ conceptual understanding. Many carefully crafted open-ended problems constitute high-stakes problems, and proper use of such problems in teaching and learning not only encourages learners’ flexible thinking but also helps detect their misconceptions. However, what is less practiced and understood is: how exactly one should aim to implement such problems in a classroom setting. Teaching pre-service middle school teachers for a few years using high-stakes (mostly open-ended problems) has given me insights that may be useful to teachers around the world. In this paper, we share my experience of teaching with high-stakes problems. We will demonstrate how user-friendly interactive graphing tools can be used in the creative process of problem-solving

Mathematics Textbook: Motivation, Experiences, and Didactical Aspect from Authors’ Perspectives

Textbooks play a vital role in the Nepali education system since they are one of the main resources for teaching and learning mathematics. Because of poor physical infrastructure and inadequate educational resources, both teachers and students heavily rely on textbooks. In this regard, this study investigated the mathematics textbook authors\u27 experiences and motivation, and what types of didactical knowledge were utilised while writing textbooks. A convenient yet purposeful sampling method was utilised to select four participants. The data analysis unveiled that each textbook author had different types of motivation and experiences, and only one participant was aware of the ideas of didactical knowledge and utilised them to some extent in textbooks. The writing process was more influenced by the examination, mathematical content, and classroom experiences. As a result, textbooks seemed to be content-heavy and examination-oriented. Additional professional development programmes likely would help authors to produce more effective textbooks in Nepal. This article was published Open Access through the CCU Libraries Open Access Publishing Fund. The article was first published in Research in Mathematics Education: https://doi.org/10.1080/14794802.2022.208660

On Infinite Quon Statistics and "Ambiguous" Statistics

We critically examine a recent suggestion that "ambiguous" statistics is equivalent to infinite quon statistics and that it describes a dilute, nonrelativistics ideal gas of extremal black holes. We show that these two types of statistics are different and that the description of extremal black holes in terms of "ambiguous" statistics cannot be applied.Comment: Latex, 9 pages, no figures, to appear in Mod.Phys.Lett.