Related papers: Dragons and Kasha
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
Dwarf galaxies provide opportunities for drawing inferences about the processes in the early universe by observing our "cosmological backyard"-the Local Group and its vicinity. This special issue of the open-access journal Advances in…
This paper outlines two approaches for mathematical, simulation, modeling, and analysis of hypothetical creatures, in particular, the dragons of HBO's television series Game of Thrones (GOT). Our first approach, the forward model, utilizes…
Algorithms are becoming more capable, and with that comes hic sunt dracones (here be dragons). The term symbolizes areas beyond our known maps. We use this term since we are stepping into an exciting, potentially dangerous, and unknown area…
In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometry and trig functions. The objective is to lead students to a…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
This recreational mathematics article shows that the game of Snakes and Ladders is intransitive: square 69 has a winning edge over 79, which in turn beats 73, which beats 69. Analysis of the game is a nice illustration of Markov chains,…
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Motivated by the evolution of complex bird songs, an abstract imitation game is proposed to study the increase of dynamical complexity: Artificial "birds" display a "song" time series to each other, and those that imitate the other's song…
Our interdisciplinary team Mathematics for Applications in Cultural Heritage (MACH) aims to use mathematical research for the benefit of the arts and humanities. Our ultimate goal is to create user-friendly software toolkits for artists,…
This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into…
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
Evolutionary multitasking has recently emerged as a novel paradigm that enables the similarities and/or latent complementarities (if present) between distinct optimization tasks to be exploited in an autonomous manner simply by solving them…
This article proposes and discusses qualitatively the use of a didactic board game in Science Education for high school students. The game contemplates in an interdisciplinary way the areas of Physics, Biology, Chemistry and Astronomy and…