Piṅgala is a mathematician (c. 300 BCE) who authored Chandah. śāstra (the science of Sanskrit metres). This is a brief note on a mathematical art project completed at the Chennai Mathematical Institute to honour Piṅgala who was responsible for the discovery of binary expansion of numbers in the context of enumeration of metres, and of the binomial coefficients which were later made explicit by ...

The study presented in this paper offers a reference framework for characterizing primary school teachers’ mathematical knowledge of the standard algorithms of the four basic arithmetic operations. The framework was first devised theoretically, from mathematical analysis of the algorithms and from past research on knowledge for teaching arithmetic operations with rational numbers. It was then a...

People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity-the capacity for symbolic reasoning-as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a ...

The mathematical problems and their solutions of the Third International Students’ Olympiad in Cryptography NSUCRYPTO’2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technolo...

In the paper we concentrate on one aspect of the experimental design: how the information coming from an experiment can be utilised for identification of a specific mathematical model. To express the consistency of the data and the model we need some quality measure, allowing to transform our intuition to numbers. As the mathematical tool we propose a version of the statistical procedure of cro...

This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...

is article attempts to broaden the phenomenologically motivated perspective of H. Weyl’s Das Kontinuum (1918) in the hope of elucidating the dišerences between the intuitive and mathematical continuum and further providing a deeper phenomenological interpretation. It is known that Weyl sought to develop an arithmetically based theory of continuum with the reasoning that one should be based on t...

When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative divi...

data envelopment analysis (dea) is a technique based on mathematical programming for evaluating the efficiency of homogeneous decision making units (dmus). in this technique, inefficient dmus are projected onto the frontier, which was constructed by the best performers. centralized resource allocation (cra) is a method in which all dmus are projected onto the efficient frontier through solving ...

One construction of exactly-solvable potentials for Fokker-Planck equation is considered based on supersymmetric quantum mechanics approach. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.Ca, 02.90.+p Submitted to Journal of Physics A: Mathematical and General